-
Brouwer Ordinals and the Shape of a Witness
de Jong et al. (2026) put an ordinal axis under decidability. That axis is past-tense, and Brouwer ordinals are the scalar specialization of our vector tropical past.
-
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.
-
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.
-
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.
-
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.