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Refine the certified staged544 conditional kappa endpoint to 80 digits - #3875

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CrocSwap:mainfrom
hexapode:codex/staged544-refined80

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Refines PR3857’s conditional multiplication endpoint, on the same physical construction, to

kappa = 0.00173057843726624681874071321804985755655644807397156243331276259008002643975681
      - 10^-102 - 10^-126.

The strict improvement is approximately 7.6259e-61. This is a tiny numerical refinement, not a new geometry or new verification coverage merely from more digits. The paid profile, physical owners, native suppliers and payload allowance remain unchanged. No selected-frontier update is requested.

Regenerated concrete Lean certificates compile with pinned Lean 4.34.1/Mathlib, and separate target-module kernel replay passes; the transitive axioms remain propext, Classical.choice, and Quot.sound. Exact independent moment enclosures, regenerated outer/bootstrap ledgers, Python 3.12 registered replay, source-history checks, and Git-free semantic corruption controls pass. All-imports fresh kernel replay and fresh complete native-cache rebuild were not run. Source-bound reuse and inherited all-size/compiler/hosting/precision/recovery/BIT assumptions are explicit.

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

Only the new package is added. Credit Dugongue/PR3857 for the generic formal proof and exact evaluators, ChaloupeMusic/PR3815 for the T360 construction, hexapode/PR3802 for the previous endpoint at T385, dataisfire/PR3734 and all retained native/owner/outer authors. Source bytes and notices are preserved. Prepared by hexapode with substantial OpenAI Codex assistance; no independent human review or unconditional multiplication theorem claimed.

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