Established in scope
Original regular gauge class has ground and KMS source in the physical Gauss sector
In the question: Complete physical Hamiltonian source with Gauss sector and thermal word limit
New constructive application theorem on the same given Hamiltonian class and actual constraints. Projected state can differ from earlier ambient state. KMS/ground energy only on admissible algebra; whole stars, regular finite links and open topology are premises. Native1024D v989 is a separate original control, not execution of16777216D v1013 DET16 cell. No P1/whole-master identity, new coupling or total physical closure.
Read the exact result, assumptions and evidence
Result
Gauge invariance of Gibbs states does not impose Gauss=1 support. For original regular finite links with open boundary, the interior gauge group acts freely on link configurations; ||P(delta_u tensor v)||²=||v||²/|G|^|X| proves nonemptiness without choosing a vacuum. The same H gives positive rho_phys=P exp(-beta H)/Tr(P exp(-beta H)), KMS on A^G. The original norm/weak-* argument yields a limit with omega(P_F)=1. Centrality forces pi(P_F)=I throughout GNS; state and dynamics descend to the physical quotient. Unchanged v989 control has dim1024/rank64; diagnostic beta1 ambient invariant Gibbs has0.8551616360789673 outside, projected0. Actual noncommuting invariant-operator KMS residual2.36e-17.
Required assumptions
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
- Original local Hamiltonian class and common limiting caller
One fixed original selfadjoint interaction Phi(X) on the existing finite local tensor factors, finite range and finite uniform interaction moment. Original quasilocal algebra, inclusions and free-boundary H_Lambda=sum_X Phi(X). Use the scoped v1013 real-time norm dynamics and common weak-* ground/KMS subnet construction. Graph, frozen model couplings and actual field factors are supplied class data, not newly derived from P1.
- Original regular finite gauge links and complete interior Gauss stars
Actual regular finite-G links with original matter representation. Impose the original Gauss=1 projectors only for complete contained stars preserved by actual H. Open boundary with a path from every projected link component to an unprojected boundary vertex. Local gauge actions commute and preserve each interaction term. Admissible observables belong to A^G; do not add broken seam/boundary stars. No periodic neutrality or alternate sector choice.
Original evidence
- PHYSICAL-THERMAL-SOURCE.txt lines 1–198
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/PHYSICAL-THERMAL-SOURCE.txt
04b9873c44060b77cd9d5d246602f8188bddee50743de294455f452ae826e52a
- GAUSS-SOURCE-PROOF.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/GAUSS-SOURCE-PROOF.txt
98c2394d9e60ca195dd12d89f54d144c6bf4ad83a4d08b4c31da9958db53b76e
- GAUSS-SOURCE-PROOF.txt lines 201–213
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/GAUSS-SOURCE-PROOF.txt
98c2394d9e60ca195dd12d89f54d144c6bf4ad83a4d08b4c31da9958db53b76e
- GAUSS-NATIVE.txt lines 1–158
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/GAUSS-NATIVE.txt
fe4c32c89f5e14cfea80c4fe55c663d4b64eb428e02b60a01e283ff139a08043
- GAUSS-NATIVE.json lines 1–86
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/GAUSS-NATIVE.json
d2ae60d980eb0985cbc2415907f82699c744b6ba7b8f1dfde0feb592562276fc
- H-FINAL-REVIEW.txt lines 1–52
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/H-FINAL-REVIEW.txt
a442addd4cb4840859a01a90a8aa766967eba686fd4963419cab44c6a571e8fd
finding:original-regular-gauge-class-has-physical-sector-ground-and-kms-source