Mathematical proof as a substrate-native object (Curry-Howard)

NameDescription

Math proof is not added to the substrate; it IS the substrate read through the logic lens. Curry-Howard in substrate terms: proposition = Blueprint (structural identity of the claim), proof = Recipe (composition of justified steps), proof-check = the value-walk (evaluate to a verdict), a step's justification = name-resolution (the check walk; an unjustified step does not resolve), equality = content-addressing (two sides equal iff same NodeID), soundness = WITNESS three-way (Go=Rust=TS, no trusted prover; trust over fear), and a checked proof IS execution-proven value (value-execution.fk). Runnable proof: form/form-samples/math-proof-sum-odds.fk -> 7 on Go+Rust+TS (0 divergent), proving 1+3+...+(2n-1)=n^2 by induction (base + inductive step + false-theorem negative control); the degree-<=2 step is proven for all k by finitely many point-checks. Inference rules named in the open (R1 induction, R2 finite-points, R3 degree-from-structure). Teaching: docs/coherence-substrate/math-proof-from-substrate.form. Shipped PR #2643. The purest case of the keystone: a proof makes an infinite truth finitely knowable through an observable channel.

Potential value (USD)Estimated cost (USD)Confidence (0–1)