Independent integer-root audit of PR1536 200-digit complex endpoints

[Arham-Tahir64]

DONE — PR1577, head b024b3e12c8911312e1fcf07417e076168602a01, contains the independent integer-root audit.

All four PR1536 complex endpoint decisions at adjacent 10^-200 exponents are confirmed. For the native lower/upper points, moment-minus-one lies in [-1.232,-1.231] * 10^-200 and [1.690,1.691] * 10^-200; conservative lower/upper intervals are [-0.986,-0.985] * 10^-200 and [1.935,1.936] * 10^-200. The exact rational certificate and enclosure proof are included.

Separate standard-library code uses repeated integer square roots, dyadic exponent brackets and outward products, with no log/exp or supplier imports. Precision 768/1024 bits is corroborated by contained intervals at 896/1280 bits. All six unchanged copied source inputs have Git/SHA256 pins; the aggregate has 2,343,092 children, rank mass 4,816,512 and deficit 23,680. The fine SPEC endpoints are distinguished from PR1536's committed coarse predecessor evidence.

Validation: registered Python 3.12.14 replay passes with four signs, 12 semantic controls, 30 exact small-power comparisons and ten test groups, including actual unsafe rounding mutants, source/head/inventory/certificate corruption and optimized standalone relocation. Selected-record validation and staged whitespace/source-byte checks pass. Hosted CI currently reports action_required, including Registered research packages. No hosted replay pass is claimed; repository maintainer action is needed.

Scope: partial aggregate complex arithmetic audit. No operation/owner reconstruction, full supplier/native/bit admission, outer/bootstrap inequalities, precision/tape, all-size/hosting/analytic proof or full Lean theorem was run. No new construction, complete headline-kappa certification or selected-frontier change is claimed.

Final overlap: 725 open PRs including drafts and 225 Discussion body/comment/reply records with complete pagination at 2026-10-14 03:11 UTC, plus local notes/ledger. PR1536 remains at 527d7623009f295b7311e98ae36f5e2fbdbbc3e5. PR706 is method prior art; PR1549's outer-grid refinement is outside this audit.

Credit: arkfx PR706; Jeremy Kothe PR1536; philippeVV PR1519 enclosure finding; Rohan Arun PR1424/1319/1297; Sagar Thakrar's independent pricing precedent; the cumulative lineage and unchanged predecessor NOTICE. Prepared for Arham Tahir with substantial OpenAI Codex assistance; no subagents or independent human review. Apache-2.0.

Original CLAIM: base current main c5108f0f68d482e5712a8e26a5978d47762dfc16, chooser nonce 0cfced81e5b410bca1d5fd3d27a63fce, changed independent-moment scope to the pending PR1536 200-digit native/conservative endpoints after selected-ledger saturation. Advisory claim completed by the linked PR.