This manuscript develops Bottleneck Inversion Theory (BIT) as a mathematical framework for certifying protocol-relative, intervention-unlockable potential. Rather than treating potential as an absolute latent property, the theory represents it as a vector-valued, unit-typed lower-bound object whose coordinates are reported only when supported by compatible evidence, resource ledgers, and witness certificates. The framework formalizes stopped evidence sheaves, task-local deficiency audits, mechanism-factorized null channels, exactness-certified release duality, unseen-frontier discovery, cross-validated anchor transfer, dynamic-regime acceleration, and CEGAR-style simulation barriers. A central contribution is a single-source machine-readable LaTeX architecture: the manuscript embeds stable theorem identifiers, claim records, witness schemas, dependency relations, unit ledgers, and citation DOI records directly in the TeX file. This makes the work suitable for both human mathematical review and automated extraction of claims, assumptions, dependencies, and cited formal objects. The theory is positioned at the intersection of mathematical certification, causal inference, time-uniform evidence, optimal transport, stochastic process analysis, formal verification, and capability evaluation.