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GAT Research Note II
Source-Recognized Physical Stiffness Geometry
Subtitle: Associator-selected magnetic reduction, physical stiffness matching, and Gromov control of Yang–Mills stiffness sublevels
Folio: GAT-RN-II
Version: v0.4.0
Status: Active research note; not intended for publication
Research notes — not peer reviewed. Trust, but verify. Always.
Website description
This technical notebook studies how a finite, source-recognized Yang–Mills Wilson carrier can retain its physical stiffness geometry under admissible refinement without changing the carrier or substituting an auxiliary energy. The construction keeps the associator-selected magnetic sector separate from the complete physical complement, replaces naive graph-gap arguments by complete-low-cluster Riesz reduction, and tracks the conditions under which magnetic, electric, target-complement, and UV–IR reserves remain uniformly positive.
The note culminates in a direct cofinal physical-completion theorem. On an exact null-ground-form compatible subsystem, the common null quotient, complete-ground projection, and stiffness form descend together before completion, producing a canonical thin physical triple
with the inherited uniform off-ground floor. Charged/module transport may remain projective and retain a nontrivial associator while the physical norm, vacuum projection, and stiffness form have a strict single-valued shadow.
Claim boundary
Compatibility and discharge architecture only. The note does not claim an independent Yang–Mills mass-gap theorem, does not identify the associator-selected magnetic carrier with the whole physical complement, and does not replace the later Lorentz-covariant invariant-mass argument.
Open edge
Identify the direct cofinal physical completion with the same whole-nerve/spacetime thin Yang–Mills system used by the long construction. In the merely relative-form case, the comparison–Mosco passage remains necessary.
Short card description
A GAT field notebook on refinement-persistent Yang–Mills stiffness: associator-selected magnetic reduction, complete-low-cluster control, uniform physical reserves, and a direct cofinal thin completion carrying the null ideal, vacuum projection, and stiffness form together.
Format
Custom GAT field-notebook LaTeX: publication-grade mathematics with visible claim, method, limit, and learning architecture.
Copyright © 2026 J. Scott Little. All rights reserved.