Established in scope
Existing thermodynamic source limit does not need bare Gibbs projectivity
In the question: Complete physical Hamiltonian source with Gauss sector and thermal word limit
Reuse later original proofs and correct excessive source requirements. v330 transfer labels are not all geometry/Higgs/matter fields. A whole S_adm field dictionary does not follow from a finite example. No phase uniqueness, limit gap or IR universality claim; no new continuum gate or total physical closure.
Read the exact result, assumptions and evidence
Result
The fully read v1013 original proof constructs common norm dynamics and at least one ground/beta-KMS state on the same A/A^G. Its whole local densities are exactly compatible by restriction; testing all matrix units gives Tr_(G-F)rho_G=rho_F. Free finite Gibbs weights themselves need not be projective. Existing whole fiber integration carries effective weights, exterior determinants and all source legs; unchanged bare spectral form is not required. A single global reference density is no general existence gate. Ledger760 makes a→0 optional and thermodynamics plus controlled IR universality binding.
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 evidence
- LATER-SOURCE.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/LATER-SOURCE.txt
2b61eee3d0dd557a1b428184c6978c78efa7d05630503f45084258a86c2381ac
- LATER-SOURCE.txt lines 201–226
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/LATER-SOURCE.txt
2b61eee3d0dd557a1b428184c6978c78efa7d05630503f45084258a86c2381ac
- BLOCKING-PATH.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/BLOCKING-PATH.txt
bb2b6ac13400c4267819de29189f00d006545fdff8c0acb80e4036757bbe05e3
- BLOCKING-PATH.txt lines 201–256
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/BLOCKING-PATH.txt
bb2b6ac13400c4267819de29189f00d006545fdff8c0acb80e4036757bbe05e3
- CONSTRUCTIVE-CRITERION.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/CONSTRUCTIVE-CRITERION.txt
60bd3ed474d25b66e94096f621209b3afb86296446ba17bc748947f8b0198f84
- CONSTRUCTIVE-CRITERION.txt lines 201–255
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/CONSTRUCTIVE-CRITERION.txt
60bd3ed474d25b66e94096f621209b3afb86296446ba17bc748947f8b0198f84
finding:existing-thermodynamic-source-needs-no-bare-gibbs-projectivity-or-mandatory-continuum