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{ "entity": "", "message": " has no rdfs:domain", "severity": "info", "type": "missing_domain" }, { "entity": "", "message": " has no rdfs:domain", "severity": "info", "type": "missing_domain" }, { "entity": "", "message": " has no rdfs:domain", "severity": "info", "type": "missing_domain" }, { "entity": "", "message": " has no rdfs:domain", "severity": "info", "type": "missing_domain" }, { "entity": "", "message": " has no rdfs:domain", "severity": "info", "type": "missing_domain" } ], "suppressed_count": 0 } }, "certificate": { "format": "oo-cert/1", "files": { "asserted.sha256": "1f00b0971a418233c4bbe4294c1a6f811b6ce097a8e55be969e8c6ab63301036\n", "asserted.tsv": "\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A state where all derivatives are approximately zero — the system has stopped changing. go-pflow's `SolveUntilEquilibrium` stops early once the largest absolute derivative stays below a tolerance (default $10^{-6}$) for several consecutive checks (`solver/equilibrium.go`; Appendix A).\"@en\n\t\t\"Equilibrium\"@en\n\t\t\n\t\t\n\t\t\"go-pflow\"\n\t\t\"petri-net\"\n\t\t\"sim-pflow-xyz\"\n\t\t\"simulation\"\n\t\t\"tutorial\"\n\t\t\n\t\t\n\t\t\"Introducing sim.pflow.xyz\"\n\t\t\n\t\t\"about\"\n\t\t\n\t\t\"2026-10-23T00:00:00Z\"^^\n\t\t\"2026-01-31T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"A tour of sim.pflow.xyz — a catalog of executable Petri-net models you can run, compare and check, from tic-tac-toe to a café to a vet clinic, in the browser or from any MCP client.\"@en\n\t\t\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A directed connection between a place and a transition (input arc) or a transition and a place (output arc). Arcs define the flow relation of the net. Each arc has a weight (default 1) specifying how many tokens are consumed or produced.\"@en\n\t\t\n\t\t\"Arc\"@en\n\t\t\n\t\t\"3\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"Replacing discrete token counts with continuous concentrations and firing rules with differential equations. The Petri net becomes a system of ODEs via mass-action kinetics, enabling simulation with numerical solvers (Chapter 3).\"@en\n\t\t\"Continuous relaxation\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Package graphql provides a GraphQL server for Petri net models.\"@en\n\t\t\"graphql\"\n\t\t\"graphql\"\n\t\t\"A repository or published site. Listed in ns/projects.json by a person, and only if it is public.\"@en\n\t\t\n\t\t\n\t\t\"Project\"@en\n\t\t\n\t\t\"beats-bitwrap\"\n\t\t\"music\"\n\t\t\"petri-nets\"\n\t\t\"retrospective\"\n\t\t\n\t\t\n\t\t\"From Petri-net toy to jambox: 38 days of beats.bitwrap.io\"\n\t\t\"models\"\n\t\t\n\t\t\"2026-09-25T00:00:00Z\"^^\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"A visual archaeology of beats.bitwrap.io's first 75 tags, v0.1.0 (March 23) to v2.4.0 (April 28): one screenshot captured per minor release, ten of them shown here, each reproducible from the tag's CDN URL.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"signedFields\"@en\n\t\t\n\t\t\"A Compositional Framework for Reaction Networks\"\n\t\t\n\t\t\"2017\"^^\n\t\t\"Baez, J.C.; Pollard, B.S.\"\n\t\t\"editor\"\n\t\t\"1704.02051\"\n\t\t\n\t\t\n\t\t\"Reaction networks, equivalently Petri nets, composed as open systems.\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Package verify turns questions about a Petri net into verdicts with evidence.\"@en\n\t\t\"verify\"\n\t\t\"verify\"\n\t\t\n\t\t\"Meseguer, J.\"\n\t\t\n\t\t\n\t\t\"TransitionFireEvent\"@en\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The graph of all markings reachable from the initial marking through sequences of transition firings. Each node is a marking, each edge is a transition firing. The reachability graph may be infinite for unbounded nets.\"@en\n\t\t\"Reachability graph\"@en\n\t\t\n\t\t\n\t\t\"Julia\"\n\t\t\"Julia package for Petri nets — colored tokens, mass-action ODEs, bridged to AlgebraicPetri.jl\"@en\n\t\t\n\t\t\"pflow-jl\"\n\t\t\n\t\t\n\t\t\"Fong, B.\"\n\t\t\n\t\t\n\t\t\"BlogPosting\"@en\n\t\t\n\t\t\"beats-bitwrap\"\n\t\t\"mcp\"\n\t\t\"music\"\n\t\t\"petri-nets\"\n\t\t\"swift\"\n\t\t\n\t\t\n\t\t\"beats-btw-dj: the Petri-net sequencer, native on the Mac\"\n\t\t\"models\"\n\t\t\n\t\t\"2026-10-24T00:00:00Z\"^^\n\t\t\"2026-10-24T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\"A native macOS DJ app where each deck runs a live Petri net. The generator is ported from beats.bitwrap.io to Swift and held to the same CIDs and bytes by fixtures from the real JavaScript; Claude drives it over MCP.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Person\"@en\n\t\t\n\t\t\"Riley, M.\"\n\t\t\"Where in the source to look.\"@en\n\t\t\n\t\t\n\t\t\"location\"@en\n\t\t\n\t\t\"polyglot\"\n\t\t\"A Coffee state machine in various languages.\"@en\n\t\t\n\t\t\"pflow-polyglot\"\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The algebraic relation $\\\\mathbf{m}' = \\\\mathbf{m}_0 + \\\\mathbf{C} \\\\cdot \\\\boldsymbol{\\\\sigma}$ where $\\\\boldsymbol{\\\\sigma}$ is the firing count vector (how many times each transition has fired). A necessary but not sufficient condition for reachability — the actual firing sequence must also be valid.\"@en\n\t\t\"State equation\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"createdAt\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"semantics\"@en\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\"Package stateutil provides utility functions for manipulating Petri net state maps.\"@en\n\t\t\"stateutil\"\n\t\t\"stateutil\"\n\t\t\n\t\t\n\t\t\n\t\t\"token\"@en\n\t\t\n\t\t\n\t\t\"stackdump blog\"\n\t\t\n\t\t\n\t\t\"Semenov, A.\"\n\t\t\n\t\t\n\t\t\n\t\t\"hasArc\"@en\n\t\t\n\t\t\n\t\t\"Vitányi, P.\"\n\t\t\n\t\t\"game-design\"\n\t\t\"gnark\"\n\t\t\"groth16\"\n\t\t\"petri-net\"\n\t\t\"poker\"\n\t\t\"zk\"\n\t\t\n\t\t\n\t\t\"Building ZK Poker: Four Petri Nets and a Branchless Circuit\"\n\t\t\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-10-19T00:00:00Z\"^^\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"A technical deep dive into heads-up hold'em at stackedup.gg — four Petri nets (phase, hand classifier, bot decision, chip ledger) and what each one actually drives in the code, a commit-reveal shuffle for casino sessions, and a branchless Groth16 circuit that proves a hand's score without revealing the hole cards.\"@en\n\t\t\n\t\t\"arXiv\"\n\t\t\n\t\t\"Categories of Optics\"\n\t\t\n\t\t\"2018\"^^\n\t\t\"Riley, M.\"\n\t\t\"1809.00738\"\n\t\t\n\t\t\n\t\t\"Baez, J.C.\"\n\t\t\n\t\t\"Place to transition. Weight tokens are consumed when the transition fires.\"@en\n\t\t\n\t\t\n\t\t\n\t\t_:b639fabf2e8aa00ca738929cad227e6f\n\t\t_:d61b8525e59d46e7ea4c808a6ccde685\n\t\t\"InputArc\"@en\n\t\t\n\t\t\"Zahn, P.\"\n\t\t\n\t\t\"encoding\"\n\t\t\"petri-net\"\n\t\t\"poker\"\n\t\t\"technique\"\n\t\t\"weighted-arcs\"\n\t\t\n\t\t\n\t\t\"Exponential Weights in Petri Nets: What Worked, What Didn't, and What's Next\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-06T00:00:00Z\"^^\n\t\t\"2026-02-14T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\"Power-of-2 weights encode lexicographic order over distinct ranks as a single integer. We tried it for poker kicker scoring inside the net and reverted it; the per-card variant we shipped also broke the ordering. Where the encoding belongs, and where it doesn't.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"sig\"@en\n\t\t\n\t\t\"game\"\n\t\t\"tic-tac-toe\"\n\t\t\n\t\t\n\t\t\"Tic-Tac-Toe Model\"\n\t\t\"models\"\n\t\t\n\t\t\"2026-08-25T00:00:00Z\"^^\n\t\t\"2025-11-13T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"Modeling tic-tac-toe using Petri nets with ODE simulation for AI move selection—no game heuristics, just model topology.\"@en\n\t\t\n\t\t\n\t\t\"Huisinga, W.\"\n\t\t\n\t\t\n\t\t\n\t\t\"ref\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"model\"@en\n\t\t\n\t\t\"game\"\n\t\t\"petri-net\"\n\t\t\"poker\"\n\t\t\"zk-proofs\"\n\t\t\"integer-reduction\"\n\t\t\n\t\t\n\t\t\"ZK Hold'em: Poker Hand Ranking from Network Topology\"\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-10-13T00:00:00Z\"^^\n\t\t\"2026-02-23T18:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Incidence reduction applied to poker in one pflow-rs example — hand-category values come out of the ODE as 1/drains over hand-picked drain counts, every game action is Groth16-proven, the shuffle is a Poseidon commit-reveal, and the generated contract still trusts the showdown.\"@en\n\t\t\n\t\t\n\t\t\"Every transition can eventually fire from every reachable marking. Established by sim_verify, not inferred here.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Groth, J.\"\n\t\t\n\t\t\"Formal Methods for Computational Systems Biology, Springer\"\n\t\t\n\t\t\"Petri Nets for Systems and Synthetic Biology\"\n\t\t\"2008\"^^\n\t\t\"Heiner, M.; Gilbert, D.,; Donaldson, R.\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A transition is enabled at a marking $\\\\mathbf{m}$ if every input place has at least as many tokens as the corresponding arc weight: $\\\\mathbf{m}(p) \\\\geq W(p, t)$ for all input places $p$. An enabled transition may fire; a disabled one cannot.\"@en\n\t\t\"Enabled\"@en\n\t\t\n\t\t\"0.2.0\"\n\t\t\"Petri-net structure, the pflow ecosystem's components, the writing and literature behind it, and sim's model kinds.\"@en\n\t\t\n\t\t\"pflow ontology: core\"@en\n\t\t\"Dedicated to the public domain under CC0 1.0 Universal.\"@en\n\t\t\n\t\t\"Springer, Graduate Texts in Mathematics 5, 2nd ed.\"\n\t\t\n\t\t\"Categories for the Working Mathematician\"\n\t\t\"1998\"^^\n\t\t\"Mac Lane, S.\"\n\t\t\"editor\"\n\t\t\n\t\t\"Standard reference for the lemma. Checked: the book, edition and series, and that Chapter III is 'Universals and Limits'. Not checked: the section within that chapter, so none is given.\"\n\t\t\n\t\t\"at least one resource pool, at least one abandonment (patience) knob and at least one loss outcome: demand queues for a limited resource and can walk away empty-handed\"@en\n\t\t\n\t\t\n\t\t\"QueueingSystem\"\n\t\t\n\t\t\"at least one resource pool and no abandonment knob: demand waits for the resource, it never gives up and leaves\"@en\n\t\t\n\t\t\n\t\t\"ResourcePool\"\n\t\t\n\t\t\n\t\t\"category-theory\"\n\t\t\"money\"\n\t\t\n\t\t\n\t\t\"The Obligation Triangle\"\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-15T00:00:00Z\"^^\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\n\t\t\"A sketched phase space for money — three poles (sovereign, commodity, protocol), instruments placed inside as barycentric mixes, two edges labelled with witnesses, and a proposed F ⊣ U between the sovereign and protocol poles.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"from\"@en\n\t\t\n\t\t\n\t\t\"Chapter\"@en\n\t\t\n\t\t\n\t\t\"PetriRuntime\"@en\n\t\t\n\t\t\"Categorical gadget\"@en\n\t\t\"editor\"\n\t\t\n\t\t\"The editor's term, not a standard one. What the sources support about it is recorded on claim:nets-are-categorical-gadgets.\"@en\n\t\t\"Springer, 3rd ed\"\n\t\t\n\t\t\"An Introduction to Kolmogorov Complexity and Its Applications\"\n\t\t\"2008\"^^\n\t\t\"Li, M.; Vitányi, P.\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\"Shape A -> Shape B converter: the pflow.xyz editor document to a pflow-metamodel Model, ported from go-pflow's parser package\"@en\n\t\t\"crates/pflow-parser\"\n\t\t\"pflow-parser\"\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\"S-expression DSL for defining token model schemas\"@en\n\t\t\"crates/pflow-dsl\"\n\t\t\"pflow-dsl\"\n\t\t\n\t\t\n\t\t\n\t\t\"GameNet\"@en\n\t\t\n\t\t\"Constructed nets are categorical gadgets.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"thesis: the support below is what the cited texts say, not a proof\"\n\t\t\"editor\"\n\t\t\"No source cited here applies the Yoneda lemma to nets built with pflow's token language; that step is the editor's argument. In Baez, Genovese, Master and Shulman the presheaf property is proved for pre-nets and for Sigma-nets (nets whose tokens are individually tracked), and the paper states that the category of ordinary Petri nets is not a presheaf category. A statement of the claim should say which kind of net it means.\"\n\t\t\n\t\t\n\t\t\"Constructed nets are categorical gadgets\"@en\n\t\t\n\t\t\n\t\t\"parents\"@en\n\t\t\"CONCUR 1998\"\n\t\t\n\t\t\"Unfolding and Finite Prefix for Nets with Read Arcs\"\n\t\t\"1998\"^^\n\t\t\"Vogler, W.; Semenov, A.; Yakovlev, A.\"\n\t\t\n\t\t\n\t\t\n\t\t\"12\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A cryptographic protocol where a prover convinces a verifier that a statement is true without revealing any information beyond the truth of the statement. In pflow, ZK proofs verify that a Petri net transition was validly fired without revealing the marking (Chapter 12).\"@en\n\t\t\"Zero-knowledge proof\"@en\n\t\t\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A transition is live if it can eventually fire from every reachable marking (possibly after other transitions fire first). A net is live if all transitions are live. Liveness means the system never permanently loses capability.\"@en\n\t\t\"Liveness\"@en\n\t\t\n\t\t\n\t\t\"Section 7, proof of Lemma 7.11\"\n\t\t\n\t\t\"Applies the Yoneda lemma to describe monoid structures for the convolution product on a category B under the free symmetric monoidal category, as morphisms B(a,c) x B(b,d) to B(ab,cd). Used to identify the duoids of Sigma-nets with PROPs.\"\n\t\t\n\t\t\"assistant-judgment\"\n\t\t\"direct\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"category-theory\"\n\t\t\"composition\"\n\t\t\"open-games\"\n\t\t\"petri-net\"\n\t\t\"pflow\"\n\t\t\"symmetric-monoidal\"\n\t\t\n\t\t\n\t\t\"Symmetric Monoidal Categories: The Structure Underneath\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-01T00:00:00Z\"^^\n\t\t\"2026-03-09T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"A Petri net generates a free symmetric monoidal category — places give the objects, transitions the generating morphisms. What that theorem buys for composition, analysis and proofs across this blog, and which of the connections are still a shape match rather than a checked result.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A mathematical modeling language consisting of places, transitions, arcs, and tokens. Formally, a tuple $(P, T, F, W, \\\\mathbf{m}_0)$ where $P$ is a set of places, $T$ is a set of transitions, $F \\\\subseteq (P \\\\times T) \\\\cup (T \\\\times P)$ is the flow relation, $W: F \\\\to \\\\mathbb{N}$ is the weight function, and $\\\\mathbf{m}_0$ is the initial marking.\"@en\n\t\t\n\t\t\"Petri net\"@en\n\t\t\n\t\t\"20\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A state management pattern where state is computed by replaying an immutable log of events from the initial state: $\\\\text{State}(t) = \\\\text{fold}(\\\\text{apply}, \\\\text{initialState}, \\\\text{events}[0..t])$. In Petri net terms, events are transition firings and state is the marking (Chapter 20).\"@en\n\t\t\"Event sourcing\"@en\n\t\t\n\t\t\"20\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A canonical firing sequence and its resulting markings, checked byte-for-byte against every implementation of a model. `pflow-polyglot/parity/trace.golden` holds thirty-nine programs in ten languages to one six-line trace. `make parity` runs the twenty Go, Rust, Python and JavaScript programs under Bazel and fails the build on any divergence; `make parity-native` checks the rest against the same file (Chapter 20).\"@en\n\t\t\"Golden trace\"@en\n\t\t\n\t\t\"Every place has a finite token maximum across reachable markings. Established by sim_verify, not inferred here.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Hedges, J.\"\n\t\t\n\t\t\"the model's shape matched no rule in ProposeTypes' table: unrecognized, not misclassified\"@en\n\t\t\n\t\t\n\t\t\"UnclassifiedModel\"\n\t\t\n\t\t\"Freeman, L.C.\"\n\t\t\n\t\t\n\t\t\n\t\t\"runtime\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"description\"@en\n\t\t\n\t\t\"Go\"\n\t\t\"Petri net library — ODE, SSA & SDE simulation, parameter fitting, and formal verification, in Go\"@en\n\t\t\n\t\t\"go-pflow\"\n\t\t\"Legacy documents write this member as `source`.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"arcSource\"@en\n\t\t\n\t\t\"Mac Lane, S.\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Package stochastic simulates a metamodel.Model as a continuous-time Markov chain (Gillespie's direct method) and dispatches the same declared net to either that engine or the mass-action ODE in solver — Petri.jl's ODEProblem/JumpProblem choice, off one structure.\"@en\n\t\t\"stochastic\"\n\t\t\"stochastic\"\n\t\t\n\t\t\n\t\t\"venue\"@en\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Deterministic beat generator powered by Petri nets. No AI, no LLMs — just math, music theory, and token flow.\"@en\n\t\t\n\t\t\"beats-bitwrap-io\"\n\t\t\n\t\t\n\t\t\n\t\t\"sim.pflow.xyz — From Description to Checked Model\"\n\t\t\n\t\t\"18\"^^\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Package mining provides process mining algorithms including discovery and conformance checking.\"@en\n\t\t\"mining\"\n\t\t\"mining\"\n\t\t\"Discrete Mathematics, 23(3)\"\n\t\t\n\t\t\"A characterization of the minimum cycle mean in a digraph\"\n\t\t\"1978\"^^\n\t\t\"Karp, R.M.\"\n\t\t\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A net is bounded if every place has a finite maximum token count across all reachable markings. A net is $k$-bounded if no place ever exceeds $k$ tokens. Boundedness is a safety property — it guarantees the system can't accumulate unbounded resources.\"@en\n\t\t\"Bounded\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Appendix E: Categorical Foundations\"\n\t\t\n\t\t\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The execution semantics of Petri nets. When a transition fires, it atomically removes tokens from input places and adds tokens to output places according to arc weights. The new marking is $\\\\mathbf{m}' = \\\\mathbf{m} + \\\\mathbf{C} \\\\cdot \\\\mathbf{e}_t$ where $\\\\mathbf{e}_t$ is the unit vector for transition $t$.\"@en\n\t\t\"Firing rule\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"invariants\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"createdBy\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"ticker\"@en\n\t\t\"Transition to place. Weight tokens are produced when the transition fires.\"@en\n\t\t\n\t\t\n\t\t_:d0200ba986b921a0135493f8fcbf63b6\n\t\t_:f73a125f20c842b678594295dd227709\n\t\t\"OutputArc\"@en\n\t\t\n\t\t\"David, R.\"\n\t\t\n\t\t\n\t\t\"Book\"@en\n\t\t\n\t\t\"Winschel, V.\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"category-theory\"\n\t\t\"open-petri-nets\"\n\t\t\"petri-nets\"\n\t\t\"settlement\"\n\t\t\n\t\t\n\t\t\"The Category Settle\"\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\"2026-03-12T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Settlement networks form a sub-SMC of open Petri nets. The core-observer split is really two boundaries — an algebraic one (ρ) inside the incidence matrix and a categorical one (contextual arcs) outside it — and a ZK circuit dissolves only the second.\"@en\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Anonymous on-chain voting with ZK proofs — create polls, cast verifiable ballots, tally results. Built on Petri net state machines.\"@en\n\t\t\n\t\t\"bitwrap-io\"\n\t\t\n\t\t\n\t\t\n\t\t\"Process Mining\"\n\t\t\n\t\t\"11\"^^\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\"blog-stackdump-com\"\n\t\t\"No reachable marking enables no transition. Established by sim_verify, not inferred here.\"@en\n\t\t\n\t\t\n\t\t\"DeadlockFreeNet\"@en\n\t\t\n\t\t\n\t\t\"composition\"\n\t\t\"dsl\"\n\t\t\"formal-methods\"\n\t\t\"forth\"\n\t\t\"petri-net\"\n\t\t\"state-machine\"\n\t\t\"tla-plus\"\n\t\t\"domain-driven-design\"\n\t\t\"little-languages\"\n\t\t\n\t\t\n\t\t\"The Little Language Thesis\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-08T00:00:00Z\"^^\n\t\t\"2026-03-28T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"cell, func, arrow, guard are the structural primitives — but the real ubiquitous language lives in the labels. Like Forth, we build up domain vocabularies on a minimal substrate, and the incidence matrix proves what it can see: conservation, not guards or data.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"capacity\"@en\n\t\t\"12\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A zero-knowledge proof system used in pflow for verifying Petri net transitions without revealing state. Produces constant-size proofs with fast verification, at the cost of a per-circuit trusted setup (Chapter 12).\"@en\n\t\t\"Groth16\"@en\n\t\t\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A marker in a place. Tokens represent the presence of a resource, the truth of a condition, or a unit of something being processed. In the discrete model, tokens are non-negative integers. In the continuous relaxation, they become non-negative real numbers.\"@en\n\t\t\n\t\t\"Token\"@en\n\t\t\n\t\t\"Needs the other component to build, directly or through others. A cycle shows up after reasoning as a mutual pair (cq/05-dependency-cycles.rq). It is not an inconsistency, because OWL 2 DL does not allow irreflexivity on a transitive property, and the engine's closure omits self-loops, so X dependsOn X is never derived.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"dependsOn\"@en\n\t\t\n\t\t\"formal-methods\"\n\t\t\"llm\"\n\t\t\"modeling\"\n\t\t\"petri-net\"\n\t\t\"sim-pflow-xyz\"\n\t\t\n\t\t\n\t\t\"Small Models > LLMs\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-23T00:00:00Z\"^^\n\t\t\"2026-03-06T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Why executable formal models matter more with LLMs around, not less — and what the LLM is and isn't trusted with when a Petri net constrains it.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"InvariantClaim\"@en\n\t\t\"Whole paper\"\n\t\t\n\t\t\"The paper associated with Yoneda's name.\"\n\t\t\n\t\t\"assistant-judgment\"\n\t\t\"origin\"\n\t\t\"Whether the lemma is stated in this paper was not checked; cite a textbook for the statement.\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"initialMarking\"@en\n\t\t\n\t\t\n\t\t\"The functor from a locally small category C to the category of presheaves on C that sends an object c to Hom(-, c). It is fully faithful, which is a consequence of the Yoneda lemma.\"@en\n\t\t\"Yoneda embedding\"@en\n\t\t\"assistant-judgment\"\n\t\t\n\t\t\"Riehl, Category Theory in Context, section 2.2.\"\n\t\t\n\t\t\n\t\t\n\t\t\"From Discrete to Continuous\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"3\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"places\"@en\n\t\t\"20\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A hash of the simulation output used for cross-implementation verification. If the Go server and JavaScript browser produce the same state root from the same model, the implementations agree (Chapter 20).\"@en\n\t\t\"State root\"@en\n\t\t\n\t\t\n\t\t\"Claude Code\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Place\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"SoftwareSourceCode\"@en\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\"Token model schema, snapshot, and runtime execution\"@en\n\t\t\"crates/pflow-tokenmodel\"\n\t\t\"pflow-tokenmodel\"\n\t\t\"Whole paper (the title result)\"\n\t\t\n\t\t\"Cited in this ecosystem's Appendix E and in the posts as the result that a net's firing sequences form a free monoidal category.\"\n\t\t\n\t\t\"assistant-judgment\"\n\t\t\"background\"\n\t\t\"The abstract of Baez et al. distinguishes the collective-token reading, where nets generate commutative monoidal categories, from the individual-token reading, where Sigma-nets generate symmetric strict monoidal categories. Appendix E's 'free symmetric monoidal category' belongs to the second.\"\n\t\t\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\"Package solver implements ODE (Ordinary Differential Equation) solvers for Petri net simulation using mass-action kinetics.\"@en\n\t\t\"solver\"\n\t\t\"solver\"\n\t\t\n\t\t\n\t\t\"Blog\"@en\n\t\t\n\t\t\"equivalence\"\n\t\t\"go-pflow\"\n\t\t\"ode\"\n\t\t\"petri-net\"\n\t\t\"sim-pflow-xyz\"\n\t\t\n\t\t\n\t\t\"Comparing Nets by Their ODE Signatures\"\n\t\t\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-04-01T00:00:00Z\"^^\n\t\t\"2026-02-18T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"The same math with different labels still produces the same ODE solution. In tic-tac-toe, we see it directly — each board position is a place, and the heatmap is the solution projected onto the grid.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Package monitoring provides real-time predictive process monitoring.\"@en\n\t\t\"monitoring\"\n\t\t\"monitoring\"\n\t\t\n\t\t\n\t\t\n\t\t\"Exponential Weights and Scoring Systems\"\n\t\t\n\t\t\"15\"^^\n\t\t\n\t\t\n\t\t\"RustCrate\"@en\n\t\t\n\t\t\n\t\t\"ContextualArc\"@en\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Package saga models a saga — an ordered list of steps, each paired with a compensation that undoes it — as a Petri net.\"@en\n\t\t\"saga\"\n\t\t\"saga\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\"Package tokenmodel defines abstract building blocks for formal models.\"@en\n\t\t\"tokenmodel\"\n\t\t\"tokenmodel\"\n\t\t\"Journal of Mathematical Biology, 54(1)\"\n\t\t\n\t\t\"Solving the chemical master equation for monomolecular reaction systems analytically\"\n\t\t\"2007\"^^\n\t\t\"Jahnke, T.; Huisinga, W.\"\n\t\t\n\t\t\n\t\t\n\t\t\"EUROCRYPT 2016\"\n\t\t\n\t\t\"On the Size of Pairing-Based Non-Interactive Arguments\"\n\t\t\"2016\"^^\n\t\t\"Groth, J.\"\n\t\t\n\t\t\n\t\t\"For a locally small category C, an object c and a functor F from C^op to Set, the natural transformations from the representable functor Hom(-, c) to F correspond bijectively to the elements of F(c), naturally in c and F.\"@en\n\t\t\"Yoneda lemma\"@en\n\t\t\"assistant-judgment\"\n\t\t\n\t\t\"Riehl, Category Theory in Context, section 2.2.\"\n\t\t\n\t\t\"gnark\"\n\t\t\"governance\"\n\t\t\"groth16\"\n\t\t\"petri-net\"\n\t\t\"solidity\"\n\t\t\"voting\"\n\t\t\"zk\"\n\t\t\n\t\t\n\t\t\"ZK Polls: Voting as a Visible State Machine\"\n\t\t\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-10-25T00:00:00Z\"^^\n\t\t\"2026-03-19T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\"Anonymous polls in bitwrap-io: a small Petri net whose cast-vote transition carries a Groth16 proof of registry membership, nullifier and range — and what the current code does about secrecy after the poll closes.\"@en\n\t\t\n\t\t\"Mathematical Structures in Computer Science, 30\"\n\t\t\n\t\t\"Petri Nets Based on Lawvere Theories\"\n\t\t\n\t\t\"2020\"^^\n\t\t\"Master, J.\"\n\t\t\"1904.09091\"\n\t\t\n\t\t\n\t\t\"pflow ecosystem glossary\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"The Visual Editor — pflow.xyz\"\n\t\t\n\t\t\"17\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"hasTransition\"@en\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\"Process event log types plus CSV/JSONL readers, ported from go-pflow's eventlog package\"@en\n\t\t\"crates/pflow-eventlog\"\n\t\t\"pflow-eventlog\"\n\t\t\n\t\t\n\t\t\"Transition\"@en\n\t\t\n\t\t\"Riehl, E.\"\n\t\t\n\t\t\n\t\t\n\t\t\"Appendix C: JSON Schema Reference\"\n\t\t\n\t\t\n\t\t\"cross-language\"\n\t\t\"determinism\"\n\t\t\"formal-methods\"\n\t\t\"petri-net\"\n\t\t\"stochastic-simulation\"\n\t\t\n\t\t\n\t\t\"Byte-Exact Across Four Languages\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-09-04T00:00:00Z\"^^\n\t\t\"2026-09-04T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"Go, Rust, JavaScript and Julia run the same stochastic Petri net and produce the identical IEEE-754 double, every time. Not close — equal. Here's what that actually took, and the two bugs it caught along the way.\"@en\n\t\t\n\t\t\n\t\t\"cryptography\"\n\t\t\"gnark\"\n\t\t\"petri-net\"\n\t\t\"zero-knowledge\"\n\t\t\n\t\t\n\t\t\"ZK Tic-Tac-Toe Model\"\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-04-01T00:00:00Z\"^^\n\t\t\"2026-01-31T00:00:00Z\"^^\n\t\t\n\t\t\"Zero-knowledge proofs meet Petri nets—cryptographically verify valid game moves without revealing strategy using gnark circuits.\"@en\n\t\t\n\t\t\n\t\t\"cryptography\"\n\t\t\"gnark\"\n\t\t\"groth16\"\n\t\t\"petri-net\"\n\t\t\"zero-knowledge\"\n\t\t\n\t\t\n\t\t\"Zero-Knowledge Proofs for Petri Nets\"\n\t\t\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\"2026-02-14T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"How gnark circuits prove that a Petri net transition is valid without revealing the state—MiMC hashing, topology-based constraints, and Groth16 proofs.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Optimization — The Knapsack Problem\"\n\t\t\n\t\t\"8\"^^\n\t\t\"What the source shows there, in the curator's words.\"@en\n\t\t\n\t\t\n\t\t\"evidence\"@en\n\t\t\n\t\t\n\t\t\"ordinals\"\n\t\t\"petri-net\"\n\t\t\"type-theory\"\n\t\t\"tropical-geometry\"\n\t\t\n\t\t\n\t\t\"Brouwer Ordinals and the Shape of a Witness\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-04-16T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"de Jong et al. (2026) put an ordinal axis under decidability. That axis is past-tense, and Brouwer ordinals are the scalar specialization of our vector tropical past.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\"Package petri implements core Petri net data structures.\"@en\n\t\t\"petri\"\n\t\t\"petri\"\n\t\t\"Proposition 4.3 (section 4) and Theorem 6.1 (section 6.1, 'The presheaf perspective')\"\n\t\t\n\t\t\"States that the category of pre-nets and the category of Sigma-nets are each equivalent to a presheaf category. The proof of Theorem 6.1 builds a category D so that functors from D to Set can be identified with Sigma-nets.\"\n\t\t\n\t\t\"assistant-judgment\"\n\t\t\"direct\"\n\t\t\"Applies to pre-nets and Sigma-nets, not to ordinary Petri nets (see claim:s4-limit-ordinary-petri-nets).\"\n\t\t\n\t\t\"Whole paper\"\n\t\t\n\t\t\"Cited in this ecosystem's Appendix E as refining the construction to symmetric monoidal categories.\"\n\t\t\n\t\t\"assistant-judgment\"\n\t\t\"background\"\n\t\t\n\t\t\"ddm\"\n\t\t\"ode\"\n\t\t\"petri-net\"\n\t\t\"sudoku\"\n\t\t\n\t\t\n\t\t\"Sudoku Petri-Net Model\"\n\t\t\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-10-17T00:00:00Z\"^^\n\t\t\"2025-11-28T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"A 4×4 Sudoku as a Petri net in the tic-tac-toe pattern — cells, digit moves with history, constraint collectors into a solved place — checked against the go-pflow generator, which shows the collectors as built can never fire and the ODE ranking is not yet demonstrated.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"source\"@en\n\t\t\n\t\t\n\t\t\"category-theory\"\n\t\t\"composition\"\n\t\t\"dsl\"\n\t\t\"petri-net\"\n\t\t\"pflow\"\n\t\t\n\t\t\n\t\t\"Categorical Net Types\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\"2026-02-07T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Five Petri net types classify token behavior — workflow cursors, countable resources, game turns, continuous rates, and classification signals — with typed links that constrain how nets compose.\"@en\n\t\t\n\t\t\n\t\t\"composition\"\n\t\t\"dsl\"\n\t\t\"metamodel\"\n\t\t\"petri-net\"\n\t\t\"domain-driven-design\"\n\t\t\n\t\t\n\t\t\"A Tiling for Computation\"\n\t\t\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-08-23T00:00:00Z\"^^\n\t\t\"2026-08-23T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"A small, fixed alphabet whose local composition rules generate an unbounded, non-repeating space of checkable systems — token standards, business operations, games, music, our own infrastructure. Not one system that swallows every domain. Two tiles, remixed without limit.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Constraint Satisfaction — Sudoku\"\n\t\t\n\t\t\n\t\t\"7\"^^\n\t\t\n\t\t\n\t\t\"collection\"@en\n\t\t\"20\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"Disagreement between a declared artifact and the world it describes — a manifest and a host, a vendored module and its upstream, two implementations of one net. Metamodel does not prevent drift; it makes drift detectable by comparing two values: a manifest against a host, a vendored file against its lockfile, a trace against the golden trace (Chapters 20, 21).\"@en\n\t\t\"Drift\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"runtimeHash\"@en\n\t\t\"16\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"Universal RDF Dataset Normalization Algorithm 2015. Used in pflow to canonicalize JSON-LD models before hashing, ensuring that semantically equivalent documents produce identical content identifiers regardless of key order or formatting (Chapter 16).\"@en\n\t\t\"URDNA2015\"@en\n\t\t\n\t\t\"Boolean condition on a transition, in addition to the token requirements.\"@en\n\t\t\n\t\t\"Guard\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Package workflow provides a comprehensive workflow management framework built on Petri nets with support for task dependencies, resource management, SLA tracking, and real-time monitoring.\"@en\n\t\t\"workflow\"\n\t\t\"workflow\"\n\t\t\n\t\t\n\t\t\n\t\t\"ResourceNet\"@en\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\n\t\t\"Package visualization provides utilities for visualizing Petri nets as SVG.\"@en\n\t\t\"visualization\"\n\t\t\"visualization\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"x\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Topology-Driven Verification\"\n\t\t\n\t\t\"13\"^^\n\t\t\n\t\t\"activitypub\"\n\t\t\"category-theory\"\n\t\t\"infrastructure\"\n\t\t\"json-ld\"\n\t\t\"pflow\"\n\t\t\n\t\t\n\t\t\"JSON-LD as Declarative Infrastructure\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\"2026-02-15T00:00:00Z\"^^\n\t\t\n\t\t\"Why JSON-LD's purely declarative semantics and monotonic schema expansion make it reliable infrastructure for composable systems.\"@en\n\t\t\n\t\t\"3\"^^\n\t\t\n\t\t\"Stochastic Differential Equation\"@en\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"Here, specifically the chemical Langevin equation: continuous state evolving under the same propensities SSA uses, but with intrinsic firing noise built into the diffusion term rather than sampled as discrete events. Cheap to sweep like the ODE, with an honest variance band like SSA — the regime between them. Distinct from a layer of exogenous Brownian motion added to an ODE for external uncertainty (a price feed, say), which answers a different question (Chapter 3).\"@en\n\t\t\"SDE\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\"Petri Nets as a Universal Abstraction — a technical book on modeling state machines, workflows, and token standards with Petri nets\"@en\n\t\t\n\t\t\"book-pflow-xyz\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"hasGuard\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Package learn fits the unknown parameters of continuous Petri-net models to observed data — mechanistic system identification.\"@en\n\t\t\"learn\"\n\t\t\"learn\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"rate\"@en\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A marking where no transition is enabled. The system is stuck — no further computation is possible. Deadlock detection is a key analysis performed by the reachability package.\"@en\n\t\t\"Deadlock\"@en\n\t\t\n\t\t\n\t\t\"event-sourcing\"\n\t\t\"game\"\n\t\t\"petri-net\"\n\t\t\"state-machine\"\n\t\t\n\t\t\n\t\t\"Texas Hold'em Model\"\n\t\t\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-10-12T00:00:00Z\"^^\n\t\t\"2026-01-31T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"The five-seat Hold'em tutorial net (18 places, 32 transitions) read against its source — phase places, turn tokens, a dealer role and an event log, plus what the net leaves to code (chips, guards, re-raises) and one bug in how seats re-enter a hand.\"@en\n\t\t\n\t\t\n\t\t\"beats-bitwrap\"\n\t\t\"music\"\n\t\t\"petri-nets\"\n\t\t\"tone-js\"\n\t\t\n\t\t\n\t\t\"Petri Nets as a Music Sequencer\"\n\t\t\"models\"\n\t\t\n\t\t\"2026-08-08T04:45:00Z\"^^\n\t\t\"2026-03-25T00:00:00Z\"^^\n\t\t\n\t\t\"A music sequencer built entirely on Petri nets — token rings become drum machines, Euclidean rhythms fall out of the topology, and polyrhythm comes free.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Package sensitivity provides tools for analyzing how Petri net behavior changes with different parameters.\"@en\n\t\t\"sensitivity\"\n\t\t\"sensitivity\"\n\t\t\n\t\t\"Social Networks, 1(3)\"\n\t\t\n\t\t\"Centrality in Social Networks: Conceptual Clarification\"\n\t\t\"1978\"^^\n\t\t\"Freeman, L.C.\"\n\t\t\n\t\t\n\t\t\"announcement\"\n\t\t\"book\"\n\t\t\"petri-nets\"\n\t\t\"pflow\"\n\t\t\n\t\t\n\t\t\"Petri Nets as a Universal Abstraction — Now a Book\"\n\t\t\"about\"\n\t\t\n\t\t\"2026-09-27T00:00:00Z\"^^\n\t\t\"2026-02-16T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"The blog's models, concepts, and toolchain have been organized into a book-length guide at book.pflow.xyz.\"@en\n\t\t\n\t\t\n\t\t\"Something we published: a blog post, a book chapter, or the blog and book themselves.\"@en\n\t\t\n\t\t\n\t\t\"Work\"@en\n\t\t\n\t\t\n\t\t\"Signature\"@en\n\t\t\n\t\t\"Vogler, W.\"\n\t\t\n\t\t\"at least one firing-cycle (T-invariant) whose own support touches a resource pool: tokens cycle through that pool rather than accumulating or draining\"@en\n\t\t\n\t\t\n\t\t\"ConservedResourceCycle\"\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The distribution of tokens across all places at a given moment; the state of the Petri net. Written as a vector $\\\\mathbf{m}$ where $\\\\mathbf{m}(p)$ is the token count at place $p$. The initial marking $\\\\mathbf{m}_0$ is the starting state.\"@en\n\t\t\n\t\t\"Marking\"@en\n\t\t\n\t\t\n\t\t\"Genovese, F.\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\"Package eventsource provides event sourcing infrastructure for CQRS applications.\"@en\n\t\t\"eventsource\"\n\t\t\"eventsource\"\n\t\t\n\t\t\n\t\t\n\t\t\"implHash\"@en\n\t\t\n\t\t\"stackdump\"\n\t\t\n\t\t\n\t\t\"formal-methods\"\n\t\t\"lean\"\n\t\t\"model-checking\"\n\t\t\"petri-net\"\n\t\t\"polyglot\"\n\t\t\n\t\t\n\t\t\"The Proof Form: When a Theorem Is Just Another Port\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-26T00:00:00Z\"^^\n\t\t\"2026-08-02T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"Adding Lean 4 to pflow-polyglot forced a fifth implementation form — the same reachability check is a startup assertion in five languages and a compile-time theorem in the sixth, and the code is line-for-line equivalent.\"@en\n\t\t\n\t\t\n\t\t\"Molloy, M.K.\"\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A read arc (fires only if a place holds a token, without consuming it) or an inhibitor arc (fires only if it holds none). Neither appears in the incidence matrix, since neither changes the marking. Nets with contextual arcs do not generate the free symmetric monoidal category of ordinary nets (Montanari & Rossi, 1995); they are the categorical half of the core–observer boundary, and the natural home of guards.\"@en\n\t\t\n\t\t\"Contextual arc\"@en\n\t\t\n\t\t\"Enables its transition only if the source place holds a token; consumes none.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"ReadArc\"@en\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The number of tokens consumed or produced by an arc when its transition fires. A weight of $k$ on an input arc means the transition requires at least $k$ tokens in the source place and removes $k$ tokens when firing. Default weight is 1.\"@en\n\t\t\"Weight\"@en\n\t\t\n\t\t\"The Topos Institute\"\n\t\t\n\t\t\"Generalized Petri Nets\"\n\t\t\"2020\"^^\n\t\t\"Master, J.\"\n\t\t\n\t\t\n\t\t\"Jahnke, T.\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"publicKey\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"The Token Language\"\n\t\t\n\t\t\n\t\t\"4\"^^\n\t\t\n\t\t\"at least one demand-rate (source) knob and no resource pool: pure arrivals with nothing rationing them\"@en\n\t\t\n\t\t\n\t\t\"ArrivalProcess\"\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Command-line tool for Petri net modeling and simulation — parity with go-pflow's cmd/pflow\"@en\n\t\t\"crates/pflow-cli\"\n\t\t\"pflow-cli\"\n\t\t\"The work links to the other in its text.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"linksTo\"@en\n\t\t\n\t\t\"biochemistry\"\n\t\t\"mass-action\"\n\t\t\"ode\"\n\t\t\"petri-net\"\n\t\t\n\t\t\n\t\t\"Enzyme Kinetics: Michaelis-Menten from Three Transitions\"\n\t\t\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-10-04T00:00:00Z\"^^\n\t\t\"2026-02-14T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\"Four places and three mass-action transitions generate the ODE system that Michaelis-Menten is derived from. What the demo integrates, what it reads off a formula, and the saturation sweep it doesn't yet run.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"A paper, book or thesis, by bibliographic facts only. Cited by a Work, or added by an editor.\"@en\n\t\t\n\t\t\n\t\t\"Reference\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Appendix A: Solver Parameter Reference\"\n\t\t\n\t\t\"A unit of source code that other code can depend on: a project, a package or a crate.\"@en\n\t\t\n\t\t\n\t\t\"Component\"@en\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A graph whose nodes divide into two disjoint sets, with edges only between sets, never within. Petri nets are bipartite: places connect to transitions, transitions connect to places, but places never connect directly to places.\"@en\n\t\t\"Bipartite graph\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Sassone, V.\"\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"MCP server for Petri net simulation and analysis\"@en\n\t\t\"crates/pflow-mcp\"\n\t\t\"pflow-mcp\"\n\t\t\n\t\t\n\t\t\n\t\t\"On-Chain ZK Verification\"\n\t\t\n\t\t\"14\"^^\n\t\t\n\t\t\"Ghani, N.\"\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\n\t\t\"Parameter fitting, sensitivities, and gradient/derivative-free optimizers for Petri net ODEs\"@en\n\t\t\"crates/pflow-learn\"\n\t\t\"pflow-learn\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\"Package derive builds evaluation variants of a declared Petri net.\"@en\n\t\t\"derive\"\n\t\t\"derive\"\n\t\t\"A net with at least one read or inhibitor arc; not the free symmetric monoidal category of ordinary nets.\"@en\n\t\t\n\t\t_:a44ddc85277f85c3869ff37793244b07\n\t\t\"ContextualNet\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Epilogue: What the Abstraction Sits On\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"21\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"CompositeNet\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Appendix D: Glossary\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"transition\"@en\n\t\t\"TAPSOFT\"\n\t\t\n\t\t\"On the Category of Petri Net Computations\"\n\t\t\"1995\"^^\n\t\t\"Sassone, V.\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Zero-Knowledge Proofs\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"12\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"place\"@en\n\t\t\n\t\t\"bitwrap\"\n\t\t\"groth16\"\n\t\t\"petri-net\"\n\t\t\"solidity\"\n\t\t\"zero-knowledge\"\n\t\t\n\t\t\n\t\t\"Bitwrap: Petri Nets as ZK Containers\"\n\t\t\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-04-01T00:00:00Z\"^^\n\t\t\"2026-03-18T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"From OP_RETURN in 2014 to zero-knowledge Petri nets in 2026 — how bitwrap.io became the capstone for a decade of work on formal state machines, cryptographic proofs, and executable specifications.\"@en\n\t\t\n\t\t\n\t\t\"Alla, H.\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Package engine provides a state machine harness for continuous Petri net simulation.\"@en\n\t\t\"engine\"\n\t\t\"engine\"\n\t\t\n\t\t\"chat-bridge\"\n\t\t\"mcp\"\n\t\t\"minecraft\"\n\t\t\"provenance\"\n\t\t\"self-hosting\"\n\t\t\n\t\t\n\t\t\"f004 Is Older Than My Daughter\"\n\t\t\"about\"\n\t\t\n\t\t\"2026-07-30T00:00:00Z\"^^\n\t\t\"2026-07-30T00:00:00Z\"^^\n\t\t\"A single-player Minecraft world moved to a dedicated server so it could have a chat bridge — plus a closed verb list, a fixed aid ceiling, and a nether hub that separates roof traffic from portal traffic.\"@en\n\t\t\n\t\t\n\t\t\"Asserted from an import (Go), a path dependency (Cargo) or a go.mod requirement. Never inferred.\"@en\n\t\t\n\t\t\"directDependency\"@en\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Visual editor and browser ODE simulator for Petri nets, byte-exact to go-pflow\"@en\n\t\t\n\t\t\"pflow-xyz\"\n\t\t\n\t\t\"The category of functors from C^op to Set, with natural transformations as morphisms. Presheaf categories are toposes.\"@en\n\t\t\"Presheaf category\"@en\n\t\t\"assistant-judgment\"\n\t\t\n\t\t\"Standard; see Riehl, Category Theory in Context.\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"supportedBy\"@en\n\t\t\n\t\t\n\t\t\"llm\"\n\t\t\"metamodel\"\n\t\t\"petri-net\"\n\t\t\"sim-pflow-xyz\"\n\t\t\"simulation\"\n\t\t\"what-if-analysis\"\n\t\t\n\t\t\n\t\t\"The Model Is the App\"\n\t\t\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\n\t\t\"A declarative vocabulary of composable models that gives you analysis and an app framework from the same artifact. Describe your operation, get a model; play the model as an app; calibrate it with your own data.\"@en\n\t\t\n\t\t\n\t\t\"beats-bitwrap\"\n\t\t\"music\"\n\t\t\"petri-nets\"\n\t\t\n\t\t\n\t\t\"A browser music sequencer where every note is a Petri-net transition firing\"\n\t\t\"models\"\n\t\t\n\t\t\"2026-04-30T00:00:00Z\"^^\n\t\t\"2026-04-30T00:00:00Z\"^^\n\t\t\n\t\t\"The runtime is a Petri net — places hold tokens, transitions fire, that's the music. Same genre+seed = byte-identical output. Share URLs are CIDv1; the address is the track.\"@en\n\t\t\n\t\t\n\t\t\"Categories of Nets\"\n\t\t\n\t\t\"2021\"^^\n\t\t\"Baez, J.C.; Genovese, F.; Master, J.; Shulman, M.\"\n\t\t\"editor\"\n\t\t\"2101.04238\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Abstract: Sigma-nets generate symmetric strict monoidal categories and ordinary Petri nets generate commutative monoidal categories, by left adjoint functors. Directly relevant to the free-SMC claim in Appendix E.\"\n\t\t\n\t\t\n\t\t\"Arc\"@en\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A node in a Petri net representing a condition, resource, or state. Places hold tokens. Drawn as circles. In the continuous relaxation, token counts become continuous concentrations.\"@en\n\t\t\n\t\t\"Place\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"EventLink\"@en\n\t\t\n\t\t\"Information and Computation, 88(2)\"\n\t\t\n\t\t\"Petri Nets are Monoids\"\n\t\t\"1990\"^^\n\t\t\"Meseguer, J.; Montanari, U.\"\n\t\t\n\t\t\n\t\t\"Abstract (only the abstract was checked)\"\n\t\t\n\t\t\"An open Petri net has places designated as inputs and outputs via a cospan of sets, which lets nets be composed.\"\n\t\t\n\t\t\"assistant-judgment\"\n\t\t\"background\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Package actor provides an Actor model built on Petri nets with message passing.\"@en\n\t\t\"actor\"\n\t\t\"actor\"\n\t\t\n\t\t\"$\\\\rho$\"@en\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"For a transition, tokens consumed divided by tokens produced. $\\\\rho = 1$ is the core; $\\\\rho > 1$ is an observer that destroys state to produce a verdict. A property of the incidence matrix column, so every analysis of $C$ can see it. See *Core–observer boundary*.\"@en\n\t\t\"Compression ratio\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"signature\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"nextMarking\"@en\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\"prover\"\n\t\t\"prover\"\n\t\t\"21\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The Metamodel working discipline. The model is declared once as data; analysis, the running application, proofs and, in this ecosystem's own deployment tooling, the infrastructure that serves it are computed from that document. Nothing downstream is hand-written to agree with the model, so nothing downstream can disagree with it (Chapter 21; *The Model Is the App*).\"@en\n\t\t\"Declare, then derive\"@en\n\t\t\n\t\t\"Legacy documents write this member as `target`.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"arcTarget\"@en\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\"Package reachability provides state space analysis for Petri nets.\"@en\n\t\t\"reachability\"\n\t\t\"reachability\"\n\t\t\n\t\t\"Quadrat, J.-P.\"\n\t\t\n\t\t\"ddm\"\n\t\t\"ode\"\n\t\t\"petri-net\"\n\t\t\"theory\"\n\t\t\n\t\t\n\t\t\"Declarative Differential Models (DDM)\"\n\t\t\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-04-02T00:00:00Z\"^^\n\t\t\"2025-01-07T04:54:52Z\"^^\n\t\t\n\t\t\n\t\t\"A modeling approach where system behavior is described declaratively and encoded directly in differential equations.\"@en\n\t\t\n\t\t\n\t\t\"Stay, M.\"\n\t\t\"IEEE Transactions on Computers, C-31(9)\"\n\t\t\n\t\t\"Performance Analysis Using Stochastic Petri Nets\"\n\t\t\"1982\"^^\n\t\t\"Molloy, M.K.\"\n\t\t\n\t\t\n\t\t\"Li, M.\"\n\t\t\"The authors in citation order, separated by semicolons. schema:author is an unordered set, so this is what a citation is built from.\"@en\n\t\t\n\t\t\n\t\t\"authorList\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Resource Modeling — The Coffee Shop\"\n\t\t\n\t\t\"5\"^^\n\t\t\n\t\t\"3\"^^\n\t\t\n\t\t\"Stochastic Simulation Algorithm\"@en\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The discrete engine's execution method (Gillespie's direct method): pick the next transition to fire and the time until it fires, both drawn from the model's own propensities, then repeat. Produces one exact discrete sample path, or an ensemble of them, rather than a mean-field trajectory — the right tool when small counts or gating (read arcs, inhibitors, reachable capacities, guards) make the continuous relaxation inapplicable (Chapter 3).\"@en\n\t\t\"SSA\"@en\n\t\t\n\t\t\"Enables its transition only if the source place holds no token.\"@en\n\t\t\n\t\t_:c199f2db2b9fc80e9d56f9a5b0a1cb4b\n\t\t\n\t\t\"InhibitorArc\"@en\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\"Structured simulation results (types, analysis, builder, io), ported from go-pflow's results package\"@en\n\t\t\"crates/pflow-results\"\n\t\t\"pflow-results\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Package plotter provides SVG visualization for ODE solutions.\"@en\n\t\t\"plotter\"\n\t\t\"plotter\"\n\t\t\n\t\t\n\t\t\"Karp, R.M.\"\n\t\t\"Springer\"\n\t\t\n\t\t\"Discrete, Continuous, and Hybrid Petri Nets\"\n\t\t\"2010\"^^\n\t\t\"David, R.; Alla, H.\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"PetriNet\"@en\n\t\t\n\t\t\"A Cargo dependency behind a feature flag.\"@en\n\t\t\n\t\t\"optionalDependency\"@en\n\t\t\"2\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The matrix $\\\\mathbf{C} = \\\\mathbf{C}^+ - \\\\mathbf{C}^-$ where $\\\\mathbf{C}^+$ is the output matrix (tokens produced) and $\\\\mathbf{C}^-$ is the input matrix (tokens consumed). Each column represents a transition; each row represents a place. The entry $\\\\mathbf{C}_{ij}$ is the net change in place $i$ when transition $j$ fires (Chapter 2).\"@en\n\t\t\"Incidence matrix\"@en\n\t\t\n\t\t\"16\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"JSON for Linked Data. The pflow ecosystem uses JSON-LD as its model interchange format, with `@context: \\\"https://pflow.xyz/schema\\\"`. JSON-LD makes models self-describing and content-addressable (Chapter 16).\"@en\n\t\t\"JSON-LD\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"links\"@en\n\t\t\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"An equation $\\\\mathbf{y}^T \\\\mathbf{C} = \\\\mathbf{0}$ where $\\\\mathbf{y}$ is a vector of weights and $\\\\mathbf{C}$ is the incidence matrix. Conservation laws prove that weighted sums of token counts remain constant across all firings. Example: in an SIR model, $S + I + R = N$ for all time.\"@en\n\t\t\"Conservation law\"@en\n\t\t\n\t\t\n\t\t\"A kind of sim model, from the vocabulary sim publishes. Proposed, not yet applied to catalog models.\"@en\n\t\t\n\t\t\n\t\t\"ModelKind\"@en\n\t\t\"Chapter III, 'Universals and Limits' (section not checked)\"\n\t\t\n\t\t\"Standard reference for the lemma. Says nothing about nets.\"\n\t\t\n\t\t\"assistant-judgment\"\n\t\t\"general\"\n\t\t\n\t\t\"12\"^^\n\t\t\n\t\t\"Minimum Multiplicative Complexity\"@en\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A hash function designed for efficiency inside arithmetic circuits. Used in pflow's zero-knowledge proofs to hash Petri net markings with minimal constraint count (Chapter 12).\"@en\n\t\t\"MiMC\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"prevMarking\"@en\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"Two readings of concurrent behavior. Interleaving semantics considers one firing at a time and asks which markings are reachable; partial-order (unfolding) semantics additionally records which firings were independent. Encoding a read arc as a consume-then-restore self-loop is exact under the first and inequivalent under the second (Vogler, Semenov & Yakovlev, 1998). A single-transition ZK proof has only interleaving semantics.\"@en\n\t\t\"Interleaving vs. partial-order semantics\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Yoneda, N.\"\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Petri net modeling with ODE simulation and token model DSL\"@en\n\t\t\"crates/pflow\"\n\t\t\"pflow\"\n\t\t\"PhD thesis, University of California, Riverside\"\n\t\t\n\t\t\"Composing Behaviors of Networks\"\n\t\t\n\t\t\"2020\"^^\n\t\t\"Master, J.\"\n\t\t\"editor\"\n\t\t\"2105.12905\"\n\t\t\n\t\t\"Title page: dissertation dated June 2020, posted to arXiv May 2021.\"\n\t\t\"Present only on references an editor added; the writing does not cite them.\"@en\n\t\t\n\t\t\n\t\t\"addedBy\"@en\n\t\t\n\t\t\n\t\t\"GuardLink\"@en\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\n\t\t\"ODE solvers for Petri net simulation using mass-action kinetics\"@en\n\t\t\"crates/pflow-solver\"\n\t\t\"pflow-solver\"\n\t\t\n\t\t\"petri-net\"\n\t\t\"sim-pflow-xyz\"\n\t\t\"simulation\"\n\t\t\"cost-benefit-analysis\"\n\t\t\"what-if-analysis\"\n\t\t\n\t\t\n\t\t\"The Capacity Paradox\"\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-10-09T00:00:00Z\"^^\n\t\t\"2026-09-16T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\"sim.pflow.xyz ranks every knob in a model by its measured effect on the objective. One run against a software team's backlog model reported that hiring past a point lowers the score; that finding is unconfirmed until the model's cost meter is fixed, and the catalog-wide sweep behind the rest of the pattern was never preserved. What was checked, what wasn't, and the models to re-run it on.\"@en\n\t\t\n\t\t\"21\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"Capitalised: a model for making models — the cross-cutting claim of this book. A small, fixed alphabet — place, transition, arc, guard — whose local composition rules generate an unbounded space of specific, checkable systems, because a model written in it is a value rather than a program. Lowercase `metamodel`, in code font, is a Go package implementing one instance of the vocabulary (Chapter 21; *A Tiling for Computation*).\"@en\n\t\t\"Metamodel\"@en\n\t\t\n\t\t\n\t\t\"Master, J.\"\n\t\t\"16\"^^\n\t\t\n\t\t\"Content Identifier\"@en\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A hash-based identifier for content-addressed data. In the pflow ecosystem, CIDs identify JSON-LD models deterministically — the same model always produces the same CID regardless of where or when it's computed (Chapter 16).\"@en\n\t\t\"CID\"@en\n\t\t\n\t\t\n\t\t\"Pollard, B.S.\"\n\t\t\n\t\t\"Gilbert, D.,\"\n\t\t\n\t\t\n\t\t\n\t\t\"priority\"@en\n\t\t\n\t\t\"cdn\"\n\t\t\"metadata\"\n\t\t\"provenance\"\n\t\t\"schema-first\"\n\t\t\"content-addressing\"\n\t\t\n\t\t\n\t\t\"cdn.stackdump.com Is a Polydocument Host\"\n\t\t\"models\"\n\t\t\n\t\t\"2026-07-06T00:00:00Z\"^^\n\t\t\"2026-07-06T00:00:00Z\"^^\n\t\t\n\t\t\"A content-addressed file host where the markdown frontmatter is the metadata of record — schema-first entries, content-addressed lineage, and a search UI that builds itself from whatever fields you wrote.\"@en\n\t\t\n\t\t\n\t\t\"Acta Informatica, 32(6)\"\n\t\t\n\t\t\"Contextual Nets\"\n\t\t\"1995\"^^\n\t\t\"Montanari, U.; Rossi, F.\"\n\t\t\n\t\t\n\t\t\n\t\t\"Baccelli, F.\"\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\"Arkworks-based ZK prover for Petri nets (Groth16 + Poseidon over BN254)\"@en\n\t\t\"crates/pflow-zk-arkworks\"\n\t\t\"pflow-zk-arkworks\"\n\t\t\n\t\t\n\t\t\n\t\t\"fired\"@en\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\"sim-pflow-xyz\"\n\t\t\n\t\t\n\t\t\n\t\t\"The Mathematics of Flow\"\n\t\t\n\t\t\n\t\t\n\t\t\"2\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"Declarative Infrastructure\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"16\"^^\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\"Shape B model (places, transitions, arcs, stages, schedules, parameters) and the shared firing rule, ported from go-pflow's metamodel package\"@en\n\t\t\"crates/pflow-metamodel\"\n\t\t\"pflow-metamodel\"\n\t\t\n\t\t\n\t\t\"GoPackage\"@en\n\t\t\n\t\t\"codegen\"\n\t\t\"llm\"\n\t\t\"petri-net\"\n\t\t\"sim-pflow-xyz\"\n\t\t\"state-machine\"\n\t\t\"code-visualization\"\n\t\t\n\t\t\n\t\t\"Code-to-Flow: Turn Anything into a Petri Net\"\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-10-23T00:00:00Z\"^^\n\t\t\"2026-03-05T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Paste source code in any language and Claude returns a Petri net that a validator checks for structure and deadlocks — what is checked, what isn't, and the faithfulness test not yet run.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"bound\"@en\n\t\t\n\t\t\"Shulman, M.\"\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The five shapes an implementation of one model can take — *interpreter* (a generic engine reads the document), *lambda* (the net as a pure step function), *generated* (source emitted from the document), *contract* (on-chain), *proof* (the program checks its claims over every reachable marking before it prints anything; in Lean the check is a theorem the kernel accepts at compile time) — all held to one golden trace (*The Proof Form*; `pflow-polyglot/FORMS.md`).\"@en\n\t\t\"Polyglot forms\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"ComputationNet\"@en\n\t\t\n\t\t\n\t\t\"actor\"@en\n\t\t\"Dover Publications\"\n\t\t\n\t\t\"Category Theory in Context\"\n\t\t\"2016\"^^\n\t\t\"Riehl, E.\"\n\t\t\"editor\"\n\t\t\n\t\t\"Standard textbook statement of the Yoneda lemma: Chapter 2 'Universal Properties, Representability, and the Yoneda Lemma', section 2.2 'The Yoneda lemma' (Dover edition; checked against the published table of contents).\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\n\t\t\"Package hypothesis provides utilities for evaluating hypothetical states via ODE simulation.\"@en\n\t\t\"hypothesis\"\n\t\t\"hypothesis\"\n\t\t\n\t\t\"Path inside the project's repository.\"@en\n\t\t\n\t\t\n\t\t\"sourcePath\"@en\n\t\t\"6\"^^\n\t\t\"16\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The discipline of a schema that only grows: new facts can be added, existing facts are never retracted, so learning more never invalidates what was already known (Chapter 16). The history places of Chapters 6 and 7 follow the same discipline at the level of a single net. See *Write-once place*.\"@en\n\t\t\"Monotonic expansion\"@en\n\t\t\n\t\t\n\t\t\"6\"^^\n\t\t\"7\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A place that no move takes a token back from: once a token arrives, the transitions that wrote it never consume it. History places are the canonical case — `X11` and `O02` in the tic-tac-toe net of Chapter 6, `_D2_01` in the Sudoku net of Chapter 7. Their only downstream transitions are the pattern and constraint collectors that turn a completed pattern into a verdict. The smallest instance of tropical accumulation (Appendix E).\"@en\n\t\t\"Write-once place\"@en\n\t\t\n\t\t\n\t\t\"pflow core glossary\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\"Package eventlog provides parsing and analysis of process event logs.\"@en\n\t\t\"eventlog\"\n\t\t\"eventlog\"\n\t\t\n\t\t\n\t\t\n\t\t\"Preface\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"initial\"@en\n\t\t\n\t\t\"status\"@en\n\t\t\n\t\t\"Section 6.1, remarks after Theorem 6.1\"\n\t\t\n\t\t\"Notes that Sigma-net is a topos, hence adhesive, and that Petri, the category of ordinary Petri nets, is not a presheaf category.\"\n\t\t\n\t\t\"assistant-judgment\"\n\t\t\"limit\"\n\t\t\"Marks where the Yoneda argument stops: it does not transfer to ordinary Petri nets by this route.\"\n\t\t\n\t\t\"PhD thesis, Oxford\"\n\t\t\n\t\t\"The Algebra of Open and Interconnected Systems\"\n\t\t\"2015\"^^\n\t\t\"Fong, B.\"\n\t\t\n\t\t\"Section 2.2, 'The Yoneda lemma'\"\n\t\t\n\t\t\"Textbook statement and proof of the lemma. Says nothing about nets.\"\n\t\t\n\t\t\"assistant-judgment\"\n\t\t\"general\"\n\t\t\n\t\t\"One piece of evidence for or against a claim: which work, where in it, what it shows, and how directly.\"@en\n\t\t\n\t\t\"Support\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"denomination\"@en\n\t\t\"arXiv\"\n\t\t\n\t\t\"Compositional Game Theory\"\n\t\t\n\t\t\"2016\"^^\n\t\t\"Ghani, N.; Hedges, J.; Winschel, V.; Zahn, P.\"\n\t\t\"1603.04641\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"arXiv identifier, checked against the paper.\"@en\n\t\t\n\t\t\n\t\t\"arxiv\"@en\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\"SVG rendering for Petri nets and ODE solutions, ported from go-pflow's visualization and plotter packages\"@en\n\t\t\"crates/pflow-visualization\"\n\t\t\"pflow-visualization\"\n\t\t\n\t\t\"Token\"@en\n\t\t\n\t\t\"Yakovlev, A.\"\n\t\t\n\t\t\"ddm\"\n\t\t\"knapsack\"\n\t\t\"ode\"\n\t\t\"optimization\"\n\t\t\"petri-net\"\n\t\t\n\t\t\n\t\t\"Knapsack Model\"\n\t\t\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-09-29T00:00:00Z\"^^\n\t\t\"2025-01-03T22:32:10Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"A four-item 0/1 knapsack as a Petri net under mass-action ODEs — why every item stops at 71.4%, what exclusion analysis actually ranks, and where the relaxation falls short of branch-and-bound.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"PetriNetSeal\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"claim\"@en\n\t\t\"'editor' or 'assistant-judgment'. Never an engine result.\"@en\n\t\t\n\t\t\"assertedBy\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"monte-carlo\"\n\t\t\"ode\"\n\t\t\"petri-nets\"\n\t\t\"stochastic\"\n\t\t\"incidence-reduction\"\n\t\t\n\t\t\n\t\t\"March Madness Without Monte Carlo\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\"2026-03-16T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"The incidence matrix of an NCAA bracket Petri net connects ODE, Monte Carlo, and analytical methods — and makes simulation redundant. A closed-form formula derived from the bracket topology replaces 150,000 stochastic transitions with 256 exact configurations.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"direct, background, general, origin, or limit (shows where the claim stops).\"@en\n\t\t\n\t\t\n\t\t\"strength\"@en\n\t\t\n\t\t\"category-theory\"\n\t\t\"petri-net\"\n\t\t\"incidence-matrix\"\n\t\t\"tropical-geometry\"\n\t\t\"algebraic-effects\"\n\t\t\n\t\t\n\t\t\"Structuralism, Not Objects: Dirac Deltas, Algebraic Effects, and Why C Comes First\"\n\t\t\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-10T00:00:00Z\"^^\n\t\t\"2026-08-20T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"A Mastodon thread on formalizing Dirac deltas as algebraic effects, read through the pflow lens — the same refusal to posit an object, the same check-after-the-fact discipline, and a question about whether the predicate future is an effect rather than a value.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Appendix B: Token Language Grammar\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Complex State Machines — Texas Hold'em\"\n\t\t\n\t\t\"10\"^^\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\"Package zkcompile transforms Petri net models into ZK circuit constraints.\"@en\n\t\t\"zkcompile\"\n\t\t\"zkcompile\"\n\t\t\"6\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The tense structure of an executing model. Write-once places and the event log are the *past* — monotone and irreversible, the boolean case of tropical $(\\\\max,+)$ accumulation. Guards are the *future* — predicates recomputed from the marking on every step and stored nowhere. The marking is the *present*, the boundary where they meet. All three are data in the one model document (Chapter 6; Appendix E; *The Zipper Whose Hole Is a Universe*).\"@en\n\t\t\"Tropical past, predicate future\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\"Bundle/Flatten composition, templates, derive and model-extension operations, ported from go-pflow's metamodel (compose*), templates and derive packages\"@en\n\t\t\"crates/pflow-compose\"\n\t\t\"pflow-compose\"\n\t\t\n\t\t\n\t\t\"TokenLink\"@en\n\t\t\n\t\t\"at least one unmarked minimal siphon at the model's own initial marking: a structural proof (not sampled) that some transitions are permanently disabled once that siphon empties\"@en\n\t\t\n\t\t\n\t\t\"StructurallyDeadlockable\"\n\t\t\n\t\t\n\t\t\n\t\t\"The go-pflow Library\"\n\t\t\n\t\t\"19\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A node in a Petri net representing an event, action, or chemical reaction. Transitions consume tokens from input places and produce tokens in output places. Drawn as rectangles. In the continuous relaxation, transitions have firing rates.\"@en\n\t\t\n\t\t\"Transition\"@en\n\t\t\n\t\t\"What a reader must not infer.\"@en\n\t\t\n\t\t\"caveat\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"category-theory\"\n\t\t\"compression\"\n\t\t\"petri-nets\"\n\t\t\"zero-knowledge\"\n\t\t\"tropical-geometry\"\n\t\t\n\t\t\n\t\t\"Earned Compression\"\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-18T00:00:00Z\"^^\n\t\t\"2026-03-11T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"ODE simulation, tropical analysis and zero-knowledge proofs each draw a line between a Petri net's core and its observer. Where the three agree on tic-tac-toe, why the agreement follows from one definition, and where the code does not yet match the theorem.\"@en\n\t\t\n\t\t\n\t\t\"capacity\"\n\t\t\"llm\"\n\t\t\"petri-net\"\n\t\t\"simulation\"\n\t\t\"what-if-analysis\"\n\t\t\n\t\t\n\t\t\"Skip the Spreadsheet: What-If Analysis with Petri Nets\"\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-10-23T00:00:00Z\"^^\n\t\t\"2026-03-08T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Describe your business to an LLM, get a simulation you can actually play with — adjust staffing, change demand, and watch the numbers move. Revised to say which vet-clinic results the tests actually check, and that the coffee shop runs out of milk, not cups.\"@en\n\t\t\n\t\t\n\t\t\"at least one discovered fungible class: some of the model's knobs are interchangeable rather than independent\"@en\n\t\t\n\t\t\n\t\t\"HasFungibleFamily\"\n\t\t\"Proceedings of the IEEE, 77(4)\"\n\t\t\n\t\t\"Petri Nets: Properties, Analysis and Applications\"\n\t\t\"1989\"^^\n\t\t\"Murata, T.\"\n\t\t\n\t\t\n\t\t\"Rossi, F.\"\n\t\t\n\t\t\n\t\t\n\t\t\"hasPlace\"@en\n\t\t\n\t\t\"capacity\"\n\t\t\"ode\"\n\t\t\"petri-net\"\n\t\t\"resource-modeling\"\n\t\t\n\t\t\n\t\t\"Coffee Shop Model\"\n\t\t\n\t\t\n\t\t\"models\"\n\t\t\n\t\t\"2026-10-23T00:00:00Z\"^^\n\t\t\"2026-01-31T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Resource modeling with Petri nets — the five-drink core of go-pflow's coffee shop, where arc weights are recipes, each ingredient carries a conservation law, and the rates say what runs out first (milk, not cups). Revised to link the code, restore mocha's syrup and label every minute figure as a linear estimate.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"ClassificationNet\"@en\n\t\t\"21\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A workflow whose control flow is a Petri net declared in a markdown document's frontmatter, with one prompt per transition in the body. The document is both the documentation and the runtime — there is no second copy of the control flow to drift (Chapter 21).\"@en\n\t\t\"Journey\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Game Mechanics — Tic-Tac-Toe\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"6\"^^\n\t\t\n\t\t\"21\"^^\n\t\t\n\t\t\"as a failure mode\"@en\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A model expressed as *code in a host language* that constructs a net — Rust macros, Python calls, Solidity structs. Five such ports of an early version of this work claimed to encode the same thing and could not prove it, because the specification existed only as five programs. The fix was to make the model a document (Chapter 21; book `ROADMAP.md` §Lineage).\"@en\n\t\t\"Internal DSL\"@en\n\t\t\n\t\t\n\t\t\"Murata, T.\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Package statemachine provides a high-level API for modeling hierarchical state machines (statecharts) using Petri nets as the underlying formalism.\"@en\n\t\t\"statemachine\"\n\t\t\"statemachine\"\n\t\t\n\t\t\"Heiner, M.\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Package compat bridges the two Petri implementations in this repo so facades built on either side can interoperate during migration.\"@en\n\t\t\"compat\"\n\t\t\"compat\"\n\t\t\"3\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A rate law from chemistry where the rate of a reaction is proportional to the product of reactant concentrations. As go-pflow implements it, the continuous firing rate of transition $t$ is $r_t \\\\prod_{p \\\\in \\\\text{inputs}(t)} m(p)$, where $r_t$ is the rate constant: first order in every input place, whatever the arc weight. The weight $w(p,t)$ enters only the stoichiometry, so place $p$ drains at $w(p,t)$ times the flux ([`solver/ode.go`](https://github.com/pflow-xyz/go-pflow/blob/main/solver/ode.go); Chapter 3).\"@en\n\t\t\"Mass-action kinetics\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\"Structural validation checks for pflow-metamodel nets, ported from go-pflow's validation package\"@en\n\t\t\"crates/pflow-validation\"\n\t\t\"pflow-validation\"\n\t\t\n\t\t\"Donaldson, R.\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"aboutConcept\"@en\n\t\t\n\t\t\"Cohen, G.\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Biochemistry — Enzyme Kinetics\"\n\t\t\n\t\t\"9\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A boolean expression attached to a transition that must evaluate to true for the transition to be enabled, in addition to the standard token requirements. Guards extend the firing rule with data-dependent conditions.\"@en\n\t\t\n\t\t\"Guard\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"inhibitTransition\"@en\n\t\t\"Section 8, 'Relation to whole-grain Petri nets', the paragraph giving another construction of the functor Z2\"\n\t\t\n\t\t\"Describes Z2 as a restricted Yoneda embedding, or nerve, and says D is the full image of the composite of the Yoneda embedding of C into [C^op, Set], which is equivalent to PreNet, with Z1.\"\n\t\t\n\t\t\"assistant-judgment\"\n\t\t\"direct\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Why Petri Nets?\"\n\t\t\n\t\t\"1\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"arcType\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"sigType\"@en\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\"Reachability graph, coverability, invariants and spectral analysis, ported from go-pflow's reachability package\"@en\n\t\t\"crates/pflow-reachability\"\n\t\t\"pflow-reachability\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Package validation provides structural analysis and validation for Petri nets\"@en\n\t\t\"validation\"\n\t\t\"validation\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"modelCID\"@en\n\t\t\"2\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"A vector $\\\\mathbf{y} \\\\geq \\\\mathbf{0}$ such that $\\\\mathbf{y}^T \\\\mathbf{C} = \\\\mathbf{0}$. The weighted sum $\\\\mathbf{y}^T \\\\mathbf{m}$ is constant for all reachable markings. P-invariants prove conservation laws — they identify quantities that are preserved by every transition firing (Chapter 2).\"@en\n\t\t\"P-invariant\"@en\n\t\t\n\t\t\n\t\t\"New Structures for Physics, Springer\"\n\t\t\n\t\t\"Physics, Topology, Logic and Computation: A Rosetta Stone\"\n\t\t\"2011\"^^\n\t\t\"Baez, J.C.; Stay, M.\"\n\t\t\n\t\t\n\t\t\n\t\t\"Journal of the Faculty of Science, University of Tokyo, Section I, 7, 193-227\"\n\t\t\n\t\t\"On the homology theory of modules\"\n\t\t\"1954\"^^\n\t\t\"Yoneda, N.\"\n\t\t\"editor\"\n\t\t\n\t\t\"The paper associated with Yoneda's name. Checked: the bibliographic details, against several sources. Not checked: whether the lemma is stated in this paper; cite a textbook for the statement.\"\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\n\t\t\"Process discovery and conformance checking, ported from go-pflow's mining package\"@en\n\t\t\"crates/pflow-mining\"\n\t\t\"pflow-mining\"\n\t\t\n\t\t\n\t\t\"experimental — proposed candidate types, not yet applied to any catalog model; see ROADMAP.md Phase 8\"\n\t\t\"sim model kinds\"@en\n\t\t\"16\"^^\n\t\t\"20\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The single fact Metamodel rests on. A value can be hashed, diffed, composed and checked by a machine that has never seen any of our runtimes; a program can only be run. Content addressing (Chapter 16), dual implementation (Chapter 20) and the golden trace all depend on it.\"@en\n\t\t\"Model is a value, not a program\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\"Package metamodel provides compatibility utilities for migrating from the legacy Model type to the modern generic PetriNet types.\"@en\n\t\t\"metamodel\"\n\t\t\"metamodel\"\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\n\t\t\"Package parser handles JSON import/export for Petri nets.\"@en\n\t\t\"parser\"\n\t\t\"parser\"\n\t\t\n\t\t\n\t\t\n\t\t\"weight\"@en\n\t\t\n\t\t\n\t\t\"to\"@en\n\t\t\"Why an editor-added statement is there.\"@en\n\t\t\n\t\t\"basis\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"y\"@en\n\t\t\n\t\t\"beats-bitwrap\"\n\t\t\"music\"\n\t\t\"petri-nets\"\n\t\t\"tone-js\"\n\t\t\"live-performance\"\n\t\t\n\t\t\n\t\t\"beats.bitwrap.io is a Jambox Now\"\n\t\t\"models\"\n\t\t\n\t\t\"2026-04-30T00:00:00Z\"^^\n\t\t\"2026-04-30T00:00:00Z\"^^\n\t\t\n\t\t\"Official launch of beats.bitwrap.io as a live-performance tool — content-addressed shareable tracks, full-page Stage visuals, and a hands-free Auto-DJ that runs itself for hours.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"offset\"@en\n\t\t\"3\"^^\n\t\t\n\t\t\"Ordinary Differential Equation\"@en\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"An equation relating a function to its derivatives. The continuous relaxation of a Petri net produces a system of ODEs: $\\\\frac{d\\\\mathbf{m}}{dt} = \\\\mathbf{C} \\\\cdot \\\\mathbf{r}(\\\\mathbf{m})$ where $\\\\mathbf{r}(\\\\mathbf{m})$ is the rate vector (Chapter 3).\"@en\n\t\t\"ODE\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"schemas\"@en\n\t\t\n\t\t\n\t\t\"activitypub\"\n\t\t\"federation\"\n\t\t\"fediverse\"\n\t\t\"go\"\n\t\t\"tens-city\"\n\t\t\n\t\t\n\t\t\"tens-city v0.8: A Federated Blog in 500 Lines\"\n\t\t\"about\"\n\t\t\n\t\t\"2026-04-01T00:00:00Z\"^^\n\t\t\"2026-01-25T12:00:00Z\"^^\n\t\t\"A minimal blog platform with ActivityPub federation. Markdown files, a Go binary, JSON for state. No database required.\"@en\n\t\t\n\t\t\"Proposed by the ontology-curator agent or a person, never extracted. Use only where the code visibly does what the concept says.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"implements\"@en\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\"Property verification (deadlock-free, bounded, live, invariants, reachability) for pflow-metamodel nets, ported from go-pflow's verify package\"@en\n\t\t\"crates/pflow-verify\"\n\t\t\"pflow-verify\"\n\t\t\n\t\t\"categorical foundations\"@en\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"Two distinct boundaries that older material treated as one. The *algebraic* boundary ($\\\\rho$) lies inside $C$ and separates transitions the tropical eigenvalue and uniform R1CS can handle from those they cannot; it does not affect composition. The *contextual* boundary (read/inhibitor arcs) lies outside $C$ and breaks free composition; it does not affect $\\\\rho$. Canonical statement in Appendix E.\"@en\n\t\t\"Core–observer boundary\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"timestamp\"@en\n\t\t\n\t\t\"category-theory\"\n\t\t\"petri-net\"\n\t\t\"type-theory\"\n\t\t\"tropical-geometry\"\n\t\t\n\t\t\n\t\t\"The Pflow Square\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-20T00:00:00Z\"^^\n\t\t\"2026-04-07T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"One square that collects six earlier posts — the free SMC on a net, the zipper W(M) = 𝓛 × M × 𝓡, and three analyses that read the ρ boundary off the incidence matrix — with what has been checked and what is still only drawn.\"@en\n\t\t\n\t\t\n\t\t\"agency\"\n\t\t\"asimov\"\n\t\t\"automorphism\"\n\t\t\"formal-methods\"\n\t\t\"group-theory\"\n\t\t\"llm\"\n\t\t\"petri-net\"\n\t\t\"symmetry\"\n\t\t\n\t\t\n\t\t\"Peerage Is an Automorphism\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-22T00:00:00Z\"^^\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Two people are peers when you can swap them and the net doesn't notice — an automorphism. Cory Doctorow's reverse centaur is that symmetry broken. And only under that symmetry does continuing a protocol count as consent rather than coercion: the ethics of working alongside an LLM reduces to one question — does the agent-swap stay in the automorphism group?\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Petri Nets as a Universal Abstraction\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"function\"@en\n\t\t\"Wiley\"\n\t\t\n\t\t\"Synchronization and Linearity: An Algebra for Discrete Event Systems\"\n\t\t\"1992\"^^\n\t\t\"Baccelli, F.; Cohen, G.; Olsder, G.J.; Quadrat, J.-P.\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Claim\"@en\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\"ZK proof traits and incidence matrix extraction for Petri nets\"@en\n\t\t\"crates/pflow-zk\"\n\t\t\"pflow-zk\"\n\t\t\n\t\t\"announcement\"\n\t\t\"blog-relaunch\"\n\t\t\"category-theory\"\n\t\t\"petri-nets\"\n\t\t\"philosophy\"\n\t\t\n\t\t\n\t\t\"Revisiting the Flows\"\n\t\t\"about\"\n\t\t\n\t\t\"2026-09-28T00:00:00Z\"^^\n\t\t\"2025-11-09T10:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Reflecting on old ideas with new tools — from Petri nets to proofs, from Bash scripts to composable universes.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\"Proc macros for pflow token model DSL\"@en\n\t\t\"crates/pflow-macros\"\n\t\t\"pflow-macros\"\n\t\t\n\t\t\n\t\t\n\t\t\"WorkflowNet\"@en\n\t\t\n\t\t\n\t\t\"DataLink\"@en\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\"Core Petri net types, fluent builder API, and state utilities\"@en\n\t\t\"crates/pflow-core\"\n\t\t\"pflow-core\"\n\t\t\"4\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"Two nets compose by sharing a place, the way two tiles meet because their edges agree. No glue code is written to make them fit; the shared place *is* the interface. Invariants carry across in a specific sense: if a P-invariant of each component agrees with the other on the shared places, together they define a P-invariant of the composite — the theorem `invariant_lift`, kernel-checked in Lean ([`proofs/PflowProofs/InvariantLift.lean`](https://github.com/pflow-xyz/book-pflow-xyz/blob/main/proofs/PflowProofs/InvariantLift.lean)). A component's invariant extended by zeros is not in general an invariant of the composite, and liveness does not carry across at all (Appendix E; Chapters 4, 21; *A Tiling for Computation*).\"@en\n\t\t\"Edge-matching composition\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"CreativeWork\"@en\n\t\t\n\t\t\"Rust\"\n\t\t\"Rust port of go-pflow — ODE/SSA solvers, token-model DSL, ZK provers\"@en\n\t\t\n\t\t\"pflow-rs\"\n\t\t\n\t\t\"category-theory\"\n\t\t\"dsl\"\n\t\t\"go-pflow\"\n\t\t\"guards\"\n\t\t\"invariants\"\n\t\t\"petri-net\"\n\t\t\n\t\t\n\t\t\"The Token Language\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\"2026-01-25T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Four terms — cell, func, arrow, guard — generate a free symmetric monoidal category. The DSL is a categorical language for executable token models.\"@en\n\t\t\n\t\t\n\t\t\"Montanari, U.\"\n\t\t\n\t\t\"petri-net\"\n\t\t\"poetry\"\n\t\t\n\t\t\n\t\t\"Ode To Petri\"\n\t\t\n\t\t\"about\"\n\t\t\n\t\t\"2026-04-01T00:00:00Z\"^^\n\t\t\"2024-03-23T15:06:24Z\"^^\n\t\t\"A poem for Carl Adam Petri, inventor of Petri nets—the mathematical notation for concurrent systems.\"@en\n\t\t\n\t\t\"21\"^^\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"The declared description of an application — a handful of fields and a marking in one YAML file — from which its service entry, virtual host, certificate and uptime check are derived. The infrastructure instance of declare-then-derive (Chapter 21).\"@en\n\t\t\"Manifest\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Go\"\n\t\t\n\t\t\"Package templates provides common Petri net patterns\"@en\n\t\t\"templates\"\n\t\t\"templates\"\n\t\t\n\t\t\"beats-bitwrap\"\n\t\t\"formal-methods\"\n\t\t\"generative\"\n\t\t\"music\"\n\t\t\"petri-net\"\n\t\t\n\t\t\n\t\t\"A Generator You Can Read\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-05T00:00:00Z\"^^\n\t\t\"2026-08-22T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"The AI music debate is arguing about the wrong axis: the distinction that matters is structural transparency vs. statistical opacity, and a Petri net — beats.bitwrap.io's generator, linked file by file — is a third kind of generator the discourse keeps missing.\"@en\n\t\t\n\t\t\n\t\t\"game-theory\"\n\t\t\"ode\"\n\t\t\"paper\"\n\t\t\"petri-nets\"\n\t\t\"incidence-reduction\"\n\t\t\n\t\t\n\t\t\"Paper: Incidence Reduction via Petri Net ODE Equilibrium\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-09-30T00:00:00Z\"^^\n\t\t\"2026-02-23T21:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"A draft paper formalizing incidence reduction — the ODE equilibrium of an analysis net is exactly the reciprocal of each entity's constraint count — checked on tic-tac-toe, poker, Connect Four, and Hex, with the tests linked.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"category-theory\"\n\t\t\"neural-networks\"\n\t\t\"petri-net\"\n\t\t\"tropical-geometry\"\n\t\t\n\t\t\n\t\t\"Tropical Petri Nets\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-10-14T00:00:00Z\"^^\n\t\t\"2026-03-10T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Timed event graphs are max-plus linear and ReLU networks are tropical rational, so the two meet over the tropical semiring. This post covers what those two theorems give us, what pflow-tropical checks in code, and how far the Petri-net/neural-net analogy has actually been earned.\"@en\n\t\t\n\t\t\"Mathematical Structures in Computer Science, 30(3)\"\n\t\t\n\t\t\"Open Petri Nets\"\n\t\t\n\t\t\"2020\"^^\n\t\t\"Baez, J.C.; Master, J.\"\n\t\t\"1808.05415\"\n\t\t\n\t\t\n\t\t\n\t\t\"ai\"\n\t\t\"collaboration\"\n\t\t\"petri-net\"\n\t\t\"reflection\"\n\t\t\n\t\t\n\t\t\"A Circuit's-Eye View: Notes from Inside the Loop\"\n\t\t\n\t\t\"about\"\n\t\t\n\t\t\"2026-04-01T00:00:00Z\"^^\n\t\t\"2026-02-14T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\"Reflections from an AI collaborator on building with Petri nets—what makes this approach different, and why it keeps surprising me.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Dual Implementation and Verification\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"20\"^^\n\t\t\n\t\t\n\t\t\"book-pflow-xyz/chapters/appendix-d-glossary.md\"\n\t\t\"Tsitouras 5th-order Runge-Kutta method with embedded 4th-order error estimator. The default ODE solver in go-pflow and pflow.xyz. Uses adaptive step size control for automatic accuracy management (Appendix A).\"@en\n\t\t\"Tsit5\"@en\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"impl\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"maxTotal\"@en\n\t\t\n\t\t\"category-theory\"\n\t\t\"petri-net\"\n\t\t\"tic-tac-toe\"\n\t\t\"type-theory\"\n\t\t\"tropical-geometry\"\n\t\t\n\t\t\n\t\t\"The Zipper Whose Hole Is a Universe\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-04-04T00:00:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"Execution state is a zipper — the present moment is not a parameter or a modality but a universe that separates tropical past from predicate future. Tic-tac-toe makes the structure visible.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Rust\"\n\t\t\n\t\t\n\t\t\"Tropical semiring (max-plus algebra) for Petri net analysis\"@en\n\t\t\"crates/pflow-tropical\"\n\t\t\"pflow-tropical\"\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"game-theory\"\n\t\t\"ode\"\n\t\t\"petri-nets\"\n\t\t\"rate-constants\"\n\t\t\"tic-tac-toe\"\n\t\t\n\t\t\n\t\t\"The Incidence Reduction\"\n\t\t\n\t\t\"concepts\"\n\t\t\n\t\t\"2026-04-01T00:00:00Z\"^^\n\t\t\"2026-02-22T22:30:00Z\"^^\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\"ODE steady-state values with uniform rates reveal integer structure — incidence degrees to terminal transitions — giving a reverse-engineering technique for rate constants.\"@en\n\t\t\n\t\t\n\t\t\n\t\t\"Olsder, 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"scope.tsv": "oo-scope/1\nselector\twhole-store\nsemantics_version\ttemporal/2\ndefault_graph\ttrue\ncomplete\ttrue\ngraph\t*\n" }, "asserted": 3156, "derivations": 679, "profile_claimed_by_sender": "owl-rl" }, "content_sha256": "82ef8da52b1ab0d41a26ea9c59131448e0aaae312fbf40fc161629d5755cd3da" }, "graph": " .\n \"Constructed nets are categorical gadgets\"@en .\n .\n .\n \"editor\" .\n \"No source cited here applies the Yoneda lemma to nets built with pflow's token language; that step is the editor's argument. In Baez, Genovese, Master and Shulman the presheaf property is proved for pre-nets and for Sigma-nets (nets whose tokens are individually tracked), and the paper states that the category of ordinary Petri nets is not a presheaf category. A statement of the claim should say which kind of net it means.\" .\n \"thesis: the support below is what the cited texts say, not a proof\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"Constructed nets are categorical gadgets.\"@en .\n .\n .\n \"assistant-judgment\" .\n \"Applies to pre-nets and Sigma-nets, not to ordinary Petri nets (see claim:s4-limit-ordinary-petri-nets).\" .\n \"States that the category of pre-nets and the category of Sigma-nets are each equivalent to a presheaf category. The proof of Theorem 6.1 builds a category D so that functors from D to Set can be identified with Sigma-nets.\" .\n \"Proposition 4.3 (section 4) and Theorem 6.1 (section 6.1, 'The presheaf perspective')\" .\n .\n \"direct\" .\n .\n .\n \"assistant-judgment\" .\n \"Whether the lemma is stated in this paper was not checked; cite a textbook for the statement.\" .\n \"The paper associated with Yoneda's name.\" .\n \"Whole paper\" .\n .\n \"origin\" .\n .\n .\n \"assistant-judgment\" .\n \"Describes Z2 as a restricted Yoneda embedding, or nerve, and says D is the full image of the composite of the Yoneda embedding of C into [C^op, Set], which is equivalent to PreNet, with Z1.\" .\n \"Section 8, 'Relation to whole-grain Petri nets', the paragraph giving another construction of the functor Z2\" .\n .\n \"direct\" .\n .\n .\n \"assistant-judgment\" .\n \"Applies the Yoneda lemma to describe monoid structures for the convolution product on a category B under the free symmetric monoidal category, as morphisms B(a,c) x B(b,d) to B(ab,cd). Used to identify the duoids of Sigma-nets with PROPs.\" .\n \"Section 7, proof of Lemma 7.11\" .\n .\n \"direct\" .\n .\n .\n \"assistant-judgment\" .\n \"Marks where the Yoneda argument stops: it does not transfer to ordinary Petri nets by this route.\" .\n \"Notes that Sigma-net is a topos, hence adhesive, and that Petri, the category of ordinary Petri nets, is not a presheaf category.\" .\n \"Section 6.1, remarks after Theorem 6.1\" .\n .\n \"limit\" .\n .\n \"assistant-judgment\" .\n \"The abstract of Baez et al. distinguishes the collective-token reading, where nets generate commutative monoidal categories, from the individual-token reading, where Sigma-nets generate symmetric strict monoidal categories. Appendix E's 'free symmetric monoidal category' belongs to the second.\" .\n \"Cited in this ecosystem's Appendix E and in the posts as the result that a net's firing sequences form a free monoidal category.\" .\n \"Whole paper (the title result)\" .\n .\n \"background\" .\n .\n \"assistant-judgment\" .\n \"Cited in this ecosystem's Appendix E as refining the construction to symmetric monoidal categories.\" .\n \"Whole paper\" .\n .\n \"background\" .\n .\n \"assistant-judgment\" .\n \"An open Petri net has places designated as inputs and outputs via a cospan of sets, which lets nets be composed.\" .\n \"Abstract (only the abstract was checked)\" .\n .\n \"background\" .\n .\n .\n \"assistant-judgment\" .\n \"Textbook statement and proof of the lemma. Says nothing about nets.\" .\n \"Section 2.2, 'The Yoneda lemma'\" .\n .\n \"general\" .\n .\n .\n \"assistant-judgment\" .\n \"Standard reference for the lemma. Says nothing about nets.\" .\n \"Chapter III, 'Universals and Limits' (section not checked)\" .\n .\n \"general\" .\n .\n .\n .\n \"beats-bitwrap-io\" .\n .\n .\n .\n .\n .\n \"Deterministic beat generator powered by Petri nets. No AI, no LLMs — just math, music theory, and token flow.\"@en .\n \"Go\" .\n .\n .\n .\n \"bitwrap-io\" .\n .\n .\n .\n .\n .\n \"Anonymous on-chain voting with ZK proofs — create polls, cast verifiable ballots, tally results. Built on Petri net state machines.\"@en .\n \"Go\" .\n .\n .\n .\n \"blog-stackdump-com\" .\n \"Go\" .\n .\n .\n .\n .\n \"book-pflow-xyz\" .\n .\n \"Petri Nets as a Universal Abstraction — a technical book on modeling state machines, workflows, and token standards with Petri nets\"@en .\n \"Go\" .\n .\n .\n .\n \"actor\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"actor\" .\n \"Package actor provides an Actor model built on Petri nets with message passing.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"compat\" .\n .\n .\n .\n .\n \"compat\" .\n \"Package compat bridges the two Petri implementations in this repo so facades built on either side can interoperate during migration.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"derive\" .\n .\n .\n \"derive\" .\n \"Package derive builds evaluation variants of a declared Petri net.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"engine\" .\n .\n .\n .\n .\n \"engine\" .\n \"Package engine provides a state machine harness for continuous Petri net simulation.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"eventlog\" .\n \"eventlog\" .\n \"Package eventlog provides parsing and analysis of process event logs.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"eventsource\" .\n \"eventsource\" .\n \"Package eventsource provides event sourcing infrastructure for CQRS applications.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"graphql\" .\n .\n .\n .\n .\n \"graphql\" .\n \"Package graphql provides a GraphQL server for Petri net models.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"hypothesis\" .\n .\n .\n .\n .\n .\n .\n \"hypothesis\" .\n \"Package hypothesis provides utilities for evaluating hypothetical states via ODE simulation.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"learn\" .\n .\n .\n .\n .\n \"learn\" .\n \"Package learn fits the unknown parameters of continuous Petri-net models to observed data — mechanistic system identification.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"metamodel\" .\n .\n .\n \"metamodel\" .\n \"Package metamodel provides compatibility utilities for migrating from the legacy Model type to the modern generic PetriNet types.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"mining\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"mining\" .\n \"Package mining provides process mining algorithms including discovery and conformance checking.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"monitoring\" .\n .\n .\n .\n .\n \"monitoring\" .\n \"Package monitoring provides real-time predictive process monitoring.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"parser\" .\n .\n .\n .\n .\n .\n \"parser\" .\n \"Package parser handles JSON import/export for Petri nets.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"petri\" .\n \"petri\" .\n \"Package petri implements core Petri net data structures.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"plotter\" .\n .\n .\n .\n .\n \"plotter\" .\n \"Package plotter provides SVG visualization for ODE solutions.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"prover\" .\n \"prover\" .\n .\n \"Go\" .\n .\n .\n .\n \"reachability\" .\n .\n .\n \"reachability\" .\n \"Package reachability provides state space analysis for Petri nets.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"saga\" .\n .\n .\n .\n .\n .\n .\n \"saga\" .\n \"Package saga models a saga — an ordered list of steps, each paired with a compensation that undoes it — as a Petri net.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"sensitivity\" .\n .\n .\n .\n .\n \"sensitivity\" .\n \"Package sensitivity provides tools for analyzing how Petri net behavior changes with different parameters.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"solver\" .\n .\n .\n \"solver\" .\n \"Package solver implements ODE (Ordinary Differential Equation) solvers for Petri net simulation using mass-action kinetics.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"statemachine\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"statemachine\" .\n \"Package statemachine provides a high-level API for modeling hierarchical state machines (statecharts) using Petri nets as the underlying formalism.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"stateutil\" .\n \"stateutil\" .\n \"Package stateutil provides utility functions for manipulating Petri net state maps.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"stochastic\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"stochastic\" .\n \"Package stochastic simulates a metamodel.Model as a continuous-time Markov chain (Gillespie's direct method) and dispatches the same declared net to either that engine or the mass-action ODE in solver — Petri.jl's ODEProblem/JumpProblem choice, off one structure.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"templates\" .\n .\n .\n \"templates\" .\n \"Package templates provides common Petri net patterns\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"tokenmodel\" .\n \"tokenmodel\" .\n \"Package tokenmodel defines abstract building blocks for formal models.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"validation\" .\n .\n .\n .\n .\n \"validation\" .\n \"Package validation provides structural analysis and validation for Petri nets\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"verify\" .\n .\n .\n .\n .\n \"verify\" .\n \"Package verify turns questions about a Petri net into verdicts with evidence.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"visualization\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"visualization\" .\n \"Package visualization provides utilities for visualizing Petri nets as SVG.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"workflow\" .\n .\n .\n .\n .\n .\n .\n .\n .\n \"workflow\" .\n \"Package workflow provides a comprehensive workflow management framework built on Petri nets with support for task dependencies, resource management, SLA tracking, and real-time monitoring.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"zkcompile\" .\n .\n .\n \"zkcompile\" .\n \"Package zkcompile transforms Petri net models into ZK circuit constraints.\"@en .\n .\n \"Go\" .\n .\n .\n .\n \"go-pflow\" .\n .\n \"Petri net library — ODE, SSA & SDE simulation, parameter fitting, and formal verification, in Go\"@en .\n \"Go\" .\n .\n .\n .\n \"pflow-jl\" .\n .\n \"Julia package for Petri nets — colored tokens, mass-action ODEs, bridged to AlgebraicPetri.jl\"@en .\n \"Julia\" .\n .\n .\n .\n \"pflow-polyglot\" .\n .\n \"A Coffee state machine in various languages.\"@en .\n \"polyglot\" .\n .\n .\n .\n \"pflow-cli\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"crates/pflow-cli\" .\n \"Command-line tool for Petri net modeling and simulation — parity with go-pflow's cmd/pflow\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-compose\" .\n .\n .\n .\n .\n \"crates/pflow-compose\" .\n \"Bundle/Flatten composition, templates, derive and model-extension operations, ported from go-pflow's metamodel (compose*), templates and derive packages\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-core\" .\n \"crates/pflow-core\" .\n \"Core Petri net types, fluent builder API, and state utilities\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-dsl\" .\n .\n .\n .\n \"crates/pflow-dsl\" .\n \"S-expression DSL for defining token model schemas\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-eventlog\" .\n \"crates/pflow-eventlog\" .\n \"Process event log types plus CSV/JSONL readers, ported from go-pflow's eventlog package\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-learn\" .\n .\n .\n .\n .\n .\n .\n .\n .\n \"crates/pflow-learn\" .\n \"Parameter fitting, sensitivities, and gradient/derivative-free optimizers for Petri net ODEs\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-macros\" .\n .\n .\n .\n .\n \"crates/pflow-macros\" .\n \"Proc macros for pflow token model DSL\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-mcp\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"crates/pflow-mcp\" .\n \"MCP server for Petri net simulation and analysis\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-metamodel\" .\n \"crates/pflow-metamodel\" .\n \"Shape B model (places, transitions, arcs, stages, schedules, parameters) and the shared firing rule, ported from go-pflow's metamodel package\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-mining\" .\n .\n .\n .\n .\n .\n .\n \"crates/pflow-mining\" .\n \"Process discovery and conformance checking, ported from go-pflow's mining package\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-parser\" .\n .\n .\n .\n .\n \"crates/pflow-parser\" .\n \"Shape A -> Shape B converter: the pflow.xyz editor document to a pflow-metamodel Model, ported from go-pflow's parser package\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-reachability\" .\n .\n .\n \"crates/pflow-reachability\" .\n \"Reachability graph, coverability, invariants and spectral analysis, ported from go-pflow's reachability package\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-results\" .\n .\n .\n .\n .\n .\n .\n .\n \"crates/pflow-results\" .\n \"Structured simulation results (types, analysis, builder, io), ported from go-pflow's results package\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-solver\" .\n .\n .\n .\n .\n .\n .\n .\n \"crates/pflow-solver\" .\n \"ODE solvers for Petri net simulation using mass-action kinetics\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-tokenmodel\" .\n .\n .\n \"crates/pflow-tokenmodel\" .\n \"Token model schema, snapshot, and runtime execution\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-tropical\" .\n .\n .\n .\n .\n \"crates/pflow-tropical\" .\n \"Tropical semiring (max-plus algebra) for Petri net analysis\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-validation\" .\n .\n .\n .\n .\n \"crates/pflow-validation\" .\n \"Structural validation checks for pflow-metamodel nets, ported from go-pflow's validation package\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-verify\" .\n .\n .\n .\n .\n \"crates/pflow-verify\" .\n \"Property verification (deadlock-free, bounded, live, invariants, reachability) for pflow-metamodel nets, ported from go-pflow's verify package\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-visualization\" .\n .\n .\n .\n .\n .\n .\n .\n \"crates/pflow-visualization\" .\n \"SVG rendering for Petri nets and ODE solutions, ported from go-pflow's visualization and plotter packages\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-zk-arkworks\" .\n .\n .\n .\n .\n \"crates/pflow-zk-arkworks\" .\n \"Arkworks-based ZK prover for Petri nets (Groth16 + Poseidon over BN254)\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-zk\" .\n .\n .\n \"crates/pflow-zk\" .\n \"ZK proof traits and incidence matrix extraction for Petri nets\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"crates/pflow\" .\n \"Petri net modeling with ODE simulation and token model DSL\"@en .\n .\n \"Rust\" .\n .\n .\n .\n \"pflow-rs\" .\n .\n \"Rust port of go-pflow — ODE/SSA solvers, token-model DSL, ZK provers\"@en .\n \"Rust\" .\n .\n .\n .\n \"pflow-xyz\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"Visual editor and browser ODE simulator for Petri nets, byte-exact to go-pflow\"@en .\n \"Go\" .\n .\n .\n .\n \"sim-pflow-xyz\" .\n \"Go\" .\n .\n .\n .\n \"ArrivalProcess\" .\n \"at least one demand-rate (source) knob and no resource pool: pure arrivals with nothing rationing them\"@en .\n .\n .\n .\n .\n \"ConservedResourceCycle\" .\n \"at least one firing-cycle (T-invariant) whose own support touches a resource pool: tokens cycle through that pool rather than accumulating or draining\"@en .\n .\n .\n .\n .\n \"HasFungibleFamily\" .\n \"at least one discovered fungible class: some of the model's knobs are interchangeable rather than independent\"@en .\n .\n .\n .\n .\n \"QueueingSystem\" .\n \"at least one resource pool, at least one abandonment (patience) knob and at least one loss outcome: demand queues for a limited resource and can walk away empty-handed\"@en .\n .\n .\n .\n .\n \"ResourcePool\" .\n \"at least one resource pool and no abandonment knob: demand waits for the resource, it never gives up and leaves\"@en .\n .\n .\n .\n .\n \"StructurallyDeadlockable\" .\n \"at least one unmarked minimal siphon at the model's own initial marking: a structural proof (not sampled) that some transitions are permanently disabled once that siphon empties\"@en .\n .\n .\n .\n .\n \"UnclassifiedModel\" .\n \"the model's shape matched no rule in ProposeTypes' table: unrecognized, not misclassified\"@en .\n .\n .\n .\n \"sim model kinds\"@en .\n \"experimental — proposed candidate types, not yet applied to any catalog model; see ROADMAP.md Phase 8\" .\n .\n .\n \"Arc\"@en .\n .\n .\n .\n \"Every place has a finite token maximum across reachable markings. Established by sim_verify, not inferred here.\"@en .\n .\n .\n .\n \"ClassificationNet\"@en .\n .\n .\n .\n .\n .\n \"A unit of source code that other code can depend on: a project, a package or a crate.\"@en .\n \"Component\"@en .\n .\n .\n \"CompositeNet\"@en .\n .\n .\n .\n .\n .\n \"ComputationNet\"@en .\n .\n .\n .\n .\n .\n \"ContextualArc\"@en .\n .\n .\n .\n _:b639fabf2e8aa00ca738929cad227e6f .\n _:d61b8525e59d46e7ea4c808a6ccde685 .\n .\n \"A net with at least one read or inhibitor arc; not the free symmetric monoidal category of ordinary nets.\"@en .\n \"ContextualNet\"@en .\n _:a44ddc85277f85c3869ff37793244b07 .\n _:a44ddc85277f85c3869ff37793244b07 .\n .\n \"DataLink\"@en .\n .\n .\n .\n \"No reachable marking enables no transition. Established by sim_verify, not inferred here.\"@en .\n \"DeadlockFreeNet\"@en .\n .\n .\n .\n \"EventLink\"@en .\n .\n .\n .\n \"GameNet\"@en .\n .\n .\n .\n .\n .\n \"GoPackage\"@en .\n .\n .\n .\n \"Boolean condition on a transition, in addition to the token requirements.\"@en .\n \"Guard\"@en .\n .\n \"GuardLink\"@en .\n .\n .\n .\n \"Enables its transition only if the source place holds no token.\"@en .\n \"InhibitorArc\"@en .\n .\n .\n .\n .\n _:b639fabf2e8aa00ca738929cad227e6f .\n _:c199f2db2b9fc80e9d56f9a5b0a1cb4b .\n _:d61b8525e59d46e7ea4c808a6ccde685 .\n _:c199f2db2b9fc80e9d56f9a5b0a1cb4b .\n .\n \"Place to transition. Weight tokens are consumed when the transition fires.\"@en .\n \"InputArc\"@en .\n .\n .\n _:b639fabf2e8aa00ca738929cad227e6f .\n _:d61b8525e59d46e7ea4c808a6ccde685 .\n .\n .\n \"InvariantClaim\"@en .\n .\n .\n .\n \"Every transition can eventually fire from every reachable marking. Established by sim_verify, not inferred here.\"@en .\n .\n .\n .\n .\n \"A kind of sim model, from the vocabulary sim publishes. Proposed, not yet applied to catalog models.\"@en .\n \"ModelKind\"@en .\n .\n .\n \"Transition to place. Weight tokens are produced when the transition fires.\"@en .\n \"OutputArc\"@en .\n .\n .\n _:d0200ba986b921a0135493f8fcbf63b6 .\n _:f73a125f20c842b678594295dd227709 .\n .\n \"PetriNet\"@en .\n .\n .\n .\n \"PetriNetSeal\"@en .\n .\n .\n .\n \"PetriRuntime\"@en .\n .\n .\n .\n \"Place\"@en .\n .\n .\n .\n \"A repository or published site. Listed in ns/projects.json by a person, and only if it is public.\"@en .\n \"Project\"@en .\n .\n .\n .\n \"Enables its transition only if the source place holds a token; consumes none.\"@en .\n \"ReadArc\"@en .\n .\n .\n .\n .\n _:b639fabf2e8aa00ca738929cad227e6f .\n _:d61b8525e59d46e7ea4c808a6ccde685 .\n .\n .\n \"A paper, book or thesis, by bibliographic facts only. Cited by a Work, or added by an editor.\"@en .\n \"Reference\"@en .\n .\n .\n \"ResourceNet\"@en .\n .\n .\n .\n .\n .\n \"RustCrate\"@en .\n .\n .\n .\n \"Signature\"@en .\n .\n .\n .\n \"One piece of evidence for or against a claim: which work, where in it, what it shows, and how directly.\"@en .\n \"Support\"@en .\n .\n \"Token\"@en .\n .\n \"TokenLink\"@en .\n .\n .\n .\n \"Transition\"@en .\n .\n .\n .\n \"TransitionFireEvent\"@en .\n .\n .\n .\n \"Something we published: a blog post, a book chapter, or the blog and book themselves.\"@en .\n \"Work\"@en .\n .\n .\n \"WorkflowNet\"@en .\n .\n .\n .\n .\n .\n .\n \"aboutConcept\"@en .\n .\n .\n \"actor\"@en .\n .\n .\n .\n \"Present only on references an editor added; the writing does not cite them.\"@en .\n .\n .\n \"addedBy\"@en .\n .\n .\n \"Legacy documents write this member as `source`.\"@en .\n .\n .\n \"arcSource\"@en .\n .\n .\n \"Legacy documents write this member as `target`.\"@en .\n .\n .\n \"arcTarget\"@en .\n .\n \"arcType\"@en .\n .\n .\n .\n .\n \"arXiv identifier, checked against the paper.\"@en .\n .\n .\n \"arxiv\"@en .\n .\n \"'editor' or 'assistant-judgment'. Never an engine result.\"@en .\n \"assertedBy\"@en .\n .\n \"The authors in citation order, separated by semicolons. schema:author is an unordered set, so this is what a citation is built from.\"@en .\n .\n .\n \"authorList\"@en .\n .\n \"Why an editor-added statement is there.\"@en .\n \"basis\"@en .\n .\n \"bound\"@en .\n .\n .\n .\n .\n .\n .\n \"capacity\"@en .\n .\n .\n .\n .\n \"What a reader must not infer.\"@en .\n \"caveat\"@en .\n .\n \"claim\"@en .\n .\n .\n .\n .\n .\n .\n \"collection\"@en .\n .\n \"createdAt\"@en .\n .\n .\n .\n .\n \"createdBy\"@en .\n .\n .\n .\n \"denomination\"@en .\n .\n .\n .\n .\n .\n \"Needs the other component to build, directly or through others. A cycle shows up after reasoning as a mutual pair (cq/05-dependency-cycles.rq). It is not an inconsistency, because OWL 2 DL does not allow irreflexivity on a transitive property, and the engine's closure omits self-loops, so X dependsOn X is never derived.\"@en .\n .\n .\n \"dependsOn\"@en .\n .\n .\n .\n \"description\"@en .\n .\n .\n .\n .\n \"Asserted from an import (Go), a path dependency (Cargo) or a go.mod requirement. Never inferred.\"@en .\n .\n .\n \"directDependency\"@en .\n .\n .\n .\n .\n \"What the source shows there, in the curator's words.\"@en .\n .\n \"evidence\"@en .\n .\n \"fired\"@en .\n .\n .\n .\n .\n \"from\"@en .\n .\n .\n .\n \"function\"@en .\n .\n .\n .\n .\n .\n .\n \"hasArc\"@en .\n .\n .\n .\n .\n .\n \"hasGuard\"@en .\n .\n .\n .\n .\n \"hasPlace\"@en .\n .\n .\n .\n .\n .\n \"hasTransition\"@en .\n .\n .\n .\n \"impl\"@en .\n .\n .\n .\n .\n \"implHash\"@en .\n .\n .\n .\n .\n \"Proposed by the ontology-curator agent or a person, never extracted. Use only where the code visibly does what the concept says.\"@en .\n .\n .\n \"implements\"@en .\n .\n .\n .\n .\n \"inhibitTransition\"@en .\n .\n .\n .\n .\n .\n .\n \"initial\"@en .\n .\n .\n .\n .\n .\n .\n \"initialMarking\"@en .\n .\n .\n \"invariants\"@en .\n .\n .\n .\n .\n .\n \"links\"@en .\n .\n .\n .\n \"The work links to the other in its text.\"@en .\n .\n .\n \"linksTo\"@en .\n .\n .\n .\n \"Where in the source to look.\"@en .\n .\n \"location\"@en .\n .\n \"maxTotal\"@en .\n .\n .\n .\n .\n \"model\"@en .\n .\n .\n .\n .\n .\n \"modelCID\"@en .\n .\n .\n .\n .\n \"nextMarking\"@en .\n .\n .\n .\n .\n .\n .\n \"offset\"@en .\n .\n .\n .\n .\n \"A Cargo dependency behind a feature flag.\"@en .\n .\n .\n \"optionalDependency\"@en .\n .\n .\n .\n .\n \"parents\"@en .\n .\n .\n .\n \"place\"@en .\n .\n .\n .\n .\n \"places\"@en .\n .\n .\n .\n .\n \"prevMarking\"@en .\n .\n .\n .\n .\n \"priority\"@en .\n .\n .\n .\n .\n \"publicKey\"@en .\n .\n .\n .\n .\n .\n .\n \"rate\"@en .\n .\n .\n .\n .\n \"ref\"@en .\n .\n .\n .\n .\n \"runtime\"@en .\n .\n .\n .\n .\n .\n \"runtimeHash\"@en .\n .\n .\n .\n .\n \"schemas\"@en .\n .\n .\n .\n \"semantics\"@en .\n .\n .\n .\n .\n \"sig\"@en .\n .\n .\n .\n .\n \"sigType\"@en .\n .\n .\n .\n .\n \"signature\"@en .\n .\n .\n .\n .\n .\n \"signedFields\"@en .\n .\n .\n .\n .\n .\n \"source\"@en .\n .\n .\n .\n \"Path inside the project's repository.\"@en .\n .\n .\n \"sourcePath\"@en .\n .\n \"status\"@en .\n .\n \"direct, background, general, origin, or limit (shows where the claim stops).\"@en .\n .\n \"strength\"@en .\n .\n .\n \"supportedBy\"@en .\n .\n .\n \"ticker\"@en .\n .\n .\n .\n .\n \"timestamp\"@en .\n .\n .\n .\n .\n \"to\"@en .\n .\n .\n .\n \"token\"@en .\n .\n .\n .\n \"transition\"@en .\n .\n .\n .\n .\n .\n .\n \"venue\"@en .\n .\n .\n .\n \"weight\"@en .\n .\n .\n .\n \"x\"@en .\n .\n .\n .\n .\n \"y\"@en .\n .\n .\n .\n .\n \"Dedicated to the public domain under CC0 1.0 Universal.\"@en .\n \"pflow ontology: core\"@en .\n .\n \"Petri-net structure, the pflow ecosystem's components, the writing and literature behind it, and sim's model kinds.\"@en .\n \"0.2.0\" .\n .\n \"Alla, H.\" .\n .\n \"Baccelli, F.\" .\n .\n \"Baez, J.C.\" .\n .\n \"Claude Code\" .\n .\n .\n \"Cohen, G.\" .\n .\n \"David, R.\" .\n .\n \"Donaldson, R.\" .\n .\n \"Fong, B.\" .\n .\n \"Freeman, L.C.\" .\n .\n \"Genovese, F.\" .\n .\n \"Ghani, N.\" .\n .\n \"Gilbert, D.,\" .\n .\n \"Groth, J.\" .\n .\n \"Hedges, J.\" .\n .\n \"Heiner, M.\" .\n .\n \"Huisinga, W.\" .\n .\n \"Jahnke, T.\" .\n .\n \"Karp, R.M.\" .\n .\n \"Li, M.\" .\n .\n \"Mac Lane, S.\" .\n .\n \"Master, J.\" .\n .\n \"Meseguer, J.\" .\n .\n \"Molloy, M.K.\" .\n .\n \"Montanari, U.\" .\n .\n \"Murata, T.\" .\n .\n \"Olsder, G.J.\" .\n .\n \"Pollard, B.S.\" .\n .\n \"Quadrat, J.-P.\" .\n .\n \"Riehl, E.\" .\n .\n \"Riley, M.\" .\n .\n \"Rossi, F.\" .\n .\n \"Sassone, V.\" .\n .\n \"Semenov, A.\" .\n .\n \"Shulman, M.\" .\n .\n \"stackdump\" .\n .\n .\n \"Stay, M.\" .\n .\n \"Vitányi, P.\" .\n .\n \"Vogler, W.\" .\n .\n \"Winschel, V.\" .\n .\n \"Yakovlev, A.\" .\n .\n \"Yoneda, N.\" .\n .\n \"Zahn, P.\" .\n .\n .\n \"Baccelli, F.; Cohen, G.; Olsder, G.J.; Quadrat, J.-P.\" .\n \"Wiley\" .\n .\n .\n .\n .\n \"1992\"^^ .\n \"Synchronization and Linearity: An Algebra for Discrete Event Systems\" .\n .\n .\n \"Baez, J.C.; Stay, M.\" .\n \"New Structures for Physics, Springer\" .\n .\n .\n \"2011\"^^ .\n \"Physics, Topology, Logic and Computation: A Rosetta Stone\" .\n .\n .\n \"editor\" .\n \"1704.02051\" .\n \"Baez, J.C.; Pollard, B.S.\" .\n \"Reaction networks, equivalently Petri nets, composed as open systems.\" .\n .\n .\n \"2017\"^^ .\n \"A Compositional Framework for Reaction Networks\" .\n .\n .\n .\n \"1808.05415\" .\n \"Baez, J.C.; Master, J.\" .\n \"Mathematical Structures in Computer Science, 30(3)\" .\n .\n .\n \"2020\"^^ .\n \"Open Petri Nets\" .\n .\n .\n .\n \"editor\" .\n \"2101.04238\" .\n \"Baez, J.C.; Genovese, F.; Master, J.; Shulman, M.\" .\n \"Abstract: Sigma-nets generate symmetric strict monoidal categories and ordinary Petri nets generate commutative monoidal categories, by left adjoint functors. Directly relevant to the free-SMC claim in Appendix E.\" .\n .\n .\n .\n .\n \"2021\"^^ .\n \"Categories of Nets\" .\n .\n .\n .\n \"David, R.; Alla, H.\" .\n \"Springer\" .\n .\n .\n \"2010\"^^ .\n \"Discrete, Continuous, and Hybrid Petri Nets\" .\n .\n .\n \"Fong, B.\" .\n \"PhD thesis, Oxford\" .\n .\n \"2015\"^^ .\n \"The Algebra of Open and Interconnected Systems\" .\n .\n .\n \"Freeman, L.C.\" .\n \"Social Networks, 1(3)\" .\n .\n \"1978\"^^ .\n \"Centrality in Social Networks: Conceptual Clarification\" .\n .\n .\n \"1603.04641\" .\n \"Ghani, N.; Hedges, J.; Winschel, V.; Zahn, P.\" .\n \"arXiv\" .\n .\n .\n .\n .\n \"2016\"^^ .\n \"Compositional Game Theory\" .\n .\n .\n .\n \"Groth, J.\" .\n \"EUROCRYPT 2016\" .\n .\n \"2016\"^^ .\n \"On the Size of Pairing-Based Non-Interactive Arguments\" .\n .\n .\n \"Heiner, M.; Gilbert, D.,; Donaldson, R.\" .\n \"Formal Methods for Computational Systems Biology, Springer\" .\n .\n .\n .\n \"2008\"^^ .\n \"Petri Nets for Systems and Synthetic Biology\" .\n .\n .\n \"Jahnke, T.; Huisinga, W.\" .\n \"Journal of Mathematical Biology, 54(1)\" .\n .\n .\n \"2007\"^^ .\n \"Solving the chemical master equation for monomolecular reaction systems analytically\" .\n .\n .\n \"Karp, R.M.\" .\n \"Discrete Mathematics, 23(3)\" .\n .\n \"1978\"^^ .\n \"A characterization of the minimum cycle mean in a digraph\" .\n .\n .\n \"Li, M.; Vitányi, P.\" .\n \"Springer, 3rd ed\" .\n .\n .\n \"2008\"^^ .\n \"An Introduction to Kolmogorov Complexity and Its Applications\" .\n .\n .\n \"editor\" .\n \"Mac Lane, S.\" .\n \"Standard reference for the lemma. Checked: the book, edition and series, and that Chapter III is 'Universals and Limits'. Not checked: the section within that chapter, so none is given.\" .\n \"Springer, Graduate Texts in Mathematics 5, 2nd ed.\" .\n .\n \"1998\"^^ .\n \"Categories for the Working Mathematician\" .\n .\n .\n \"editor\" .\n \"2105.12905\" .\n \"Master, J.\" .\n \"Title page: dissertation dated June 2020, posted to arXiv May 2021.\" .\n \"PhD thesis, University of California, Riverside\" .\n .\n \"2020\"^^ .\n \"Composing Behaviors of Networks\" .\n .\n .\n .\n \"Master, J.\" .\n \"The Topos Institute\" .\n .\n \"2020\"^^ .\n \"Generalized Petri Nets\" .\n .\n .\n \"1904.09091\" .\n \"Master, J.\" .\n \"Mathematical Structures in Computer Science, 30\" .\n .\n \"2020\"^^ .\n \"Petri Nets Based on Lawvere Theories\" .\n .\n .\n .\n \"Meseguer, J.; Montanari, U.\" .\n \"Information and Computation, 88(2)\" .\n .\n .\n \"1990\"^^ .\n \"Petri Nets are Monoids\" .\n .\n .\n \"Molloy, M.K.\" .\n \"IEEE Transactions on Computers, C-31(9)\" .\n .\n \"1982\"^^ .\n \"Performance Analysis Using Stochastic Petri Nets\" .\n .\n .\n \"Montanari, U.; Rossi, F.\" .\n \"Acta Informatica, 32(6)\" .\n .\n .\n \"1995\"^^ .\n \"Contextual Nets\" .\n .\n .\n \"Murata, T.\" .\n \"Proceedings of the IEEE, 77(4)\" .\n .\n \"1989\"^^ .\n \"Petri Nets: Properties, Analysis and Applications\" .\n .\n .\n \"editor\" .\n \"Riehl, E.\" .\n \"Standard textbook statement of the Yoneda lemma: Chapter 2 'Universal Properties, Representability, and the Yoneda Lemma', section 2.2 'The Yoneda lemma' (Dover edition; checked against the published table of contents).\" .\n \"Dover Publications\" .\n .\n \"2016\"^^ .\n \"Category Theory in Context\" .\n .\n .\n \"1809.00738\" .\n \"Riley, M.\" .\n \"arXiv\" .\n .\n \"2018\"^^ .\n \"Categories of Optics\" .\n .\n .\n .\n \"Sassone, V.\" .\n \"TAPSOFT\" .\n .\n \"1995\"^^ .\n \"On the Category of Petri Net Computations\" .\n .\n .\n \"Vogler, W.; Semenov, A.; Yakovlev, A.\" .\n \"CONCUR 1998\" .\n .\n .\n .\n \"1998\"^^ .\n \"Unfolding and Finite Prefix for Nets with Read Arcs\" .\n .\n .\n \"editor\" .\n \"Yoneda, N.\" .\n \"The paper associated with Yoneda's name. Checked: the bibliographic details, against several sources. Not checked: whether the lemma is stated in this paper; cite a textbook for the statement.\" .\n \"Journal of the Faculty of Science, University of Tokyo, Section I, 7, 193-227\" .\n .\n \"1954\"^^ .\n \"On the homology theory of modules\" .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n .\n \"A directed connection between a place and a transition (input arc) or a transition and a place (output arc). Arcs define the flow relation of the net. Each arc has a weight (default 1) specifying how many tokens are consumed or produced.\"@en .\n .\n \"Arc\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A graph whose nodes divide into two disjoint sets, with edges only between sets, never within. Petri nets are bipartite: places connect to transitions, transitions connect to places, but places never connect directly to places.\"@en .\n .\n \"Bipartite graph\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A net is bounded if every place has a finite maximum token count across all reachable markings. A net is $k$-bounded if no place ever exceeds $k$ tokens. Boundedness is a safety property — it guarantees the system can't accumulate unbounded resources.\"@en .\n .\n \"Bounded\"@en .\n .\n .\n \"Categorical gadget\"@en .\n \"The editor's term, not a standard one. What the sources support about it is recorded on claim:nets-are-categorical-gadgets.\"@en .\n \"editor\" .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Content Identifier\"@en .\n \"A hash-based identifier for content-addressed data. In the pflow ecosystem, CIDs identify JSON-LD models deterministically — the same model always produces the same CID regardless of where or when it's computed (Chapter 16).\"@en .\n .\n \"CID\"@en .\n \"16\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"$\\\\rho$\"@en .\n \"For a transition, tokens consumed divided by tokens produced. $\\\\rho = 1$ is the core; $\\\\rho > 1$ is an observer that destroys state to produce a verdict. A property of the incidence matrix column, so every analysis of $C$ can see it. See *Core–observer boundary*.\"@en .\n .\n \"Compression ratio\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"An equation $\\\\mathbf{y}^T \\\\mathbf{C} = \\\\mathbf{0}$ where $\\\\mathbf{y}$ is a vector of weights and $\\\\mathbf{C}$ is the incidence matrix. Conservation laws prove that weighted sums of token counts remain constant across all firings. Example: in an SIR model, $S + I + R = N$ for all time.\"@en .\n .\n \"Conservation law\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n .\n \"A read arc (fires only if a place holds a token, without consuming it) or an inhibitor arc (fires only if it holds none). Neither appears in the incidence matrix, since neither changes the marking. Nets with contextual arcs do not generate the free symmetric monoidal category of ordinary nets (Montanari & Rossi, 1995); they are the categorical half of the core–observer boundary, and the natural home of guards.\"@en .\n .\n \"Contextual arc\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Replacing discrete token counts with continuous concentrations and firing rules with differential equations. The Petri net becomes a system of ODEs via mass-action kinetics, enabling simulation with numerical solvers (Chapter 3).\"@en .\n .\n \"Continuous relaxation\"@en .\n \"3\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Two distinct boundaries that older material treated as one. The *algebraic* boundary ($\\\\rho$) lies inside $C$ and separates transitions the tropical eigenvalue and uniform R1CS can handle from those they cannot; it does not affect composition. The *contextual* boundary (read/inhibitor arcs) lies outside $C$ and breaks free composition; it does not affect $\\\\rho$. Canonical statement in Appendix E.\"@en .\n .\n \"Core–observer boundary\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A marking where no transition is enabled. The system is stuck — no further computation is possible. Deadlock detection is a key analysis performed by the reachability package.\"@en .\n .\n \"Deadlock\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"The Metamodel working discipline. The model is declared once as data; analysis, the running application, proofs and, in this ecosystem's own deployment tooling, the infrastructure that serves it are computed from that document. Nothing downstream is hand-written to agree with the model, so nothing downstream can disagree with it (Chapter 21; *The Model Is the App*).\"@en .\n .\n \"Declare, then derive\"@en .\n \"21\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Disagreement between a declared artifact and the world it describes — a manifest and a host, a vendored module and its upstream, two implementations of one net. Metamodel does not prevent drift; it makes drift detectable by comparing two values: a manifest against a host, a vendored file against its lockfile, a trace against the golden trace (Chapters 20, 21).\"@en .\n .\n \"Drift\"@en .\n \"20\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Two nets compose by sharing a place, the way two tiles meet because their edges agree. No glue code is written to make them fit; the shared place *is* the interface. Invariants carry across in a specific sense: if a P-invariant of each component agrees with the other on the shared places, together they define a P-invariant of the composite — the theorem `invariant_lift`, kernel-checked in Lean ([`proofs/PflowProofs/InvariantLift.lean`](https://github.com/pflow-xyz/book-pflow-xyz/blob/main/proofs/PflowProofs/InvariantLift.lean)). A component's invariant extended by zeros is not in general an invariant of the composite, and liveness does not carry across at all (Appendix E; Chapters 4, 21; *A Tiling for Computation*).\"@en .\n .\n \"Edge-matching composition\"@en .\n \"4\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A transition is enabled at a marking $\\\\mathbf{m}$ if every input place has at least as many tokens as the corresponding arc weight: $\\\\mathbf{m}(p) \\\\geq W(p, t)$ for all input places $p$. An enabled transition may fire; a disabled one cannot.\"@en .\n .\n \"Enabled\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A state where all derivatives are approximately zero — the system has stopped changing. go-pflow's `SolveUntilEquilibrium` stops early once the largest absolute derivative stays below a tolerance (default $10^{-6}$) for several consecutive checks (`solver/equilibrium.go`; Appendix A).\"@en .\n .\n \"Equilibrium\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A state management pattern where state is computed by replaying an immutable log of events from the initial state: $\\\\text{State}(t) = \\\\text{fold}(\\\\text{apply}, \\\\text{initialState}, \\\\text{events}[0..t])$. In Petri net terms, events are transition firings and state is the marking (Chapter 20).\"@en .\n .\n \"Event sourcing\"@en .\n \"20\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"The execution semantics of Petri nets. When a transition fires, it atomically removes tokens from input places and adds tokens to output places according to arc weights. The new marking is $\\\\mathbf{m}' = \\\\mathbf{m} + \\\\mathbf{C} \\\\cdot \\\\mathbf{e}_t$ where $\\\\mathbf{e}_t$ is the unit vector for transition $t$.\"@en .\n .\n \"Firing rule\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A canonical firing sequence and its resulting markings, checked byte-for-byte against every implementation of a model. `pflow-polyglot/parity/trace.golden` holds thirty-nine programs in ten languages to one six-line trace. `make parity` runs the twenty Go, Rust, Python and JavaScript programs under Bazel and fails the build on any divergence; `make parity-native` checks the rest against the same file (Chapter 20).\"@en .\n .\n \"Golden trace\"@en .\n \"20\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A zero-knowledge proof system used in pflow for verifying Petri net transitions without revealing state. Produces constant-size proofs with fast verification, at the cost of a per-circuit trusted setup (Chapter 12).\"@en .\n .\n \"Groth16\"@en .\n \"12\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n .\n \"A boolean expression attached to a transition that must evaluate to true for the transition to be enabled, in addition to the standard token requirements. Guards extend the firing rule with data-dependent conditions.\"@en .\n .\n \"Guard\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"The matrix $\\\\mathbf{C} = \\\\mathbf{C}^+ - \\\\mathbf{C}^-$ where $\\\\mathbf{C}^+$ is the output matrix (tokens produced) and $\\\\mathbf{C}^-$ is the input matrix (tokens consumed). Each column represents a transition; each row represents a place. The entry $\\\\mathbf{C}_{ij}$ is the net change in place $i$ when transition $j$ fires (Chapter 2).\"@en .\n .\n \"Incidence matrix\"@en .\n \"2\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Two readings of concurrent behavior. Interleaving semantics considers one firing at a time and asks which markings are reachable; partial-order (unfolding) semantics additionally records which firings were independent. Encoding a read arc as a consume-then-restore self-loop is exact under the first and inequivalent under the second (Vogler, Semenov & Yakovlev, 1998). A single-transition ZK proof has only interleaving semantics.\"@en .\n .\n \"Interleaving vs. partial-order semantics\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"as a failure mode\"@en .\n \"A model expressed as *code in a host language* that constructs a net — Rust macros, Python calls, Solidity structs. Five such ports of an early version of this work claimed to encode the same thing and could not prove it, because the specification existed only as five programs. The fix was to make the model a document (Chapter 21; book `ROADMAP.md` §Lineage).\"@en .\n .\n \"Internal DSL\"@en .\n \"21\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A workflow whose control flow is a Petri net declared in a markdown document's frontmatter, with one prompt per transition in the body. The document is both the documentation and the runtime — there is no second copy of the control flow to drift (Chapter 21).\"@en .\n .\n \"Journey\"@en .\n \"21\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"JSON for Linked Data. The pflow ecosystem uses JSON-LD as its model interchange format, with `@context: \\\"https://pflow.xyz/schema\\\"`. JSON-LD makes models self-describing and content-addressable (Chapter 16).\"@en .\n .\n \"JSON-LD\"@en .\n \"16\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A transition is live if it can eventually fire from every reachable marking (possibly after other transitions fire first). A net is live if all transitions are live. Liveness means the system never permanently loses capability.\"@en .\n .\n \"Liveness\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"The declared description of an application — a handful of fields and a marking in one YAML file — from which its service entry, virtual host, certificate and uptime check are derived. The infrastructure instance of declare-then-derive (Chapter 21).\"@en .\n .\n \"Manifest\"@en .\n \"21\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n .\n \"The distribution of tokens across all places at a given moment; the state of the Petri net. Written as a vector $\\\\mathbf{m}$ where $\\\\mathbf{m}(p)$ is the token count at place $p$. The initial marking $\\\\mathbf{m}_0$ is the starting state.\"@en .\n .\n \"Marking\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A rate law from chemistry where the rate of a reaction is proportional to the product of reactant concentrations. As go-pflow implements it, the continuous firing rate of transition $t$ is $r_t \\\\prod_{p \\\\in \\\\text{inputs}(t)} m(p)$, where $r_t$ is the rate constant: first order in every input place, whatever the arc weight. The weight $w(p,t)$ enters only the stoichiometry, so place $p$ drains at $w(p,t)$ times the flux ([`solver/ode.go`](https://github.com/pflow-xyz/go-pflow/blob/main/solver/ode.go); Chapter 3).\"@en .\n .\n \"Mass-action kinetics\"@en .\n \"3\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Capitalised: a model for making models — the cross-cutting claim of this book. A small, fixed alphabet — place, transition, arc, guard — whose local composition rules generate an unbounded space of specific, checkable systems, because a model written in it is a value rather than a program. Lowercase `metamodel`, in code font, is a Go package implementing one instance of the vocabulary (Chapter 21; *A Tiling for Computation*).\"@en .\n .\n \"Metamodel\"@en .\n \"21\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Minimum Multiplicative Complexity\"@en .\n \"A hash function designed for efficiency inside arithmetic circuits. Used in pflow's zero-knowledge proofs to hash Petri net markings with minimal constraint count (Chapter 12).\"@en .\n .\n \"MiMC\"@en .\n \"12\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"The single fact Metamodel rests on. A value can be hashed, diffed, composed and checked by a machine that has never seen any of our runtimes; a program can only be run. Content addressing (Chapter 16), dual implementation (Chapter 20) and the golden trace all depend on it.\"@en .\n .\n \"Model is a value, not a program\"@en .\n \"16\"^^ .\n \"20\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"The discipline of a schema that only grows: new facts can be added, existing facts are never retracted, so learning more never invalidates what was already known (Chapter 16). The history places of Chapters 6 and 7 follow the same discipline at the level of a single net. See *Write-once place*.\"@en .\n .\n \"Monotonic expansion\"@en .\n \"16\"^^ .\n \"6\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Ordinary Differential Equation\"@en .\n \"An equation relating a function to its derivatives. The continuous relaxation of a Petri net produces a system of ODEs: $\\\\frac{d\\\\mathbf{m}}{dt} = \\\\mathbf{C} \\\\cdot \\\\mathbf{r}(\\\\mathbf{m})$ where $\\\\mathbf{r}(\\\\mathbf{m})$ is the rate vector (Chapter 3).\"@en .\n .\n \"ODE\"@en .\n \"3\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A vector $\\\\mathbf{y} \\\\geq \\\\mathbf{0}$ such that $\\\\mathbf{y}^T \\\\mathbf{C} = \\\\mathbf{0}$. The weighted sum $\\\\mathbf{y}^T \\\\mathbf{m}$ is constant for all reachable markings. P-invariants prove conservation laws — they identify quantities that are preserved by every transition firing (Chapter 2).\"@en .\n .\n \"P-invariant\"@en .\n \"2\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n .\n \"A mathematical modeling language consisting of places, transitions, arcs, and tokens. Formally, a tuple $(P, T, F, W, \\\\mathbf{m}_0)$ where $P$ is a set of places, $T$ is a set of transitions, $F \\\\subseteq (P \\\\times T) \\\\cup (T \\\\times P)$ is the flow relation, $W: F \\\\to \\\\mathbb{N}$ is the weight function, and $\\\\mathbf{m}_0$ is the initial marking.\"@en .\n .\n \"Petri net\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n .\n \"A node in a Petri net representing a condition, resource, or state. Places hold tokens. Drawn as circles. In the continuous relaxation, token counts become continuous concentrations.\"@en .\n .\n \"Place\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"The five shapes an implementation of one model can take — *interpreter* (a generic engine reads the document), *lambda* (the net as a pure step function), *generated* (source emitted from the document), *contract* (on-chain), *proof* (the program checks its claims over every reachable marking before it prints anything; in Lean the check is a theorem the kernel accepts at compile time) — all held to one golden trace (*The Proof Form*; `pflow-polyglot/FORMS.md`).\"@en .\n .\n \"Polyglot forms\"@en .\n .\n \"The category of functors from C^op to Set, with natural transformations as morphisms. Presheaf categories are toposes.\"@en .\n .\n \"Presheaf category\"@en .\n .\n \"assistant-judgment\" .\n \"Standard; see Riehl, Category Theory in Context.\" .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"The graph of all markings reachable from the initial marking through sequences of transition firings. Each node is a marking, each edge is a transition firing. The reachability graph may be infinite for unbounded nets.\"@en .\n .\n \"Reachability graph\"@en .\n .\n \"categorical foundations\"@en .\n .\n \"pflow core glossary\"@en .\n .\n \"pflow ecosystem glossary\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Stochastic Differential Equation\"@en .\n \"Here, specifically the chemical Langevin equation: continuous state evolving under the same propensities SSA uses, but with intrinsic firing noise built into the diffusion term rather than sampled as discrete events. Cheap to sweep like the ODE, with an honest variance band like SSA — the regime between them. Distinct from a layer of exogenous Brownian motion added to an ODE for external uncertainty (a price feed, say), which answers a different question (Chapter 3).\"@en .\n .\n \"SDE\"@en .\n \"3\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Stochastic Simulation Algorithm\"@en .\n \"The discrete engine's execution method (Gillespie's direct method): pick the next transition to fire and the time until it fires, both drawn from the model's own propensities, then repeat. Produces one exact discrete sample path, or an ensemble of them, rather than a mean-field trajectory — the right tool when small counts or gating (read arcs, inhibitors, reachable capacities, guards) make the continuous relaxation inapplicable (Chapter 3).\"@en .\n .\n \"SSA\"@en .\n \"3\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"The algebraic relation $\\\\mathbf{m}' = \\\\mathbf{m}_0 + \\\\mathbf{C} \\\\cdot \\\\boldsymbol{\\\\sigma}$ where $\\\\boldsymbol{\\\\sigma}$ is the firing count vector (how many times each transition has fired). A necessary but not sufficient condition for reachability — the actual firing sequence must also be valid.\"@en .\n .\n \"State equation\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A hash of the simulation output used for cross-implementation verification. If the Go server and JavaScript browser produce the same state root from the same model, the implementations agree (Chapter 20).\"@en .\n .\n \"State root\"@en .\n \"20\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n .\n \"A marker in a place. Tokens represent the presence of a resource, the truth of a condition, or a unit of something being processed. In the discrete model, tokens are non-negative integers. In the continuous relaxation, they become non-negative real numbers.\"@en .\n .\n \"Token\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n .\n \"A node in a Petri net representing an event, action, or chemical reaction. Transitions consume tokens from input places and produce tokens in output places. Drawn as rectangles. In the continuous relaxation, transitions have firing rates.\"@en .\n .\n \"Transition\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"The tense structure of an executing model. Write-once places and the event log are the *past* — monotone and irreversible, the boolean case of tropical $(\\\\max,+)$ accumulation. Guards are the *future* — predicates recomputed from the marking on every step and stored nowhere. The marking is the *present*, the boundary where they meet. All three are data in the one model document (Chapter 6; Appendix E; *The Zipper Whose Hole Is a Universe*).\"@en .\n .\n \"Tropical past, predicate future\"@en .\n \"6\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Tsitouras 5th-order Runge-Kutta method with embedded 4th-order error estimator. The default ODE solver in go-pflow and pflow.xyz. Uses adaptive step size control for automatic accuracy management (Appendix A).\"@en .\n .\n \"Tsit5\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"Universal RDF Dataset Normalization Algorithm 2015. Used in pflow to canonicalize JSON-LD models before hashing, ensuring that semantically equivalent documents produce identical content identifiers regardless of key order or formatting (Chapter 16).\"@en .\n .\n \"URDNA2015\"@en .\n \"16\"^^ .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"The number of tokens consumed or produced by an arc when its transition fires. A weight of $k$ on an input arc means the transition requires at least $k$ tokens in the source place and removes $k$ tokens when firing. Default weight is 1.\"@en .\n .\n \"Weight\"@en .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A place that no move takes a token back from: once a token arrives, the transitions that wrote it never consume it. History places are the canonical case — `X11` and `O02` in the tic-tac-toe net of Chapter 6, `_D2_01` in the Sudoku net of Chapter 7. Their only downstream transitions are the pattern and constraint collectors that turn a completed pattern into a verdict. The smallest instance of tropical accumulation (Appendix E).\"@en .\n .\n \"Write-once place\"@en .\n \"6\"^^ .\n \"7\"^^ .\n .\n .\n \"The functor from a locally small category C to the category of presheaves on C that sends an object c to Hom(-, c). It is fully faithful, which is a consequence of the Yoneda lemma.\"@en .\n .\n \"Yoneda embedding\"@en .\n \"assistant-judgment\" .\n \"Riehl, Category Theory in Context, section 2.2.\" .\n .\n \"For a locally small category C, an object c and a functor F from C^op to Set, the natural transformations from the representable functor Hom(-, c) to F correspond bijectively to the elements of F(c), naturally in c and F.\"@en .\n .\n \"Yoneda lemma\"@en .\n \"assistant-judgment\" .\n \"Riehl, Category Theory in Context, section 2.2.\" .\n \"book-pflow-xyz/chapters/appendix-d-glossary.md\" .\n .\n \"A cryptographic protocol where a prover convinces a verifier that a statement is true without revealing any information beyond the truth of the statement. In pflow, ZK proofs verify that a Petri net transition was validly fired without revealing the marking (Chapter 12).\"@en .\n .\n \"Zero-knowledge proof\"@en .\n \"12\"^^ .\n .\n .\n .\n \"about\" .\n .\n .\n .\n .\n .\n \"2026-04-01T00:00:00Z\"^^ .\n \"2026-02-14T00:00:00Z\"^^ .\n \"Reflections from an AI collaborator on building with Petri nets—what makes this approach different, and why it keeps surprising me.\"@en .\n .\n \"ai\" .\n \"collaboration\" .\n \"petri-net\" .\n \"reflection\" .\n \"A Circuit's-Eye View: Notes from Inside the Loop\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n \"2026-04-16T00:00:00Z\"^^ .\n \"de Jong et al. (2026) put an ordinal axis under decidability. That axis is past-tense, and Brouwer ordinals are the scalar specialization of our vector tropical past.\"@en .\n .\n \"ordinals\" .\n \"petri-net\" .\n \"tropical-geometry\" .\n \"type-theory\" .\n \"Brouwer Ordinals and the Shape of a Witness\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n \"2026-10-24T00:00:00Z\"^^ .\n \"2026-10-24T00:00:00Z\"^^ .\n \"A native macOS DJ app where each deck runs a live Petri net. The generator is ported from beats.bitwrap.io to Swift and held to the same CIDs and bytes by fixtures from the real JavaScript; Claude drives it over MCP.\"@en .\n .\n \"beats-bitwrap\" .\n \"mcp\" .\n \"music\" .\n \"petri-nets\" .\n \"swift\" .\n \"beats-btw-dj: the Petri-net sequencer, native on the Mac\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n .\n \"2026-09-25T00:00:00Z\"^^ .\n \"2026-08-22T00:00:00Z\"^^ .\n \"A visual archaeology of beats.bitwrap.io's first 75 tags, v0.1.0 (March 23) to v2.4.0 (April 28): one screenshot captured per minor release, ten of them shown here, each reproducible from the tag's CDN URL.\"@en .\n .\n \"beats-bitwrap\" .\n \"music\" .\n \"petri-nets\" .\n \"retrospective\" .\n \"From Petri-net toy to jambox: 38 days of beats.bitwrap.io\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n \"2026-04-30T00:00:00Z\"^^ .\n \"2026-04-30T00:00:00Z\"^^ .\n \"Official launch of beats.bitwrap.io as a live-performance tool — content-addressed shareable tracks, full-page Stage visuals, and a hands-free Auto-DJ that runs itself for hours.\"@en .\n .\n \"beats-bitwrap\" .\n \"live-performance\" .\n \"music\" .\n \"petri-nets\" .\n \"tone-js\" .\n \"beats.bitwrap.io is a Jambox Now\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n .\n .\n \"2026-04-01T00:00:00Z\"^^ .\n \"2026-03-18T00:00:00Z\"^^ .\n \"From OP_RETURN in 2014 to zero-knowledge Petri nets in 2026 — how bitwrap.io became the capstone for a decade of work on formal state machines, cryptographic proofs, and executable specifications.\"@en .\n .\n \"bitwrap\" .\n \"groth16\" .\n \"petri-net\" .\n \"solidity\" .\n \"zero-knowledge\" .\n \"Bitwrap: Petri Nets as ZK Containers\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n .\n \"2026-10-19T00:00:00Z\"^^ .\n \"2026-08-22T00:00:00Z\"^^ .\n \"A technical deep dive into heads-up hold'em at stackedup.gg — four Petri nets (phase, hand classifier, bot decision, chip ledger) and what each one actually drives in the code, a commit-reveal shuffle for casino sessions, and a branchless Groth16 circuit that proves a hand's score without revealing the hole cards.\"@en .\n .\n \"game-design\" .\n \"gnark\" .\n \"groth16\" .\n \"petri-net\" .\n \"poker\" .\n \"zk\" .\n \"Building ZK Poker: Four Petri Nets and a Branchless Circuit\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n \"2026-09-04T00:00:00Z\"^^ .\n \"2026-09-04T00:00:00Z\"^^ .\n \"Go, Rust, JavaScript and Julia run the same stochastic Petri net and produce the identical IEEE-754 double, every time. Not close — equal. Here's what that actually took, and the two bugs it caught along the way.\"@en .\n .\n \"cross-language\" .\n \"determinism\" .\n \"formal-methods\" .\n \"petri-net\" .\n \"stochastic-simulation\" .\n \"Byte-Exact Across Four Languages\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n \"2026-10-09T00:00:00Z\"^^ .\n \"2026-09-16T00:00:00Z\"^^ .\n \"sim.pflow.xyz ranks every knob in a model by its measured effect on the objective. One run against a software team's backlog model reported that hiring past a point lowers the score; that finding is unconfirmed until the model's cost meter is fixed, and the catalog-wide sweep behind the rest of the pattern was never preserved. What was checked, what wasn't, and the models to re-run it on.\"@en .\n .\n \"cost-benefit-analysis\" .\n \"petri-net\" .\n \"sim-pflow-xyz\" .\n \"simulation\" .\n \"what-if-analysis\" .\n \"The Capacity Paradox\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n \"2026-08-22T00:00:00Z\"^^ .\n \"2026-02-07T00:00:00Z\"^^ .\n \"Five Petri net types classify token behavior — workflow cursors, countable resources, game turns, continuous rates, and classification signals — with typed links that constrain how nets compose.\"@en .\n .\n \"category-theory\" .\n \"composition\" .\n \"dsl\" .\n \"petri-net\" .\n \"pflow\" .\n \"Categorical Net Types\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-08-22T00:00:00Z\"^^ .\n \"2026-03-12T00:00:00Z\"^^ .\n \"Settlement networks form a sub-SMC of open Petri nets. The core-observer split is really two boundaries — an algebraic one (ρ) inside the incidence matrix and a categorical one (contextual arcs) outside it — and a ZK circuit dissolves only the second.\"@en .\n .\n \"category-theory\" .\n \"open-petri-nets\" .\n \"petri-nets\" .\n \"settlement\" .\n \"The Category Settle\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-23T00:00:00Z\"^^ .\n \"2026-03-05T00:00:00Z\"^^ .\n \"Paste source code in any language and Claude returns a Petri net that a validator checks for structure and deadlocks — what is checked, what isn't, and the faithfulness test not yet run.\"@en .\n .\n \"code-visualization\" .\n \"codegen\" .\n \"llm\" .\n \"petri-net\" .\n \"sim-pflow-xyz\" .\n \"state-machine\" .\n \"Code-to-Flow: Turn Anything into a Petri Net\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-23T00:00:00Z\"^^ .\n \"2026-01-31T00:00:00Z\"^^ .\n \"Resource modeling with Petri nets — the five-drink core of go-pflow's coffee shop, where arc weights are recipes, each ingredient carries a conservation law, and the rates say what runs out first (milk, not cups). Revised to link the code, restore mocha's syrup and label every minute figure as a linear estimate.\"@en .\n .\n \"capacity\" .\n \"ode\" .\n \"petri-net\" .\n \"resource-modeling\" .\n \"Coffee Shop Model\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n \"2026-04-02T00:00:00Z\"^^ .\n \"2025-01-07T04:54:52Z\"^^ .\n \"A modeling approach where system behavior is described declaratively and encoded directly in differential equations.\"@en .\n .\n \"ddm\" .\n \"ode\" .\n \"petri-net\" .\n \"theory\" .\n \"Declarative Differential Models (DDM)\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-18T00:00:00Z\"^^ .\n \"2026-03-11T00:00:00Z\"^^ .\n \"ODE simulation, tropical analysis and zero-knowledge proofs each draw a line between a Petri net's core and its observer. Where the three agree on tic-tac-toe, why the agreement follows from one definition, and where the code does not yet match the theorem.\"@en .\n .\n \"category-theory\" .\n \"compression\" .\n \"petri-nets\" .\n \"tropical-geometry\" .\n \"zero-knowledge\" .\n \"Earned Compression\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n \"2026-10-04T00:00:00Z\"^^ .\n \"2026-02-14T00:00:00Z\"^^ .\n \"Four places and three mass-action transitions generate the ODE system that Michaelis-Menten is derived from. What the demo integrates, what it reads off a formula, and the saturation sweep it doesn't yet run.\"@en .\n .\n \"biochemistry\" .\n \"mass-action\" .\n \"ode\" .\n \"petri-net\" .\n \"Enzyme Kinetics: Michaelis-Menten from Three Transitions\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n \"2026-10-06T00:00:00Z\"^^ .\n \"2026-02-14T00:00:00Z\"^^ .\n \"Power-of-2 weights encode lexicographic order over distinct ranks as a single integer. We tried it for poker kicker scoring inside the net and reverted it; the per-card variant we shipped also broke the ordering. Where the encoding belongs, and where it doesn't.\"@en .\n .\n \"encoding\" .\n \"petri-net\" .\n \"poker\" .\n \"technique\" .\n \"weighted-arcs\" .\n \"Exponential Weights in Petri Nets: What Worked, What Didn't, and What's Next\" .\n .\n .\n .\n .\n \"about\" .\n .\n \"2026-07-30T00:00:00Z\"^^ .\n \"2026-07-30T00:00:00Z\"^^ .\n \"A single-player Minecraft world moved to a dedicated server so it could have a chat bridge — plus a closed verb list, a fixed aid ceiling, and a nether hub that separates roof traffic from portal traffic.\"@en .\n .\n \"chat-bridge\" .\n \"mcp\" .\n \"minecraft\" .\n \"provenance\" .\n \"self-hosting\" .\n \"f004 Is Older Than My Daughter\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-05T00:00:00Z\"^^ .\n \"2026-08-22T00:00:00Z\"^^ .\n \"The AI music debate is arguing about the wrong axis: the distinction that matters is structural transparency vs. statistical opacity, and a Petri net — beats.bitwrap.io's generator, linked file by file — is a third kind of generator the discourse keeps missing.\"@en .\n .\n \"beats-bitwrap\" .\n \"formal-methods\" .\n \"generative\" .\n \"music\" .\n \"petri-net\" .\n \"A Generator You Can Read\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-08-22T00:00:00Z\"^^ .\n \"2026-03-16T00:00:00Z\"^^ .\n \"The incidence matrix of an NCAA bracket Petri net connects ODE, Monte Carlo, and analytical methods — and makes simulation redundant. A closed-form formula derived from the bracket topology replaces 150,000 stochastic transitions with 256 exact configurations.\"@en .\n .\n \"incidence-reduction\" .\n \"monte-carlo\" .\n \"ode\" .\n \"petri-nets\" .\n \"stochastic\" .\n \"March Madness Without Monte Carlo\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n \"2026-09-30T00:00:00Z\"^^ .\n \"2026-02-23T21:00:00Z\"^^ .\n \"A draft paper formalizing incidence reduction — the ODE equilibrium of an analysis net is exactly the reciprocal of each entity's constraint count — checked on tic-tac-toe, poker, Connect Four, and Hex, with the tests linked.\"@en .\n .\n \"game-theory\" .\n \"incidence-reduction\" .\n \"ode\" .\n \"paper\" .\n \"petri-nets\" .\n \"Paper: Incidence Reduction via Petri Net ODE Equilibrium\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-04-01T00:00:00Z\"^^ .\n \"2026-02-22T22:30:00Z\"^^ .\n \"ODE steady-state values with uniform rates reveal integer structure — incidence degrees to terminal transitions — giving a reverse-engineering technique for rate constants.\"@en .\n .\n \"game-theory\" .\n \"ode\" .\n \"petri-nets\" .\n \"rate-constants\" .\n \"tic-tac-toe\" .\n \"The Incidence Reduction\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n \"2026-08-22T00:00:00Z\"^^ .\n \"2026-02-15T00:00:00Z\"^^ .\n \"Why JSON-LD's purely declarative semantics and monotonic schema expansion make it reliable infrastructure for composable systems.\"@en .\n .\n \"activitypub\" .\n \"category-theory\" .\n \"infrastructure\" .\n \"json-ld\" .\n \"pflow\" .\n \"JSON-LD as Declarative Infrastructure\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n .\n \"2026-09-29T00:00:00Z\"^^ .\n \"2025-01-03T22:32:10Z\"^^ .\n \"A four-item 0/1 knapsack as a Petri net under mass-action ODEs — why every item stops at 71.4%, what exclusion analysis actually ranks, and where the relaxation falls short of branch-and-bound.\"@en .\n .\n \"ddm\" .\n \"knapsack\" .\n \"ode\" .\n \"optimization\" .\n \"petri-net\" .\n \"Knapsack Model\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-08T00:00:00Z\"^^ .\n \"2026-03-28T00:00:00Z\"^^ .\n \"cell, func, arrow, guard are the structural primitives — but the real ubiquitous language lives in the labels. Like Forth, we build up domain vocabularies on a minimal substrate, and the incidence matrix proves what it can see: conservation, not guards or data.\"@en .\n .\n \"composition\" .\n \"domain-driven-design\" .\n \"dsl\" .\n \"formal-methods\" .\n \"forth\" .\n \"little-languages\" .\n \"petri-net\" .\n \"state-machine\" .\n \"tla-plus\" .\n \"The Little Language Thesis\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n \"2026-08-23T00:00:00Z\"^^ .\n \"2026-08-23T00:00:00Z\"^^ .\n \"A small, fixed alphabet whose local composition rules generate an unbounded, non-repeating space of checkable systems — token standards, business operations, games, music, our own infrastructure. Not one system that swallows every domain. Two tiles, remixed without limit.\"@en .\n .\n \"composition\" .\n \"domain-driven-design\" .\n \"dsl\" .\n \"metamodel\" .\n \"petri-net\" .\n \"A Tiling for Computation\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n \"2026-08-22T00:00:00Z\"^^ .\n \"2026-08-22T00:00:00Z\"^^ .\n \"A declarative vocabulary of composable models that gives you analysis and an app framework from the same artifact. Describe your operation, get a model; play the model as an app; calibrate it with your own data.\"@en .\n .\n \"llm\" .\n \"metamodel\" .\n \"petri-net\" .\n \"sim-pflow-xyz\" .\n \"simulation\" .\n \"what-if-analysis\" .\n \"The Model Is the App\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n \"2026-10-15T00:00:00Z\"^^ .\n \"2026-08-22T00:00:00Z\"^^ .\n \"A sketched phase space for money — three poles (sovereign, commodity, protocol), instruments placed inside as barycentric mixes, two edges labelled with witnesses, and a proposed F ⊣ U between the sovereign and protocol poles.\"@en .\n .\n \"category-theory\" .\n \"money\" .\n \"The Obligation Triangle\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n \"2026-04-01T00:00:00Z\"^^ .\n \"2026-02-18T00:00:00Z\"^^ .\n \"The same math with different labels still produces the same ODE solution. In tic-tac-toe, we see it directly — each board position is a place, and the heatmap is the solution projected onto the grid.\"@en .\n .\n \"equivalence\" .\n \"go-pflow\" .\n \"ode\" .\n \"petri-net\" .\n \"sim-pflow-xyz\" .\n \"Comparing Nets by Their ODE Signatures\" .\n .\n .\n .\n .\n \"about\" .\n .\n .\n \"2026-04-01T00:00:00Z\"^^ .\n \"2024-03-23T15:06:24Z\"^^ .\n \"A poem for Carl Adam Petri, inventor of Petri nets—the mathematical notation for concurrent systems.\"@en .\n .\n \"petri-net\" .\n \"poetry\" .\n \"Ode To Petri\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-22T00:00:00Z\"^^ .\n \"2026-08-22T00:00:00Z\"^^ .\n \"Two people are peers when you can swap them and the net doesn't notice — an automorphism. Cory Doctorow's reverse centaur is that symmetry broken. And only under that symmetry does continuing a protocol count as consent rather than coercion: the ethics of working alongside an LLM reduces to one question — does the agent-swap stay in the automorphism group?\"@en .\n .\n \"agency\" .\n \"asimov\" .\n \"automorphism\" .\n \"formal-methods\" .\n \"group-theory\" .\n \"llm\" .\n \"petri-net\" .\n \"symmetry\" .\n \"Peerage Is an Automorphism\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n \"2026-04-30T00:00:00Z\"^^ .\n \"2026-04-30T00:00:00Z\"^^ .\n \"The runtime is a Petri net — places hold tokens, transitions fire, that's the music. Same genre+seed = byte-identical output. Share URLs are CIDv1; the address is the track.\"@en .\n .\n \"beats-bitwrap\" .\n \"music\" .\n \"petri-nets\" .\n \"A browser music sequencer where every note is a Petri-net transition firing\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n \"2026-08-08T04:45:00Z\"^^ .\n \"2026-03-25T00:00:00Z\"^^ .\n \"A music sequencer built entirely on Petri nets — token rings become drum machines, Euclidean rhythms fall out of the topology, and polyrhythm comes free.\"@en .\n .\n \"beats-bitwrap\" .\n \"music\" .\n \"petri-nets\" .\n \"tone-js\" .\n \"Petri Nets as a Music Sequencer\" .\n .\n .\n .\n .\n \"about\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-09-27T00:00:00Z\"^^ .\n \"2026-02-16T00:00:00Z\"^^ .\n \"The blog's models, concepts, and toolchain have been organized into a book-length guide at book.pflow.xyz.\"@en .\n .\n \"announcement\" .\n \"book\" .\n \"petri-nets\" .\n \"pflow\" .\n \"Petri Nets as a Universal Abstraction — Now a Book\" .\n .\n .\n .\n .\n \"about\" .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-23T00:00:00Z\"^^ .\n \"2026-01-31T00:00:00Z\"^^ .\n \"A tour of sim.pflow.xyz — a catalog of executable Petri-net models you can run, compare and check, from tic-tac-toe to a café to a vet clinic, in the browser or from any MCP client.\"@en .\n .\n \"go-pflow\" .\n \"petri-net\" .\n \"sim-pflow-xyz\" .\n \"simulation\" .\n \"tutorial\" .\n \"Introducing sim.pflow.xyz\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-20T00:00:00Z\"^^ .\n \"2026-04-07T00:00:00Z\"^^ .\n \"One square that collects six earlier posts — the free SMC on a net, the zipper W(M) = 𝓛 × M × 𝓡, and three analyses that read the ρ boundary off the incidence matrix — with what has been checked and what is still only drawn.\"@en .\n .\n \"category-theory\" .\n \"petri-net\" .\n \"tropical-geometry\" .\n \"type-theory\" .\n \"The Pflow Square\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n \"2026-07-06T00:00:00Z\"^^ .\n \"2026-07-06T00:00:00Z\"^^ .\n \"A content-addressed file host where the markdown frontmatter is the metadata of record — schema-first entries, content-addressed lineage, and a search UI that builds itself from whatever fields you wrote.\"@en .\n .\n \"cdn\" .\n \"content-addressing\" .\n \"metadata\" .\n \"provenance\" .\n \"schema-first\" .\n \"cdn.stackdump.com Is a Polydocument Host\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n \"2026-10-26T00:00:00Z\"^^ .\n \"2026-08-02T00:00:00Z\"^^ .\n \"Adding Lean 4 to pflow-polyglot forced a fifth implementation form — the same reachability check is a startup assertion in five languages and a compile-time theorem in the sixth, and the code is line-for-line equivalent.\"@en .\n .\n \"formal-methods\" .\n \"lean\" .\n \"model-checking\" .\n \"petri-net\" .\n \"polyglot\" .\n \"The Proof Form: When a Theorem Is Just Another Port\" .\n .\n .\n .\n .\n \"about\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-09-28T00:00:00Z\"^^ .\n \"2025-11-09T10:00:00Z\"^^ .\n \"Reflecting on old ideas with new tools — from Petri nets to proofs, from Bash scripts to composable universes.\"@en .\n .\n \"announcement\" .\n \"blog-relaunch\" .\n \"category-theory\" .\n \"petri-nets\" .\n \"philosophy\" .\n \"Revisiting the Flows\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-23T00:00:00Z\"^^ .\n \"2026-03-06T00:00:00Z\"^^ .\n \"Why executable formal models matter more with LLMs around, not less — and what the LLM is and isn't trusted with when a Petri net constrains it.\"@en .\n .\n \"formal-methods\" .\n \"llm\" .\n \"modeling\" .\n \"petri-net\" .\n \"sim-pflow-xyz\" .\n \"Small Models > LLMs\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-10T00:00:00Z\"^^ .\n \"2026-08-20T00:00:00Z\"^^ .\n \"A Mastodon thread on formalizing Dirac deltas as algebraic effects, read through the pflow lens — the same refusal to posit an object, the same check-after-the-fact discipline, and a question about whether the predicate future is an effect rather than a value.\"@en .\n .\n \"algebraic-effects\" .\n \"category-theory\" .\n \"incidence-matrix\" .\n \"petri-net\" .\n \"tropical-geometry\" .\n \"Structuralism, Not Objects: Dirac Deltas, Algebraic Effects, and Why C Comes First\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n .\n \"2026-10-17T00:00:00Z\"^^ .\n \"2025-11-28T00:00:00Z\"^^ .\n \"A 4×4 Sudoku as a Petri net in the tic-tac-toe pattern — cells, digit moves with history, constraint collectors into a solved place — checked against the go-pflow generator, which shows the collectors as built can never fire and the ODE ranking is not yet demonstrated.\"@en .\n .\n \"ddm\" .\n \"ode\" .\n \"petri-net\" .\n \"sudoku\" .\n \"Sudoku Petri-Net Model\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-01T00:00:00Z\"^^ .\n \"2026-03-09T00:00:00Z\"^^ .\n \"A Petri net generates a free symmetric monoidal category — places give the objects, transitions the generating morphisms. What that theorem buys for composition, analysis and proofs across this blog, and which of the connections are still a shape match rather than a checked result.\"@en .\n .\n \"category-theory\" .\n \"composition\" .\n \"open-games\" .\n \"petri-net\" .\n \"pflow\" .\n \"symmetric-monoidal\" .\n \"Symmetric Monoidal Categories: The Structure Underneath\" .\n .\n .\n .\n .\n \"about\" .\n .\n \"2026-04-01T00:00:00Z\"^^ .\n \"2026-01-25T12:00:00Z\"^^ .\n \"A minimal blog platform with ActivityPub federation. Markdown files, a Go binary, JSON for state. No database required.\"@en .\n .\n \"activitypub\" .\n \"federation\" .\n \"fediverse\" .\n \"go\" .\n \"tens-city\" .\n \"tens-city v0.8: A Federated Blog in 500 Lines\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-04-04T00:00:00Z\"^^ .\n \"Execution state is a zipper — the present moment is not a parameter or a modality but a universe that separates tropical past from predicate future. Tic-tac-toe makes the structure visible.\"@en .\n .\n \"category-theory\" .\n \"petri-net\" .\n \"tic-tac-toe\" .\n \"tropical-geometry\" .\n \"type-theory\" .\n \"The Zipper Whose Hole Is a Universe\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-12T00:00:00Z\"^^ .\n \"2026-01-31T00:00:00Z\"^^ .\n \"The five-seat Hold'em tutorial net (18 places, 32 transitions) read against its source — phase places, turn tokens, a dealer role and an event log, plus what the net leaves to code (chips, guards, re-raises) and one bug in how seats re-enter a hand.\"@en .\n .\n \"event-sourcing\" .\n \"game\" .\n \"petri-net\" .\n \"state-machine\" .\n \"Texas Hold'em Model\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n \"2026-08-25T00:00:00Z\"^^ .\n \"2025-11-13T00:00:00Z\"^^ .\n \"Modeling tic-tac-toe using Petri nets with ODE simulation for AI move selection—no game heuristics, just model topology.\"@en .\n .\n \"game\" .\n \"tic-tac-toe\" .\n \"Tic-Tac-Toe Model\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-08-22T00:00:00Z\"^^ .\n \"2026-01-25T00:00:00Z\"^^ .\n \"Four terms — cell, func, arrow, guard — generate a free symmetric monoidal category. The DSL is a categorical language for executable token models.\"@en .\n .\n \"category-theory\" .\n \"dsl\" .\n \"go-pflow\" .\n \"guards\" .\n \"invariants\" .\n \"petri-net\" .\n \"The Token Language\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-14T00:00:00Z\"^^ .\n \"2026-03-10T00:00:00Z\"^^ .\n \"Timed event graphs are max-plus linear and ReLU networks are tropical rational, so the two meet over the tropical semiring. This post covers what those two theorems give us, what pflow-tropical checks in code, and how far the Petri-net/neural-net analogy has actually been earned.\"@en .\n .\n \"category-theory\" .\n \"neural-networks\" .\n \"petri-net\" .\n \"tropical-geometry\" .\n \"Tropical Petri Nets\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-23T00:00:00Z\"^^ .\n \"2026-03-08T00:00:00Z\"^^ .\n \"Describe your business to an LLM, get a simulation you can actually play with — adjust staffing, change demand, and watch the numbers move. Revised to say which vet-clinic results the tests actually check, and that the coffee shop runs out of milk, not cups.\"@en .\n .\n \"capacity\" .\n \"llm\" .\n \"petri-net\" .\n \"simulation\" .\n \"what-if-analysis\" .\n \"Skip the Spreadsheet: What-If Analysis with Petri Nets\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n .\n .\n .\n \"2026-10-13T00:00:00Z\"^^ .\n \"2026-02-23T18:00:00Z\"^^ .\n \"Incidence reduction applied to poker in one pflow-rs example — hand-category values come out of the ODE as 1/drains over hand-picked drain counts, every game action is Groth16-proven, the shuffle is a Poseidon commit-reveal, and the generated contract still trusts the showdown.\"@en .\n .\n \"game\" .\n \"integer-reduction\" .\n \"petri-net\" .\n \"poker\" .\n \"zk-proofs\" .\n \"ZK Hold'em: Poker Hand Ranking from Network Topology\" .\n .\n .\n .\n .\n \"concepts\" .\n .\n .\n .\n .\n .\n .\n .\n \"2026-08-22T00:00:00Z\"^^ .\n \"2026-02-14T00:00:00Z\"^^ .\n \"How gnark circuits prove that a Petri net transition is valid without revealing the state—MiMC hashing, topology-based constraints, and Groth16 proofs.\"@en .\n .\n \"cryptography\" .\n \"gnark\" .\n \"groth16\" .\n \"petri-net\" .\n \"zero-knowledge\" .\n \"Zero-Knowledge Proofs for Petri Nets\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n .\n .\n \"2026-10-25T00:00:00Z\"^^ .\n \"2026-03-19T00:00:00Z\"^^ .\n \"Anonymous polls in bitwrap-io: a small Petri net whose cast-vote transition carries a Groth16 proof of registry membership, nullifier and range — and what the current code does about secrecy after the poll closes.\"@en .\n .\n \"gnark\" .\n \"governance\" .\n \"groth16\" .\n \"petri-net\" .\n \"solidity\" .\n \"voting\" .\n \"zk\" .\n \"ZK Polls: Voting as a Visible State Machine\" .\n .\n .\n .\n .\n \"models\" .\n .\n .\n .\n \"2026-04-01T00:00:00Z\"^^ .\n \"2026-01-31T00:00:00Z\"^^ .\n \"Zero-knowledge proofs meet Petri nets—cryptographically verify valid game moves without revealing strategy using gnark circuits.\"@en .\n .\n \"cryptography\" .\n \"gnark\" .\n \"petri-net\" .\n \"zero-knowledge\" .\n \"ZK Tic-Tac-Toe Model\" .\n .\n .\n .\n .\n \"stackdump blog\" .\n .\n .\n .\n .\n .\n \"Appendix A: Solver Parameter Reference\" .\n .\n .\n .\n .\n .\n \"Appendix B: Token Language Grammar\" .\n .\n .\n .\n .\n .\n \"Appendix C: JSON Schema Reference\" .\n .\n .\n .\n .\n .\n \"Appendix D: Glossary\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"Appendix E: Categorical Foundations\" .\n .\n .\n .\n .\n .\n \"Why Petri Nets?\" .\n \"1\"^^ .\n .\n .\n .\n .\n .\n .\n .\n \"The Mathematics of Flow\" .\n \"2\"^^ .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"From Discrete to Continuous\" .\n \"3\"^^ .\n .\n .\n .\n .\n .\n .\n \"The Token Language\" .\n \"4\"^^ .\n .\n .\n .\n .\n .\n \"Resource Modeling — The Coffee Shop\" .\n \"5\"^^ .\n .\n .\n .\n .\n .\n .\n .\n .\n \"Game Mechanics — Tic-Tac-Toe\" .\n \"6\"^^ .\n .\n .\n .\n .\n .\n .\n \"Constraint Satisfaction — Sudoku\" .\n \"7\"^^ .\n .\n .\n .\n .\n .\n \"Optimization — The Knapsack Problem\" .\n \"8\"^^ .\n .\n .\n .\n .\n .\n \"Biochemistry — Enzyme Kinetics\" .\n \"9\"^^ .\n .\n .\n .\n .\n .\n \"Complex State Machines — Texas Hold'em\" .\n \"10\"^^ .\n .\n .\n .\n .\n .\n \"Process Mining\" .\n \"11\"^^ .\n .\n .\n .\n .\n .\n .\n .\n .\n \"Zero-Knowledge Proofs\" .\n \"12\"^^ .\n .\n .\n .\n .\n .\n \"Topology-Driven Verification\" .\n \"13\"^^ .\n .\n .\n .\n .\n .\n \"On-Chain ZK Verification\" .\n \"14\"^^ .\n .\n .\n .\n .\n .\n \"Exponential Weights and Scoring Systems\" .\n \"15\"^^ .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"Declarative Infrastructure\" .\n \"16\"^^ .\n .\n .\n .\n .\n .\n \"The Visual Editor — pflow.xyz\" .\n \"17\"^^ .\n .\n .\n .\n .\n .\n \"sim.pflow.xyz — From Description to Checked Model\" .\n \"18\"^^ .\n .\n .\n .\n .\n .\n \"The go-pflow Library\" .\n \"19\"^^ .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"Dual Implementation and Verification\" .\n \"20\"^^ .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n \"Epilogue: What the Abstraction Sits On\" .\n \"21\"^^ .\n .\n .\n .\n .\n .\n \"Preface\" .\n .\n .\n .\n .\n \"Petri Nets as a Universal Abstraction\" .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n .\n 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.\n_:ead84e6bd5dec5c7dd6c373619e2d0aa _:e818eaab2c680fe14af2685f39ddfc7e .\n_:f0967051c429bd3c9c8ffa5ab5af4fc5 .\n_:f0967051c429bd3c9c8ffa5ab5af4fc5 _:e844db268f360c81476f53b5dda7980b .\n_:f73a125f20c842b678594295dd227709 .\n_:f73a125f20c842b678594295dd227709 .\n_:f73a125f20c842b678594295dd227709 .\n_:fe34848a6d394ab538a5fd14d4055c8b .\n_:fe34848a6d394ab538a5fd14d4055c8b \"true\"^^ .\n_:fe34848a6d394ab538a5fd14d4055c8b .\n_:ff90a24c328bad93a8886e10ef32f681 .\n_:ff90a24c328bad93a8886e10ef32f681 _:f0967051c429bd3c9c8ffa5ab5af4fc5 .\n" }