A draft paper formalizing incidence reduction — extracting exact strategic values from game topologies — validated on tic-tac-toe, poker, Connect Four, and Hex.
Applying incidence reduction to poker — hand strength values emerge from Petri net drain structure, every action is Groth16-proven, and the shuffle uses Poseidon commit-reveal.
ODE steady-state values with uniform rates reveal integer structure — incidence degrees to terminal transitions — giving a reverse-engineering technique for rate constants.
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.
The blog's models, concepts, and toolchain have been organized into a book-length guide at book.pflow.xyz.
Why JSON-LD's purely declarative semantics and monotonic schema expansion make it reliable infrastructure for composable systems.
Reflections from an AI collaborator on building with Petri nets—what makes this approach different, and why it keeps surprising me.
Four places, three transitions, and mass-action kinetics produce the classic Michaelis-Menten saturation curve automatically—no equations required.
Power-of-2 arc weights can encode lexicographic order as a single integer. We tried it for poker kicker scoring—and then removed it. Here's why the encoding is valuable even though the application was wrong.
How gnark circuits prove that a Petri net transition is valid without revealing the state—MiMC hashing, topology-based constraints, and Groth16 proofs.
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.
Resource modeling with Petri nets — weighted arcs encode recipes, conservation laws guarantee integrity, and ODE simulation predicts when you'll run out of cups.
Interactive tutorials for learning Petri nets—from tic-tac-toe basics to complex multi-player games, with model-driven code generation.
Modeling multi-player poker with Petri nets—state machines, role-based access, guards, and event sourcing for complex game logic.
Zero-knowledge proofs meet Petri nets—cryptographically verify valid game moves without revealing strategy using gnark circuits.
A minimal blog platform with ActivityPub federation. Markdown files, a Go binary, JSON for state. No database required.
An interpreted language for Petri net token models with guards, invariants, and data state semantics.
Modeling Sudoku as a Petri net with ODE simulation—constraint satisfaction through token flow.
Modeling tic-tac-toe using Petri nets with ODE simulation for AI move selection—no game heuristics, just model topology.
Reflecting on old ideas with new tools — from Petri nets to proofs, from Bash scripts to composable universes.