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

This version adds a focused topology supplement to the version 1.1 verification and reconstruction record. It preserves all 22 earlier files byte-for-byte, including the independent correction note, original audit monograph, annotated manuscript, clean reconstruction, and published source and provenance files. Start with 14_s6_topology_update_readers_guide_2026-09-05.pdf, a short reading map to the precise input, new calculations, complete proof locations and limitations. The version-specific citation is doi:10.5281/zenodo.22346462. The new cusp calculation determines two different postcompositions of the original marked quotient q2 on the smooth compact source X. The angle-forgetting map g:X to S3 is based null-homotopic: its complete regular inverse three-torus, with the actual derivative framing, bounds an explicit collared framed D2 times T2 in one original cusp chart times an interval. The proof retains the full holomorphic period correction and does not use a sphere identification for this conclusion. Retaining the cusp angle gives H=p3 q2:X to S4. With the fixed based diffeomorphism d:S6 to X used in the reconstruction as input, [H d] is the nonzero class eta4 composed with eta5 in pi6(S4)=Z/2. The proof computes the full normal four-frame of the inverse two-torus and its Arf invariant one. Thus q2 is not based null-homotopic; its full order is not determined. The ordered smash with the complex Hopf map has literal type S9 to S6 and represents 12 nu6 in pi9(S6)=Z/24. Three suspensions give 12 nu9 in pi12(S9). Composing with the stated marked peripheral character produces values (12,0,12), with kernel chi inverse of 2 Z/12; it is not a reduction-compatible lift modulo 12. These are calculations for the specified candidate cusp maps. The underlying stable homotopy groups, framed-bordism methods and integral identity eta cubed = 12 nu are classical; see Hatcher, Algebraic Topology, printed pp. 384-385. The higher torus wrap also gives an explicit rank-six-to-rank-four lattice quotient, a holomorphic map of the higher local cusp tori with connected elliptic kernel, and its compatible toric filling morphism. It calculates the Euler-characteristic obstruction for the unchanged direct rank-three filling pattern and proves the specified equal-diagonal octonionic cone compactification pair (B25,S24). The octonionic flag F4/Spin(8) is compared through the stated maps; its known topology and cohomology are attributed to Mare and Willems. This does not complete a globally glued higher-torus family. The two frozen technical PDFs are 15_s6_higher_torus_and_cusp_update_2026-09-05.pdf (50 pages) and 16_s6_cone_sphere_routes_2026-09-05.pdf (64 pages). They include complete displayed mathematical arguments and are reproduced unchanged. 17_s6_selected_topology_sources_2026-09-05.zip supplies their exact TeX, bibliography, guide, portable build, exact supporting checker and selected sanitized audit evidence. Files 18 and 19 supply version notes and an integrity manifest. Historical companion/local-source locators in the frozen papers are resolved by the new guide and source README; these 5 September editions were not part of the preceding DOI's source ZIP. The original candidate remains attributed to Levent Alpöge's supplied manuscript, with its disclosed Fable/Claude contribution. The papers state their geometric input explicitly. The framing calculations do not independently establish the candidate's global complex structure or sphere identification. This supplement does not claim a complex structure on S6 or disprove CDP20. It does not construct a compact complex higher sphere, complete the three-filling global analytic gluing, or establish physical spacetime or a continuum quantum field theory. Separate finite-coupling, exceptional and arithmetic investigations are outside this batch. The independent correction note retains its original status. The original AI-assisted verification and reconstruction provenance remains visible. New additions are mathematical research drafts, not a claim of journal peer review or independent specialist certification. Exact algebra checks support the written proofs; they are not a machine formalization or independent global candidate validation. Earlier README, citation, metadata and checksums remain unchanged historical artifacts.