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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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Paper: Incidence Reduction via Petri Net ODE Equilibrium
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.
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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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Comparing Nets by Their ODE Signatures
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.
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Enzyme Kinetics: Michaelis-Menten from Three Transitions
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.
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Coffee Shop Model
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.
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Sudoku Petri-Net Model
Modeling Sudoku as a Petri net with ODE simulation—constraint satisfaction through token flow.
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Declarative Differential Models (DDM)
A modeling approach where system behavior is described declaratively and encoded directly in differential equations.
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Knapsack Model
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.