Classification: exact identities, proved implications, and open input. No new interval certificate, positive window, arithmetic sign estimate, API, uniform floor, G2, or RH proof.
The total near-radical lemma detects every negative bounded perturbation. Every nonzero finite change to the prime-shift coefficients has negative directions in both parities, hence negative compact tests for the altered complete forms. The altered family has finite first-zero windows and retains the corresponding support geometry and modified affine-potential equation. It does not retain the original arithmetic near-radical identity.
For a fixed coefficient pattern scaled by epsilon, the v1.53 residual gives
an analytic first-zero upper bound lambda_* = O(sqrt(log(1/epsilon))).
Constants depend on the fixed pattern; there is no numerical threshold or
matching lower bound. Bounded perturbations preserve the uniform-floor
objective. Exact scalar compensation and an RH-conditional limiting lower
edge follow from v1.36; they do not establish its open sign input.
What changed from the standalone checkpoint: this version integrates the proof into the complete manuscript, links its actual theorem dependencies, registers NS-57 and the scoped NS-58 next question, and archives a fresh Maxima replay plus full-build validation. The original private email and personal correspondence are not included.
From the repository root:
maxima --no-init --quit-on-error --very-quiet --batch=evidence/v156/exact-checks.mac
./manuscript/build.sh
python3 tools/verify_manifest.py v156
Actual complete build: 291 pages, zero undefined/duplicate references and zero overfull boxes. This release is incremental, not cumulative.