Certified computation plus the proved spectral-energy projection implication.
The complete ground transform has a unique simple real zero in
(gamma_1 - 1/10, gamma_1 + 1/10). This is a local enclosure, not a claim
that it is the first transform zero or that its discrepancy from gamma_1
has a known sign. G2 and RH remain open.
The substantive change is the complete even-sector separator 1e-67. The old global separator 1e-73 makes the same endpoint test inconclusive. No new window, eigensolve, trial support, residual cutoff or tail assembly is introduced. All archived infinite-tail errors remain in the inherited Schur comparison. The ordinary error bounds compare the unit trial with its nonzero orthogonal ground projection, which need not be unit norm.
new_section.tex: complete proof and scope.certify_ground_zero.py: interval verifier at 1024/1280 bits.ground_zero_b1024.json, ground_zero_b1280.json: saved gates and input hashes.check_independent.py, independent_checks.json: second implementation
using principal determinants and direct centered cosine integrals; no
independent-agent or external audit is claimed.scope_review.md: same-agent proof and provenance review.research-report-2026-09-21-v1.html: original report, before task-ID reconciliation.research-report-2026-09-21-v2.html: current user-facing report (NS-18).integration_checks.json: concurrent-main preservation and unchanged source checks.build_report.json: actual manuscript build and diagnostics.Replay from the repository root, writing fresh files:
.venv/bin/python -B evidence/v142/certify_ground_zero.py --bits 1024 --output /tmp/ground-zero-1024-replay.json
.venv/bin/python -B evidence/v142/certify_ground_zero.py --bits 1280 --output /tmp/ground-zero-1280-replay.json
.venv/bin/python -B evidence/v142/check_independent.py --output /tmp/ground-zero-check-replay.json
python3 tools/verify_manifest.py v142
./manuscript/build.sh
The verifier refuses to overwrite an output. Use new paths for later runs. The second implementation also checks the archived reports and dependency hashes. Python 3.14.6 and python-flint 0.9.0 were used.
Inherited evidence: exact v1.25/v1.26 frozen even trial, saved complete even residual enclosures at 768/896 bits, and v1.40 simple-even ground theorem. Only the small inherited final gates are replayed; this is explicitly not a fresh evaluation of every old residual row. Cutoff convergence is not an assumption: the old analytic remote bound covers the entire tail. NS-1’s two missing historical evidence groups remain OPEN and are not used by this new result.
The original NS-17 claim commit is preserved; the completed task is NS-18 after reconciliation with concurrent main. Its separate documentation task NS-17 remains open. No mathematical claim changed during reconciliation.
NS-17 is now integrated at the five requested anchors. See ns17_inserts/,
ns17_integration.json, build_report_ns17.json, and the separately versioned
research-report-2026-09-21-v3.html. The determinacy and matrix-structure
claims were qualified; the original drafts remain unchanged. Zhu citations
use the single key Zhu2026. The finer NS-18 discrepancy is still in progress.