tropical-semiring.md

tropical PCS the (min,+) PCS backend for zheng. optimization workloads (shortest path, assignment, Viterbi, transport) prove natively through their algebraic structure. the tropical semiring has no additive inverse — min(a,b) cannot be undone — so the PCS delegates commitment to Brakedown (PCS₁)…

tropical-semiring jets — tropical (min,+) five jets for (min,+) semiring operations. optimization, assignment, decoding. no separate nox instantiation — tropical operations decompose to existing patterns (branch + lt). jets accelerate common compositions. proved via Assayer (tropical…

the tropical semiring: min replaces + the tropical semiring replaces addition with min and multiplication with ordinary addition. the result is an algebraic structure that encodes optimization — shortest paths, minimum cost flows, scheduling — as linear algebra. trop exists because this encoding…