Verification and Reconstruction of a Claimed Complex Structure on S6: An AI-Produced Validate/Repair/Disprove Record

This edition adds the complete public mathematical project frozen on 6 September 2026 and its five-page key-advances reader to the existing S6 verification and reconstruction collection. Start with 26_s6_key_advances_frozen_2026-09-06.pdf, then use 29_S6_FROZEN_PROJECT_GUIDE_2026-09-09.md to locate the complete papers and calculations. The publication date is 9 September; the archived mathematical checkpoint remains explicitly 6 September. The retained material includes exact marked cusp maps, higher-rung lattice and toric morphisms, period calculations, finite spectral calculations, triality and lattice constructions, arithmetic investigations, complete authored proofs and reproducibility programs. The full archive contains 1,079 files and 221,140,515 uncompressed bytes. Its per-file manifests account for retained mathematical sources and public derivatives. All 28 files of the previous published version remain unchanged in this version and are also retained in the frozen archive. The directly downloadable LaTeX reproduces the five-page reader; the full paper tree and supporting dependencies are in the source ZIP. The five-page reader is an entry point, not a replacement for the full proofs. Historical annotations and review conclusions retain their dates. This collection does not independently establish the candidate's global complex structure or sphere identification, does not establish a counterexample to CDP20, and does not claim a Yang–Mills mass-gap resolution. Finite exact checks have the stated scope of their corresponding calculations. The original supplied construction retains its attribution to Levent Alpöge with the disclosed Fable/Claude contribution; the reconstruction and subsequent calculations remain identified as AI-assisted work. GitHub reading guide and source mirror. Related but separately archived continuations: Yang–Mills spectral and state maps and corrected Navier–Stokes reconstruction. The live Overleaf workbench can contain later work than this frozen edition. Private workflow logs, credentials and local literature collections are not part of the new package. Existing creator and license metadata and earlier public versions are preserved.