Generated Gates Inherit Their Generator's Blind Spots: A Diversity Floor for Self-Generated Verification

A representation-theoretic account of why gates generated by a model family inherit that family's blind spots. Modeling a gate by the indistinguishability relation of its underlying family F — with stealth set Σ_F of faults the family cannot separate from acceptable artifacts — the paper proves: (GG1, inheritance) any gate constructed within F has a blind set containing Σ_F, so a generated gate cannot do better than the family it is built from; and (GG2, self-generation floor) a closed system that generates its own gates from a single founding family has an escape floor exactly λ_F, a fixed point invariant to generation depth, recursion, and prompt diversity. The floor is lowerable only by an exogenous distinction source: a genuinely different family, whose independent stealth set multiplies the floor down to λ_F·λ_N, or a reality-grounded gate that consults ground truth rather than any family's representation and is the unique non-representational escape. The results generalize the classical theory of coincident failures in N-version programming to the regime where the versions and their checkers are produced from within one representational family. Identifies the self-generation floor as the origin of the stealth mass that caps reliable horizon in long-horizon agentic work (companion: https://doi.org/10.5281/zenodo.20820968). Includes a self-contained Python simulation reproducing all numerical results in Table 1.