[jamesyc]

Pinned PR596 native moment and finite scalar closure

Author-checked conditional κ = 16127213726553 / 10000000000000000 = 0.0016127213726553, bound to historical selected commit 5996f90. This package preserves that exact source context; later selected records or the eventual publication base do not replace its numerical data.

Four unchanged accepted Lean sources prove:

• The nine-term native complex rational moment, with one ordinary outward ceiling and no fallback. Its exact upper minus one is −35031 / 250000000000000000000000000000.
• The corresponding Real logarithm/exponential enclosure and strict moment bound below one.
• Seven ordered finite bootstrap updates, including all minimum, ceiling and cutoff branches, reaching the recorded endpoint.
• All 47 recomputed strict outer slacks, seven margins and their minimum, three balanced identities, and the strict κ grid bracket.

The package imports five existing public outputs: two from PR585 at 809915a and three from PR605 at d676cf3. It copies no generic helper source or runtime inventory. The immutable PR605 references reconstruct the existing 3,260 cached runtime pairs.

The guarded public reproduction retained those five outputs and compiled only the four included roots. All nine object hashes and all four fresh raw logs match their accepted references exactly. It records 30 new and 20 retained probes, 50 reachable in total. Fresh compiler time was 14.735855385 seconds; FIFO wait was 0.002720421 seconds, with guard durations recorded separately. Every root stayed within the existing 60-second/4-GiB hard and 40-second/3.5-GiB review limits. Independent terminal review passed; the final package keeps the sole measured-status record in REPLAY_SUMMARY.json.

This result leaves initial-saving and bit-saving validity, provider/profile and recurrence realization, scalar/budget interpretation, physical execution and all-size transfer as separate obligations. The bit and conservative-complex fallback-bearing branches are not certified by the native moment result. It is not a full integer-multiplication theorem at κ.

The Lean proofs, finite transcription, metadata and prose were substantially prepared with OpenAI assistance and independently source-reviewed. Upstream contributors and tools retain attribution in NOTICE.md and SOURCE_BINDING.json. Candidate-specific aggregate checks and hosted CI require their own exact receipts; this local Lean reproduction does not claim them.

Exact candidate and current-base context

Candidate deb26103657d3190e3a655c5f6a332982fdecfc3 contains only two author-preserving package commits on f567884aeb8851b6e794af1184119a3bfbe1e631: 17 added files, 336,612 bytes, four unchanged Lean sources. Its parent selects conditional κ = 1661634653669567 / 1000000000000000000 = 0.001661634653669567. That value was separately author-checked against the parent's selected result and PR799 assembly; the Lean package continues to certify the historical PR596 data and κ stated above.

A bounded candidate-specific readback also transports the previously measured standalone Python 3.13 verify-research result: 211 declared input bodies, all 28 actual output/command identities, 72 freshly resolved standard-library-only local origins and 204 static provenance links match exactly. The sole Makefile difference is inverted explicitly: unrelated frontier targets and the top-level frontier selection changed, while this standalone target did not. No new scientific target or supplier was run for this transport. It does not cover top-level make verify, the new frontier targets, hosted CI, or whole-repository correctness. The original runtime boundary and its limits are preserved.

The four fresh proof sources were screened against the selected repository and open/closed pull requests before handoff, including PR585/PR605 helper reuse. The publisher will recheck exact main, branch leases and duplicates immediately before the write.