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

This research checkpoint contains complete finite-regulator Yang-Mills spectral and state calculations and their explicitly unfinished continuum continuation. Start with 01_quantum_blocking_local_energy_2026-09-08.pdf, the 46-page quantum-blocking, corrected Fabel tensor, lowest-band and local-energy manuscript. The 72-page spatial companion gives retained cusp/refinement maps, actual-vacuum estimates, spectral escape and degeneration, and source-specific Navier-Stokes curvature/current calculations. The complete source archive includes both manuscripts, the six-part fixed-box/Gamma/state-observable companion, authored proof inputs, correction notices and diagnostic programs/results. The independently sealed 24-file quantum author package is also preserved unchanged. The work retains the original finite Hamiltonians, couplings, gauge actions, open boundaries, actual interacting vacua and raw spectral measures. It constructs specified finite-regulator states, local-energy matrix elements and limiting representations. The Gamma cyclic representation is not a reconstruction of local interacting Yang-Mills theory; retaining its full origin amplitude window adds a zero-energy sector. The common local continuum algebra, higher-mode joint limit and interacting four-dimensional continuum remain unfinished. No Millennium Prize resolution is claimed. Exact finite checks and explicitly labeled numerical diagnostics support the written derivations; they do not certify a nonlinear continuum or independent specialist review. The programme developed from the S6/cusp research record, whose existing publications are unchanged. That record attributes the source candidate to Levent Alpöge's supplied manuscript with its disclosed Fable/Claude contribution. Human research directions and possible connections informed the AI-assisted calculations; the edition retains successful bounded results, failed routes, exact obstructions and dated corrections. Public stewardship is attributed to KokunoYumeto. The supplied sources retain the full mathematical arguments and their primary references. OpenAI's publicly released Finite Time Blowup for Navier-Stokes entered this programme on 8 September 2026. The source history distinguishes the preserved 165-page edition from the later 166-page capture and the formal source commit 8937a8f4cbc7abaab5e9e97d1cc7f5d2319d9538. Targeted source statements and bridges were studied; a full independent analytic or Lean-kernel verification of the external existence proof is not claimed here. The external manuscript is separate from the earlier stationary Fabel polynomial. The README identifies the exact hashes, capture dates, antecedent human work and public source announcement. No unsupported priority or misconduct allegation is made. The evolving read-only research workbenches are the S6 workbench, Erdős-Strauss workbench, Navier-Stokes workbench, and an additional public research workbench. These are provenance links, not claims that unrelated results are included in this deposit. The source archive is the complete selected Yang-Mills checkpoint; private transcripts, account paths, credentials and downloaded third-party publication bodies are excluded. The authored work is released under the programme's CC0-1.0 scope; linked third-party works retain their own rights.