TFPT scientific source excerpt Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/GAUSS-SOURCE-PROOF.txt Original file SHA-256: 98c2394d9e60ca195dd12d89f54d144c6bf4ad83a4d08b4c31da9958db53b76e Inclusive original lines: 201-213 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000201 | primary Hamiltonian lattice literature: Grundling-Rudolph, 000202 | https://arxiv.org/abs/1108.2129 , and their dynamics/physical-ground-state 000203 | construction https://arxiv.org/abs/1512.06319 . These support the separate 000204 | roles of gauge invariance and enforcing Gauss law; the elementary finite- 000205 | group proof(2)-(8) here is written out and does not import their unbounded 000206 | compact-group dynamics theorem as a new premise for the finite class. 000207 | 000208 | The given original Gauss=1 constraint fixes the sector in(2). Enforcing 000209 | that already required constraint introduces no new interaction, geometric 000210 | measure, time, statistical coupling or discretionary physical sector. 000211 | Unfixed boundary fluxes/thermodynamic phases are not declared uniquely 000212 | selected by this existence proof. Controlled IR universality remains in 000213 | its original role; no continuum a->0 requirement is added.