Passes 4253–4260: corrected atlas

Current semantic certificate 3288f5e40029f4742d40f8349de820cd4b3677f1e944838ee1f234ae438fcc40.

4253 — retracted by Pass 4329

The stored Z2731 assignment has the base eight-cycle (3,52,4,48,8,66,18,53) with signed voltage sum 1328−542+801−1587 = 0 mod 2731. Its lift therefore has girth exactly 8, not at least 16. The historical vector is retained as a falsifier, not a green cover certificate.

4254 — fault-aware holonomic CZ model

Oppositely oriented latitude loops give φ(δ)=π cos δ, cancelling first-order common polar calibration error. The finite bright-state model does not establish fault tolerance.

4255 — metastable population spectrum

The coexistence Fokker–Planck population-generator gap converges to 4.37527×10−8; this is not a full density-matrix Liouvillian certificate.

4256 — architecture-scoped 45-auxiliary clock

Within the frozen shared-condition architecture, 13 pair ancillas + 24 final conditions + 8 reused flags gives 45 auxiliaries. No global optimum over all three-local clock encodings is claimed.

4257 — full 19-mode communication bounds

The baseline effective outside-signal channel has τ=0.2830095941. In 512 frozen disorder samples, 510 have τ≤1/2, two exceed one half, and none is entanglement breaking. Unrestricted capacity of the two high-τ cases remains open.

4258–4259 — finite spectral and modular results

The exact normalized spectral-form-factor plateau is 0.3209375. The point–line harmonic entanglement Hamiltonian has two finite modular energies, 2.63391579385 (×1) and 4.03202440074 (×24), plus 15 spectators.

4260 — conditional tree calculation

For a degree-four tree, vmax=2√3J and B(r)=2·3r−1. The 4,373-node radius-seven ball requires a girth-at-least-16 cover and is not realized by the retracted Pass 4253 lift. It is not a strict Lieb–Robinson velocity or physical c.

Boundary: surviving statements are finite holonomic, stochastic, clock, Gaussian-channel, spectral, modular, or conditional tree-model results.