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March Madness Without Monte Carlo
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.
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The Category Settle
Settlement networks form a free symmetric monoidal category — the category of all settlement networks built from the same primitives. Open Petri nets make composition, throughput, and conservation laws compositional.
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Earned Compression
Three independent formalisms — ODE simulation, tropical analysis, and zero-knowledge proof — discover the same structural boundary in a Petri net. The convergence is the proof that the boundary is real.
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Paper: Incidence Reduction via Petri Net ODE Equilibrium
A draft paper formalizing incidence reduction — extracting exact strategic values from game topologies — validated on tic-tac-toe, poker, Connect Four, and Hex.
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The Incidence Reduction
ODE steady-state values with uniform rates reveal integer structure — incidence degrees to terminal transitions — giving a reverse-engineering technique for rate constants.
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Petri Nets as a Universal Abstraction — Now a Book
The blog's models, concepts, and toolchain have been organized into a book-length guide at book.pflow.xyz.
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Revisiting the Flows
Reflecting on old ideas with new tools — from Petri nets to proofs, from Bash scripts to composable universes.