SEPTEMBER 21, 2026 · MANUSCRIPT V1.41 · REPORT VERSION 3

The saved certificate and newer diagnostics are integrated.

The v1.41 candidate has been reconciled with main at commit 289961d in an isolated worktree and validated for the user-authorized publication. The later diagnostic results, coverage analysis, drafts and retractions are retained. G2 and RH remain open. No new window was computed.

What the combined version establishes

Certified computation. Eight local transform-zero discrepancies for the existing λ = 3, N = 120 compression reproduce CCM §6, Figure 1. The first is approximately 1.582329697193127 × 10⁻³⁴. The interval gates passed at 768 and 1024 bits in the resumed verification. The verifier, original assembler and both saved reports remain byte-identical in this integration.

Exact correction. The old NS-14 reconstruction omitted the (−1)ⁿ centering phase and evaluated a different function. Its sinc-lattice conclusion is withdrawn. This is a diagnostic error, not a negative Weil direction or a disproof of convergence. The numerical zero benchmark cannot distinguish A from cA + sI for c > 0; that limitation is explicit.

Numerical illustration. The broader 170-value CCM reproduction remains in its diagnostic directory. It is preserved separately from the eight certified local root statements. No complete-ground zero transfer or cofinal convergence follows from either.

Conflict resolution

The task board credits the diagnostic and certificate work separately. NS-3’s citations and half-width translation are integrated. NS-4b’s detailed analysis is retained and linked from the manuscript: the probe theorem covers one of the ten recorded closures; the protected-orbit theorem covers none as recorded; the live concentration mechanism lies outside both.

The research map retains the broader numerical observation and adds the finite-compression certificate as a distinct result. The circle/line-symbol retraction is preserved, and the obsolete KMS summary is not restored. All files in the later diagnostic, coverage and draft groups were checked byte-for-byte against the fetched main commit. The older reports remain available at their original paths.

Verification and remaining gaps

The actual manuscript build produces 215 pages, with 0 undefined or duplicate references and 0 overfull boxes. Pyright reports 0 errors and 0 warnings for the certificate script. The v1.41 manifest is regenerated for the integrated artifacts.

The older v1.34–v1.37 manifests retain the same historical missing-file and mismatch counts seen before the merge. These were not rewritten to conceal the discrepancies. The v1.26, v1.31 and v1.38–v1.40 evidence manifests verify.

Open inputs. Both NS-1 evidence groups remain OPEN: the original later scripts and witnesses are unavailable, and the v1.31 report alone is insufficient. NS-6 remains a separately preserved draft. Complete-ground zero locations, cofinal convergence, G2 and RH remain open.

Preservation checks · Integrated build record · Prior report · Evidence ledger

W₄ ≥ 0 and its simple even ground remain the fixed-window results of v1.40. This integration supplies no RH or G2 claim.