Yang-Mills spectral and state maps: finite-regulator calculations and continuum research checkpoint

Abstract

This edition archives the entire public canonical mathematical workbench underlying the Yang-Mills spectral and state research programme. It contains the original S6 manuscript and transcription, cumulative reconstruction, all tracked standalone manuscripts and supplied readers, the full TeX/Bib hierarchy, authored proof inputs, reproducibility programs and recorded results, correction history, mathematical reviews and established sanitized public provenance. The frozen Overleaf source is commit c501b11ff6caf6db195e5dc06b2b22724e886955, recorded at 21:41:28 UTC on 8 September 2026: 1,280 tracked files and 131,935,037 exact Git-blob bytes. Start with 05_quantum_full_local_spectrum_53p_2026-09-08.pdf, the current 53-page quantum-blocking, full-Fabel-tensor, local-energy and full local-spectrum reader. The supplied spatial-continuum reader has 108 pages and the volume-uniform-vacuum reader has 62 pages. These are the exact reader bytes present in the captured project; they are not new publisher builds. The entire workbench ZIP contains their complete cumulative sources and all other tracked mathematical companions, including the finite-box/Gamma/state-observable continuation. The reading map and edition guide explain the source hierarchy, successful bounded results, failed routes, dated corrections, exact source hashes and differing historical source/build generations. The full public archive has 1,983 members with a per-file SHA-256 manifest and complete accounting of every tracked input and recursively every historical ZIP member. Historical containers are expanded into inspectable directories. Public mathematical bytes are retained exactly unless explicitly marked as public derivatives removing private locators or nonmathematical personal/operational material. Private task instructions, cloud-operation logs, compiler caches, credentials and fresh raw session exports are not publication material; local-only downloaded third-party literature collections are not copied. Established public sanitized provenance already tracked in the project is retained. This complete public workbench is not the selected 84-file source ZIP of the first checkpoint. All six original files remain unchanged in this additive version and in the original published version. The mathematics retains specified finite Hamiltonians, physical couplings, gauge actions, actual interacting vacua, raw state norms, spectral measures and explicitly proved state/operator maps. Quantum Section16 constructs a free transverse-field common-state representation and a complete positive-time two-creation spectral map. Neither that construction nor the associated radial/Gamma and spatial maps establish survival of the nonabelian interaction in a four-dimensional continuum. The interacting continuum and Millennium implication remain unfinished. No Yang-Mills mass-gap resolution is claimed. Exact finite diagnostics support the written calculations in their stated scope; this archival edition does not claim independent complete theorem verification. The programme developed from the S6/cusp publication family, which remains unchanged. That source record retains the supplied manuscript's attribution to Levent Alpöge and disclosed Fable/Claude contribution. Human research suggestions and connections informed the subsequent AI-assisted calculations; the archive preserves original artifacts, mathematical evidence, external feedback, failures and corrected conclusions alongside the developed results. Public stewardship remains KokunoYumeto under the established CC0-1.0 scope for the authored edition. Original and linked third-party works retain their attributions and rights; capture timestamps alone do not establish priority. OpenAI's publicly released Finite Time Blowup for Navier-Stokes entered this programme on 8 September 2026. The retained source history distinguishes the initial 165-page edition, later 166-page capture and formal-source commit 8937a8f4cbc7abaab5e9e97d1cc7f5d2319d9538, targeted source/algebra checks and the unperformed complete independent analytic/kernel verification. The external manuscript is distinct from the earlier stationary Fabel polynomial. Precise source dates, hashes and scope remain in the original README and current authored proof sources; no unsupported priority or misconduct allegation is made. The separate Navier-Stokes publication has its own record and is not changed or duplicated here. Live read-only provenance workbenches: S6, Erdős-Strauss, Navier-Stokes, and an additional public research workbench. These evolving links are provenance, not a claim that all separate projects or later work are contained in the frozen archive.