Triad-Guided Proof Techniques: A Practical Protocol for Identity, Distinction, and Binding in Long Derivations

A proof protocol that prevents drift, degeneracy, and sprawl using Triad Logic gates. This paper introduces Triad-Guided Proof Techniques: a practical protocol for building and auditing long mathematical and technical derivations using Triad Logic (TL) as a normative constraint scaffold. Each non-trivial proof move is accepted only if it passes three gates simultaneously: Identity (constraint preservation), Distinction (degeneracy resistance via adversarial unit tests), and Binding (goal-connected progress). The paper formalizes a proof state S = (Gamma, Delta, G, D) where D is a dependency graph that tracks which claims support which goals. It defines the Triad Step Certificate (TSC) as a step-level acceptance criterion, and it introduces proof telemetry measures for tracking proof debt (open obligations, orphan lemmas, and goal-distance). A copy/paste Proof Audit Log template is included so that proofs can be certified, reproducible, and easier to review. The result is an engineering-style toolkit for preventing meaning drift, trivial collapses, and irrelevant lemma sprawl while improving auditability and reuse.