Spacetime and Feynman diagrams are dismissed at the outset.
What remains is a punctured disk, non-crossing curves upon it, and their edge-length coordinates uij.
The amplitude arises at once as an integral over the combinatorial polytope carved by u ≥ 0 — no diagram sum, no perturbative expansion.
Runtime state and evaluation order are dismissed at the outset.
What remains is an expression tree, signs + / − / 0 pinned to its nodes, and the combinatorial relations of coproduct ⊙ and product ,.
The program's meaning is read out before execution: 2629 → 2205 instructions, 2 min → a few milliseconds — established by proof, not by run.
((a,b),c)(a,b),c ↦ a,(b,c)uij+ / − / 0uij = ∏ (1−ukl)sign(f g) = sign f · sign guij ≥ 0⊙ (interpunct),u₁₃, u₁₄. A flip to the dashed diagonals is a combinatorial transition between covers of the same structure — not a time evolution.
⊙ nodes are the curve coproduct; gold , nodes are the product; the leaf signs + / − / 0 correspond to the boundary values of uij.
Surfaceology extracts the scattering amplitude from the positive region of a combinatorial polytope of non-crossing curves on a disk — bypassing spacetime, propagators, and loop summation. Gauge choices and perturbative expansions are not paths that constitute the answer; they are maps that merely cover it.
Sign extracts a program's meaning from the consistent region of combinatorial relations between the signs + / − / 0 pinned on its expression tree — bypassing evaluation order, runtime branching, and garbage collection. Test runs and iterative type-inference are not paths that constitute the answer; they are maps that merely cover it.
What is common to both is the demand itself: the reading is static. Under two vocabularies — physics and language — the same single epistemology is being repeated.