Scoped exclusion
Internal Hodge structure exists, full even CAR is not the coordinate algebra
In the question: Historical: common source, state and event selection
Excludes only full even internal CAR as coordinate algebra with J_H; positive Hodge signs conditional on rank/metric/volume. No physical CAR, J, KO6, spacetime or E=C5 origin derivation. Proper compatible subalgebras and originally derived symmetry breaking remain possible. Whole-space antiunitarity is not automatically the quaternionic W factor of a different triple.
Read the exact result, assumptions and evidence
Result
For the given E=C5, J_H²=1, J_HΓ=-ΓJ_H and (ΓJ_H)²=-1 hold on ΛE. Internal CAR is End(ΛE), its even part End(S+)⊕End(S-). J_H swaps both blocks and maps this full algebra onto itself; order zero would require commutativity. An explicit matrix-unit commutator has rank2. The full internal algebra is thus not a spectral coordinate algebra with this J_H. A selected left/right bimodule subalgebra remains missing. Reuse the existing SU5 no-selector: unmarked exterior algebra and trace balance select no3+2 projector.
Required assumptions
- Given unmarked Hermitian rank-five carrier with volume
Given E=C5 with Hermitian metric and unit complex volume, F=ΛE, Γ=(-1)^degree and conjugate-linear Hodge J_H. Neither3+2, named particle/gauge modules nor Yukawas are inserted. Internal Clifford operators are not identified with physical local fermion fields; rank5 and volume are not newly source-derived.
- 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 evidence
- LOCAL_ALGEBRA_PROOF.txt lines 108–172
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/seam-joint-source-origin-audit-20261016/LOCAL_ALGEBRA_PROOF.txt
caabb04e2449b2e12ff674690dbc8ee37feb0a043543cd667df8085eb93b9e26
finding:internal-even-car-hodge-is-not-coordinate-algebra