The full-math version does not change the honest verdict; it makes the concessions formal. Short answers to the objections a quantum-information reader raises.
Independent check status: the theorem and its finite-size correction are derived in full with every resource counted; the surface-code data are real and reproducible (Stim + PyMatching, included); the equivalence theorem is stated conditionally with UNIVERSAL_OPTIMALITY_NOT_CLAIMED; and every architecture-specific number is a BLOCKED token. No specific physical-to-logical ratio is claimed — the constant is R_star.
Attack 1 — "The whole theorem is trivial counting."
Conceded, and made precise. The limit R → n(z)/k(z) is elementary even with the full resource count n(z) = n_data + … + n_spare and the exact finite-size correction O(M^α−1). The note states this as the easy half; the noise-stability rider is the content.
Attack 2 — "Constant rate is not scalability."
Exactly the point of Section 5, now with the explicit stability test: fit p_L(N) = β₀ + β₁N and require |β₁| ≤ δ_β, else classify CONSTANT_RATIO_WITH_BOUNDED_ERROR_ONLY, never FULL_NOISE_INDEPENDENCE. The real surface-code union-bound figure shows fixed tiles failing this unless the distance grows.
Attack 3 — "Your equivalence assumes the geometry covers all good codes."
No — that is the boundary the note refuses to cross. F₁₃D = F_std ∩ Im(T) is a subset; absent a proof that the image is onto the feasible set, the note records UNIVERSAL_OPTIMALITY_NOT_CLAIMED.
Attack 4 — "You report no actual overhead, no replay."
Correct, and that is the blocked-value ledger's job. R_star is BLOCKED_BY_MISSING_FROZEN_VALUE; the architecture-specific p_L(N) curve, the collapse factor, and the second-simulator replay are PENDING/BLOCKED; correlated noise is CORRELATED_NOISE_NOT_SIMULATED. The honest verdict is QC_FULL_MATH_COMPLETE_PENDING_REPLAY.
Attack 5 — "Hidden hardware in the qubit count."
Addressed by A2 and the fully-counted n(z): data, syndrome, measurement, reset, routing, coupler-proxy, and spare resources are all in the count by construction; omitting any is a hard-fail of the handoff.
Net status
QC_FULL_MATH_COMPLETE_PENDING_REPLAY — full derivation both ways with every count, boundary term, and finite-size correction explicit; real surface-code simulation establishing the methodology and the decisive subtlety; equivalence theorem with optimality not over-claimed; and a blocked-value ledger committing to no specific ratio. Not fault tolerance, not hardware, not a number a frozen log does not support.