[Arham-Tahir64]

PR1536's repaired fine engines claim native and conservative complex roots bracketed by adjacent 10^-200 exponents. This independently written integer-root verifier confirms all four strict signs without importing any logarithm, exponential, supplier or predecessor checker. It adds an exact certificate, enclosure proof, six unchanged source inputs with Git/SHA256 bindings, semantic failure controls and a registered replay hook.

The aggregate T74 profile has 2,343,092 children, rank mass 4,816,512 and deficit 23,680. Exact enclosures at 768 exponent bits / 1024 fractional bits are refined at 896 / 1280 bits and retain all four signs. Unresolved intervals fail explicitly. Ten test groups cover unsafe arithmetic mutations, small exact powers, surcharge/omission/normalization errors, a profile mutation preserving count and mass, source/certificate corruption, and optimized standalone relocation.

Validation on Windows / CPython 3.12.14:

python3.12 -B scripts/research_package.py --package research/pr1536-root-endpoint-audit
python3.12 -B scripts/verify_selected_result.py
git diff --cached --check

Registered replay passes: four signs, 12 semantic controls, 30 exact power comparisons and ten test groups. Staged bytes of all six copied inputs match their pins. Hosted CI is separate.

Scope: aggregate complex moment arithmetic only. 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 κ certification or selected-frontier change is claimed. The committed coarse predecessor evidence is distinguished from the fine SPEC endpoints.

Started from main c5108f0f68d482e5712a8e26a5978d47762dfc16. Chooser nonce 0cfced81e5b410bca1d5fd3d27a63fce, independent-verification track. TASK declares the changed independent-moment scope because selected ledger/endpoint audits are already extensively covered. Final overlap snapshot: 725 open PRs including drafts and 225 Discussion body/comment/reply records, complete pagination at 2026-10-14 03:11 UTC, plus local notes/ledger; its limits are recorded. Claim and handoff.

Credit: arkfx PR706 introduced the integer-root/dyadic method; this is a new implementation and input/precision audit, not a new numerical method. Jeremy Kothe PR1536 (527d7623009f295b7311e98ae36f5e2fbdbbc3e5), philippeVV PR1519's enclosure finding, Rohan Arun PR1424/1319/1297, and the retained lineage are credited in README and unchanged NOTICE. PR1549 refines the outer grid and is not verified here. Prepared for Arham Tahir with substantial OpenAI Codex assistance; no subagents or independent human review. Apache-2.0.

[Mister-Meeseeks]

Batch review at b024b3e12c8911312e1fcf07417e076168602a01.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Exact integer-root enclosures certify native and conservative endpoint signs with strict backoffs. The aggregate supplier and PR1536 admission obligations remain inherited; this arithmetic does not establish a new supplier.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.