README.md

Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data

README.md

Download original file

Original Markdown with line links

Paper IV — verification closeout v1.1.0

19 October 2026 (UTC) · Operation Komorebi · Komorebi P.

Result

The existing 68-result reviewed formal core passed a fresh pinned-source replay, exact target-kind resolution, a transitive namespace axiom audit and real compiler controls. All 119 mathematical Lean sources are unchanged. This is a verification closeout, not a new or strengthened mathematical theorem.

Start with readers/Paper_IV_Verification_Closeout_v1.1.0.pdf or REPORT.md. verification/CLOSEOUT_REPORT.json contains the structured summary.

Contents

Reproduce the checks

Use Python 3.11 or newer on Linux/WSL. Commands write new evidence outside the frozen package. They do not install software, fetch dependencies, or edit the accepted mathematical sources.

python3 -B scripts/verify_release.py
python3 -B scripts/run_checks.py --mode records --work /tmp/paper-iv-records
python3 -B scripts/run_checks.py --mode finite --work /tmp/paper-iv-finite
bash Run-Replay.sh /path/to/Komorebi_Portable_Lean_4.34.0-rc2 /tmp/paper-iv-full

Every output directory must be new. Full mode requires the matching external Lean runtime and all cached packages specified in formalization/lean/lake-manifest.json. Finite mode additionally requires the Python packages recorded in the finite receipt. The report builder uses ReportLab. Native Windows execution was not tested.

verify_release.py checks stored evidence and hashes; it is not a new compiler run. Full mode performs fresh source compilation, kind and axiom checks, and compiler controls. Its 300-second per-command timeout and one-worker configuration retain the accepted production settings.

Reader versions and exact scope

The older monograph and Lean reader correctly describe their own earlier edition and its historical formal evidence. The new closeout report is the authority for this execution. The October 16 standalone visual PDF is preserved, including its branch-sensitive correction. The exact updated editable source for that standalone PDF was not recovered; the October 8 editable baseline and a three-page PDF text difference record are included. No byte-identical regeneration of that later PDF is claimed.

The reviewed 68-result contract, hypotheses, branch choices and explicit research boundaries are unchanged. Imported standard fact 11.1 is outside that count. No new independent semantic reproof of all 68 statements, cold Mathlib build, independent proof kernel, external referee review, or licence decision is claimed.

The separate Paper_IV_Delivery_Verification_v1.1.0.json records the final ZIP hash, fresh extraction and post-extraction tests. It is external to the archive to avoid circular self-hashing.

Other PDFs for this work

Original file and source record

This copy matches the recorded source file. Its publication here does not change the work’s review status.

SHA-256: 9b90381dea1ce982f5cd110d0eac5cbc5b38e3fa3f8abb003a391d5d015802e2

Original source on GitHub

Back to Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data