A Single-Orbit Bridge Lemma for the Riemann Hypothesis: Localizing NBBD Boundary Defects to a Cross-Orbit Orthogonality Condition (Montgomery-Grade)

v3 (2026-07-12) — register-honesty update of the single-orbit bridge lemma. Concept-DOI (always resolves to latest): 10.5281/zenodo.20601020. Two substantive corrections, both strengthening the note rather than retracting, from an independent three-node review:

1. Theorem 1 is upgraded to a pointwise, threshold-free strict inequality |A_O(x)|² < |2S_O(x)|² for every x > 0 (no threshold X₀). The v2 proof's description of the cross term as “oscillatory” is corrected: because σ fixes γ, ρ+conj(ρ̃)=1 exactly, so the cross term is non-oscillatory with strictly positive real part. Appendix A (the oscillatory X₀ threshold) is thereby superseded.
2. An explicit caveat records that the terminal variance threshold V(X) ≪ X^{2+ε} is RH-equivalent, so the variance route must not be presented as reducing RH to a weaker standard hypothesis.

Proposition 1 and the §1 unconditional core are unchanged. The remaining obstruction is the cross-orbit orthogonality of the {S_O} — a Schur-complement lower bound of Montgomery-grade difficulty, conjecturally implied by Montgomery-type spacing genericity (not proven equivalent). This is a conditional structural result with an unconditionally-proven single-orbit core; it is not a proof of the Riemann Hypothesis.

The two v3 corrections were derived independently by Fable-5 (Anthropic) and GPT-5.6 Sol (OpenAI) — two frontier models from different laboratories, run with no shared context, which converged — together with the fleet reasoner, which supplied the two-directional proof of the V(X) RH-equivalence. The mathematics is the human author's responsibility; AI systems are contributors, not authors of record.

Version lineage: v1 2026-06-08 (10.5281/zenodo.20601021); v2 2026-06-20 (10.5281/zenodo.20773126); v3 2026-07-12 (this version).