Conditional result
Full CAR and the same positive time force the source vacuum
In the question: Common clock sectors, quartic geometry and operational reconstruction
Conditional on the full odd-CAR image in the same OS representation and time. Even CAR alone is insufficient: one-mode CAR_even=C⊕C has trivial dynamics and arbitrary ground-state occupation. The reduction does not construct the missing P1 image.
Read the exact result, assumptions and evidence
Result
For FULL CAR, antilinear a(f), same Bogoliubov time with gapped K and H≥0,HΩ=0, one gets a(P+f)Ω=0 and a(P−f)*Ω=0. CAR forces P−=1_(K<0), gauge invariance and Wick. After this operator/time identification, the quasifree vacuum is not an independent premise.
Required assumptions
- Full CAR image and same positive vacuum time as a conditional hypothesis
Conditional reduction: the FULL graded local CAR algebra including odd fields and adjoints belongs to the same OS vacuum representation; original time restricts to a(f)→a(exp(itK)f) for the same selfadjoint gapped one-particle K; H≥0 and HΩ=0. The P1 embedding/time identification is not established. Even CAR alone is insufficient.
- Original P1, boundary, seed and local restriction definitions
Reviewed originals: P1 declares oriented seam, reflection-positive kernel, unit winding and c3; stronger T_boundary includes A_+ as data; operational seed takes A_loc, time, reflection, state, seam class and collar operator as inputs. A_adm(O) is A/A*-invariant restriction of supplied local insertions. Compare without P2/E8/target spinor assumptions and without presuming an original gauge/microscopic localization intertwiner.
Original evidence
- GROUND-STATE-SOURCE-REDUCTION.txt lines 1–200
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/paper-source-reconstruction-20261025/GROUND-STATE-SOURCE-REDUCTION.txt
908420944efb265dbb57f5fc53e2331a416170f76a626f75e14f3445299046cb
- GROUND-STATE-SOURCE-REDUCTION.txt lines 201–266
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/paper-source-reconstruction-20261025/GROUND-STATE-SOURCE-REDUCTION.txt
908420944efb265dbb57f5fc53e2331a416170f76a626f75e14f3445299046cb
finding:full-car-positive-time-forces-source-vacuum