Tooling: exact integer exponential intervals with pinned replay evidence

[steph4n-gh]

The independent PR626 owner checker evaluates exponential bounds through repeated rational reductions. This adds an opt-in integer kernel that returns exactly the same bounds: degree-16 Taylor polynomial, identical tail, and identical 200-bit outward rounding. The unchanged complete checker runs through a source-pinned adapter on the archived PR622 native inputs.

Status: tooling improvement; no new κ. The kernel is approximately 13× faster, but the full checker improves only modestly: final 15-pair runs measured 2–3% less wall time, and an earlier run showed only 0.5%. All raw runs are retained. No substantial full-check or frontier-replay speedup is claimed.

Local interpreter	Kernel median (900 calls)	Complete owner check median
Python 3.14.4 / macOS arm64	0.62026 → 0.04810 s (12.90×)	0.38281 → 0.37411 s
Python 3.13.5 / macOS arm64	0.63399 → 0.04867 s (13.03×)	0.41303 → 0.40023 s

Validation:

• 11 focused tests pass on both local interpreters, including an optimized-Python suite.
• 276 boundary and 480 seed-91 rational pairs agree exactly with the pinned reference, including 1024-bit denominators. A separate direct-power/factorial oracle and higher-order certified enclosures check the arithmetic.
• Five polynomial/tail/rounding negative mechanisms and 32 whole-check subprocess controls pass. Repinned owner/plan/native corruptions and both failed moment thresholds are rejected by the original checker in both engines.
• All complete-check receipts match the frozen baseline byte for byte. Timed kernel outputs also match exactly. Final receipts bind measurement and candidate code hashes.
• The selected source-inventory check and whitespace check pass; frozen sources, upstream/, default commands and the selected certificate remain unchanged.

Reproduce from a full checkout using only Python 3.11+ standard library:

python3 -B -m unittest discover -s research/exact-exp-performance -p 'test_*.py' -v
python3 -B research/exact-exp-performance/benchmark.py --pairs 15 --out /tmp/exact-exp-benchmark.json

Use a fresh benchmark output file. Expected: 11 tests pass and PASS_EXACT_EXP_BENCHMARK. The README contains the exact equivalence argument, source map and full limitations.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. OS-random assignment seed: 91, verification engineering. No pinned sprint coordination issue exists; the claim and result are recorded locally. Refreshed 491 open PRs through #671 plus body searches for exact_intervals and exponential. #667 addresses logarithms in a different engine; #662, #367 and #452 address other workloads. None is a code dependency.

The reference checker is credited to Chafik Boukhalfa/chafreaky (#626), suppliers/dispatch to Jeremy Kothe (#622/#623), with the full inherited attribution and AI disclosures retained in NOTICE.md. Prepared for Stephan Arrington with substantial OpenAI Codex assistance; Apache-2.0.

The full supplier rebuild, controller replay, 47-inequality assembly, make verify and Lean were not rerun for this isolated adapter. Dedicated Linux CI is supplied but is separate from the recorded local results. All-size/compiler/hosting/precision/tape/analytic obligations remain inherited; finite equality is not a formal proof of the multiplication theorem.

[Mister-Meeseeks]

Integrated at ee055dc44815497927ef618fc985b93c2dcbda2a in the 20-PR pilot, retaining your original commit, source notices and contributor credit.

Exact integer exponential enclosure replacement. All 11 tests passed, including original-checker controls. Integer Horner polynomial, geometric tail and outward rounding reviewed. Runtime improvement not rebenchmarked.

The scoped package check passed at 7519539e28eaa59f6cb1ebc7a83413ade5521afa. This is research integration; the selected κ and inherited theorem assumptions are unchanged. Review, evidence and attribution. Thank you for the contribution.