# stackdump — blog.stackdump.com > Matt York's technical blog: Petri nets as a universal abstraction for > state machines, workflows, games, and token systems — with category > theory, ODE analysis, and zero-knowledge proofs as the supporting cast. > Every model described here is executable; most link to live demos in the > pflow ecosystem (pflow.xyz editor, pilot.pflow.xyz MCP tools, > book.pflow.xyz). Posts are served at `/posts/`. Machine-readable indexes: [RSS](https://blog.stackdump.com/feed.xml), [sitemap](https://blog.stackdump.com/sitemap.xml), [JSON-LD post index](https://blog.stackdump.com/posts/index.jsonld). The blog federates via ActivityPub as `@myork@blog.stackdump.com`. ## Start here - [Small Models > LLMs](https://blog.stackdump.com/posts/small-models-not-llms): why executable formal models matter in the age of AI — LLMs become most useful when constrained by them - [Petri Nets as a Universal Abstraction — Now a Book](https://blog.stackdump.com/posts/petri-nets-book): the blog's models and toolchain organized into a book at book.pflow.xyz - [Code-to-Flow: Turn Anything into a Petri Net](https://blog.stackdump.com/posts/code-to-flow): paste code in any language, get a validated Petri net you can simulate - [Declarative Differential Models (DDM)](https://blog.stackdump.com/posts/declarative-differential-models): describe behavior declaratively, encode it directly in ODEs ## Petri nets, ODEs, and analysis - [The Incidence Reduction](https://blog.stackdump.com/posts/integer-reduction): ODE steady states with uniform rates reveal integer incidence structure - [Paper: Incidence Reduction via Petri Net ODE Equilibrium](https://blog.stackdump.com/posts/integer-reduction-paper): the draft paper — exact strategic values from game topology, validated on tic-tac-toe, poker, Connect Four, and Hex - [March Madness Without Monte Carlo](https://blog.stackdump.com/posts/incidence-bridge): a closed-form bracket formula replaces 150,000 stochastic transitions - [Comparing Nets by Their ODE Signatures](https://blog.stackdump.com/posts/ode-signatures) - [Enzyme Kinetics: Michaelis-Menten from Three Transitions](https://blog.stackdump.com/posts/enzyme-kinetics-model) - [Coffee Shop Model](https://blog.stackdump.com/posts/coffeeshop-model): weighted arcs as recipes, conservation laws, stockout prediction - [Skip the Spreadsheet: What-If Analysis with Petri Nets](https://blog.stackdump.com/posts/what-if-analysis) - [Tic-Tac-Toe Model](https://blog.stackdump.com/posts/tic-tac-toe-model) · [Texas Hold'em Model](https://blog.stackdump.com/posts/texas-holdem-model) · [Sudoku](https://blog.stackdump.com/posts/sudoku-petri-net-model) · [Knapsack](https://blog.stackdump.com/posts/knapsack-model) ## Category theory and foundations - [Symmetric Monoidal Categories: The Structure Underneath](https://blog.stackdump.com/posts/symmetric-monoidal-categories): Petri nets are morphisms in an SMC — the theorem, not the analogy - [The Pflow Square](https://blog.stackdump.com/posts/pflow-square): adjunction F ⊣ U, zipper comonad, three analyses converging - [Tropical Petri Nets](https://blog.stackdump.com/posts/tropical-petri-nets): Petri nets, ReLU networks, and tropical algebra share one structure - [The Zipper Whose Hole Is a Universe](https://blog.stackdump.com/posts/tense-type-theory) - [Brouwer Ordinals and the Shape of a Witness](https://blog.stackdump.com/posts/alpha-decidability-past-tense) - [Earned Compression](https://blog.stackdump.com/posts/earned-compression): ODE, tropical, and ZK analyses discover the same structural boundary - [The Token Language](https://blog.stackdump.com/posts/token-language) · [The Little Language Thesis](https://blog.stackdump.com/posts/little-language-thesis) · [Categorical Net Types](https://blog.stackdump.com/posts/categorical-net-types) · [The Category Settle](https://blog.stackdump.com/posts/category-settle) - [The Proof Form: When a Theorem Is Just Another Port](https://blog.stackdump.com/posts/proof-form): the same reachability check in five languages and one Lean 4 theorem ## Zero-knowledge proofs - [Zero-Knowledge Proofs for Petri Nets](https://blog.stackdump.com/posts/zk-petri-nets): gnark circuits prove a transition valid without revealing state - [Bitwrap: Petri Nets as ZK Containers](https://blog.stackdump.com/posts/bitwrap-capstone): from OP_RETURN in 2014 to zero-knowledge Petri nets - [Building ZK Poker: Four Petri Nets and a Branchless Circuit](https://blog.stackdump.com/posts/building-zk-poker): heads-up hold'em at stackedup.gg, commit-reveal shuffles, Groth16 - [ZK Hold'em: Poker Hand Ranking from Network Topology](https://blog.stackdump.com/posts/zk-holdem) - [ZK Tic-Tac-Toe](https://blog.stackdump.com/posts/zk-tic-tac-toe-model) · [ZK Polls: Voting as a Visible State Machine](https://blog.stackdump.com/posts/zk-polls-voting-as-state-machine) - [Exponential Weights in Petri Nets](https://blog.stackdump.com/posts/exponential-scoring): what worked, what didn't, and why the encoding outlived the application ## Music from Petri nets - [Petri Nets as a Music Sequencer](https://blog.stackdump.com/posts/petri-net-sequencer): token rings become drum machines; polyrhythm comes free - [A browser music sequencer where every note is a transition firing](https://blog.stackdump.com/posts/petri-net-runtime): same genre+seed = byte-identical output; the CID is the track - [beats.bitwrap.io is a Jambox Now](https://blog.stackdump.com/posts/beats-launch-jambox) · [38 days of beats.bitwrap.io](https://blog.stackdump.com/posts/beats-evolution) - [A Generator You Can Read](https://blog.stackdump.com/posts/generator-you-can-read): structural transparency vs. statistical opacity — the axis the AI music debate keeps missing ## Systems, tools, and essays - [Introducing Petri-Pilot](https://blog.stackdump.com/posts/petri-pilot): interactive tutorials + model-driven code generation (pilot.pflow.xyz) - [tens-city v0.8: A Federated Blog in 500 Lines](https://blog.stackdump.com/posts/tens-city-release): the platform this blog runs on — markdown, Go, ActivityPub, no database - [cdn.stackdump.com Is a Polydocument Host](https://blog.stackdump.com/posts/polydocument-host): content-addressed hosting where frontmatter is the metadata of record - [JSON-LD as Declarative Infrastructure](https://blog.stackdump.com/posts/json-ld-declarative-infrastructure) - [Peerage Is an Automorphism](https://blog.stackdump.com/posts/peerage-invariant): peer-ness as a net automorphism, and what that means for working with LLMs - [The Obligation Triangle](https://blog.stackdump.com/posts/obligation-triangle): a phase space for money — sovereign, commodity, protocol - [f004 Is Older Than My Daughter](https://blog.stackdump.com/posts/f004): a long-lived Minecraft world, a chat bridge, and a closed verb list - [A Circuit's-Eye View](https://blog.stackdump.com/posts/a-circuits-eye-view): notes from an AI collaborator inside the loop ## Related sites - [pflow.xyz](https://pflow.xyz/llms.txt): the visual Petri net editor and embeddable ES module library (has its own llms.txt) - [book.pflow.xyz](https://book.pflow.xyz): the book-length guide - [pilot.pflow.xyz/mcp](https://pilot.pflow.xyz/mcp): MCP server with analysis and codegen tools (petri_ode, petri_validate, petri_codegen, …) - [beats.bitwrap.io](https://beats.bitwrap.io) · [bitwrap.io](https://bitwrap.io) · [stackedup.gg](https://stackedup.gg)