Established in scope
Original Hamiltonian class has complete thermal Euclidean word source and reflection positivity
In the question: Complete physical Hamiltonian source with Gauss sector and thermal word limit
Complete bounded physical word source of the supplied class, not a positive Grassmann/ghost configuration space. Thermal reflection is not automatically a separate P1 seam reflection. Ambient and physical subnet states remain distinct. q[0]=1 normalizes only this local source; original unnormalized Z_rel, reference and energy offsets are not replaced. No unbounded field limit, IR universality, general4D covariance or fundamental total promotion.
Read the exact result, assumptions and evidence
Result
All ordered bounded real multitime words and Dyson sources converge on the same original Hamiltonian source. Whole Euclidean thermal words obey volume-independent Schatten Holder |S_k|<=product||A_i||. Fixed Gaussian smearing gives complex-time norm convergence; uniform local derivation bound and multilinear Holder continuity remove smearing. Thus all unsmeared ordered words converge in the same subnet, without assuming unsmeared imaginary-time norm convergence. Whole source series have majorant exp(sum||J_i||_1||A_i||). Reflected half-circle word kernel Tr(B_F*B_G)/Z is a Hilbert-Schmidt Gram matrix, so positivity survives the limit. Canonical beta-s reflection and -is for latest-left ordering are explicit.
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.
- Given thermal parameter and bounded admissible source legs
Given beta>0 and actual bounded local physical insertions, in particular the even admissible algebra when parity requires it. Insertions preserve the Gauss projectors used. Retain original real time tau_t=exp(itH)·exp(-itH), word order and subnet. Thermal reflection is beta-s with adjoint/word reversal. Do not identify another P1 reflection or whole master caller without its original map. Keep original unnormalized reference factors and energy offsets separately.
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
- EUCLIDEAN-SOURCE-REVIEW.txt lines 1–199
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/EUCLIDEAN-SOURCE-REVIEW.txt
090a2c8e818ee24b053a41182d126940741037ee2ccc9bbfa4e7dc52f3a8ef13
- 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
- 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-hamiltonian-class-has-complete-thermal-euclidean-word-source-and-rp