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The Pflow Square
One commutative square encoding the full categorical structure — the adjunction F ⊣ U, the zipper comonad W = UF, and the convergence of three analyses on a single structural boundary.
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The Zipper Whose Hole Is a Universe
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.
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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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Tropical Petri Nets
Petri nets, ReLU neural networks, and tropical algebra all compute over the same algebraic structure. Tropical algebra is the formalism that makes this precise.
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Symmetric Monoidal Categories: The Structure Underneath
Petri nets are morphisms in a symmetric monoidal category. This isn't an analogy — it's the theorem that explains why composition, analysis, and proofs all work the way they do.
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JSON-LD as Declarative Infrastructure
Why JSON-LD's purely declarative semantics and monotonic schema expansion make it reliable infrastructure for composable systems.
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Categorical Net Types
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.
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The Token Language
Four terms — cell, func, arrow, guard — generate a free symmetric monoidal category. The DSL is a categorical language for executable token models.