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The Obligation Triangle
A phase space for money — three poles (sovereign, commodity, protocol), edges as couplings with witnesses, interior positions as instruments.
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Structuralism, Not Objects: Dirac Deltas, Algebraic Effects, and Why C Comes First
A Mastodon thread on formalizing Dirac deltas as algebraic effects, read through the pflow lens — the same refusal to posit an object, the same check-after-the-fact discipline, and a question about whether the predicate future is an effect rather than a value.
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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 sub-SMC of open Petri nets. The core-observer split is really two boundaries — an algebraic one (ρ) inside the incidence matrix and a categorical one (contextual arcs) outside it — and a ZK circuit dissolves only the second.
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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.
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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.