Kernel-check the staged supplier moment and refine conditional κ

[Dugongue]

The current PR #3802/#3815 construction publishes a 24-digit moment endpoint. This package proves the actual seven-term real-power moment in Lean and refines its conditional multiplication endpoint to

κ = 0.001730578437266246818740713218049857556556448073971562433312
    − 10⁻⁸² − 10⁻¹⁰⁶.

The gain is about 7.1321804986 × 10⁻²⁵. It is a tiny numerical refinement, with new verification coverage; the physical word, allocation and selected frontier are unchanged.

Lean 4.34.1 / pinned Mathlib checks Staged544.actual_rpow_moment_lt_one, including every logarithm/exponential bound, by composing sufficient rational Taylor inequalities through our existing MathProof moment-transfer proof. Its transitive axioms are only propext, Classical.choice, and Quot.sound. Fresh source compilation and separate target-module kernel replay pass. An additional all-imports --fresh attempt exceeded 300 seconds and is recorded as a timeout, not a pass.

The registered Python 3.12 replay passes: exact current clock/1,321,920 owner roles and all 2,551 cap patterns, both 723-column arbitrary-dirty words, independent root signs, 47 bootstrap rows, 63 modern outer rows and 17 original controls. The actual Git-free CLI accepts its complete input and rejects source, proof-data, claim, result and optimization corruptions. Immutable runtime source bytes are vendored with exact origins, so no foreign pending Git objects are required. Full native caches and the general compiler/hosting/source/precision/outer/BIT hypotheses remain inherited; no fresh complete native rebuild or unconditional multiplication theorem is claimed.

Credit ChaloupeMusic/#3815 for the T360 clock/fill and cap, hexapode/#3802 for first publishing the same previous endpoint at T385, dataisfire/#3734 for staged helper 544, Ross Richardson/#3605, zxv/#3638/#3682, roger-sato/#3642/#3693, Sagar Thakrar/#3687, and all retained native/owner/outer authors. The package preserves notices, documents its MathProof precedent, and discloses substantial OpenAI Codex assistance. Failed bounded new-word searches are preserved as scoped search history, not claimed as global obstructions.

Reproduce:

python3.12 -B scripts/research_package.py --package research/staged544-certified-endpoint
python3.12 -B scripts/check_research_commit.py --package research/staged544-certified-endpoint --check-source-history

The README gives the portable Lean build and direct Git-free replay. VALIDATION.json, PROOF.md, OVERLAP.md, and structured open questions state exact evidence and remaining obligations. No merge, other-PR closure, or selected-frontier update is requested.