Established in scope
Whole separated original source retains bound gauge weights
In the question: Complete physical Hamiltonian source with Gauss sector and thermal word limit
Conditional whole-source reduction, not solved rest lattice.256 rest states per cell,256^V at volume. No v1013 gauge/P1 clock identity from center order. Mirror source words require actual gauge insertion and graded order. v1007 mirror hopping outside class. No blanket dismissal of other parents, primitive coupling derivation or physical total promotion.
Read the exact result, assumptions and evidence
Result
Ambient rest source factors exactly as ZR[J] product Zm. With actual product gauge action,same physical Gauss trace reduces to |G|^-|Vint| sum_g TrR[UR(g)e^-beta HR ordered rest source] product_x[aTrUm,x+b<phi|Um,x|phi>]. Explicit canonical Gamma(r),det r1 gives a det(I+r)+b. Original Spin10 center q^N has four weights65536a+b,256a+b,b,256a+b,directly checked. Preserve weights and unnormalized Z0.
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.
- Literal separated DET16 mirror factor of v1013 table
Exactly original v1013 table: only DET16 acts on separate16-mode Fock factor; Hm=2(I-Pphi), original v1002 Pphi and phi=pi/7. Six other rows act on physical edge/link/clock factors, rest dimension256 per cell. No additional mirror hopping as in v1007. Supplied table coupling, not primitive P1 selection.
- Actual product gauge action and rest-source legs
Actual supplied original finite gauge action factors as UR(g) tensor product Um,x(gx), preserves same H and uses same original whole Gauss projector. Rest-source legs are gauge compatible. No concrete v1013 mirror representation or P1 clock identity is added from group order. Gamma(r),det r1,no implementer phase is only explicitly supplied subcase.
- 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
- DET16-WHOLE-SOURCE-REDUCTION.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/DET16-WHOLE-SOURCE-REDUCTION.txt
fc43fcfef453bb278b8f5c28123078331a36d1e4350672b45c47a5d99c992897
- DET16-WHOLE-SOURCE-REDUCTION.txt lines 201–217
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/DET16-WHOLE-SOURCE-REDUCTION.txt
fc43fcfef453bb278b8f5c28123078331a36d1e4350672b45c47a5d99c992897
- R104-REVIEW.txt lines 1–57
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/R104-REVIEW.txt
b2706681f27fda41d93fe760499f45ed561cc6d4da980a320b366b30a64110e8
- 001-section-the-concrete-uniformly-local-class.tex lines 32–118
Source checked at this snapshot
Original location and fingerprint
documents/articles--2026-08-30--tfpt_thermodynamic_dynamics_en/sections/001-section-the-concrete-uniformly-local-class.tex
9f53a07911c9e2e8f6b2f594b7c154f5a8dc0faeb2e9a429cc04a229cc6f4294
- v1002_spin10_mirror_projector.py lines 204–267
Source checked at this snapshot
Original location and fingerprint
verification/v1002_spin10_mirror_projector.py
84f7cd7987887ee071d7e05872285ab274ae329f6bcfa693be69bb52add19a4c
- v1002_spin10_mirror_projector.py lines 311–315
Source checked at this snapshot
Original location and fingerprint
verification/v1002_spin10_mirror_projector.py
84f7cd7987887ee071d7e05872285ab274ae329f6bcfa693be69bb52add19a4c
- tfpt2p1d_master_assembly_probe.py lines 26–35
Source checked at this snapshot
Original location and fingerprint
experiments/tfpt-discovery/tfpt2p1d_master_assembly_probe.py
2cb1d4dcc3d6a2e27503e8e6f812e05da966de3410fc793c7b62ee06cbed78eb
- tfpt2p1d_master_assembly_probe.py lines 66–73
Source checked at this snapshot
Original location and fingerprint
experiments/tfpt-discovery/tfpt2p1d_master_assembly_probe.py
2cb1d4dcc3d6a2e27503e8e6f812e05da966de3410fc793c7b62ee06cbed78eb
finding:r104-separated-det16-factor-reduces-whole-source-with-bound-gauge-weights