Vacuum Readjustment under Gauge-Cell Attachment
J. Scott Little · v0.3.3 · October 27, 2026
Working preprint — not peer reviewed
An added gauge cell has a vacuum of its own. So does the graph to which it is attached. But the two vacua cannot simply be multiplied together and declared the ground state of the joined system. The shared electric edge matters.
This paper calculates that difference on an untruncated, four-edge SU(2) gauge graph. An exact receiving identity measures how electric response in the added cell couples to transport in the existing graph. At full native coupling, the joint ground state cannot factor across the chosen cycle-variable partition. A gauge-invariant old-vacuum spectral test detects the difference.
There is a further distinction: preserving the old cycle-factor vacuum test is not the same as retaining the old edge Hamiltonian after attachment. The supplement proves the latter operator's ground projection and shows explicitly why those two tests begin from different baselines. The paper also distinguishes vacuum matching from preservation of a fixed observable comparison, and provides an Abelian control.
The result is about a finite graph with untruncated compact-group rotor Hilbert spaces. It is not a proof of spacetime localization, a continuum limit, or the Yang–Mills mass gap.
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Release note
Version 0.3.2 adds a direct proof of the retained old-edge spectral comparison, separates its baseline from the cycle-factor vacuum test, and revises the opening and closing prose for a more direct authorial voice. The receiving theorem, native nonfactorization result, and precise limitations are unchanged.
Version 0.3.3 repairs unresolved equation references and citations through a complete multi-pass compilation. A scalable Latin Modern font is used for the letter. No mathematical statements or proofs were changed.