Scoped exclusion
Full free equatorial algebra fails one fixed reflection
In the question: Common clock sectors, quartic geometry and operational reconstruction
Only full globally neutral even free CAR algebra on the union under a fixed reflection. No automatic claim about local gauge invariance in original admissible algebra. Separate parity/gauge per face is additional data. Positive annulus source remains valid.
Read the exact result, assumptions and evidence
Result
The two components of p^-1(|x|<1) lie on opposite positive and negative time halves for each fixed S or hS reflection. Actual NS Green kernel gives a globally U1 neutral even normal-ordered word :barpsi(f+)psi(g-): with strictly negative reflected norm for compact supports in both faces. Analytic interior witness is independent of boundary and vertex choices.
Required assumptions
- Existing C2 group with untwisted raw flat spin pullbacks
On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed.
- Original full four-mark inversion and distinct equatorial Real slots
The supplied marked base has x->ix and the inversion x->1/x already present in v512. Compare their actual lift to E:y²=x⁴−1,retaining the original four-marked base circle Gamma=|x|1. v510/v519 distinguish pointwise equatorial x->1/bar x from the OS family x->mu bar x acting along Gamma. These operations must not be identified in a source comparison. The old free carrier is named;no general physical P1 equality is presumed.
- Ramified holomorphic half-form trace of the given C2 spin line
Retain actual E:y²=x⁴−1, its already supplied Q fixed nontrivial NS NS spin-line class alpha and normalized Szego kernel. Holomorphic trace includes sqrt(dz/dx), while ordinary flat coefficient p_*alpha remains separate. No extra Q linearization phase, positive equal-time CAR covariance or smooth circle domain is assumed.
- Actual L2 half-form trace on full marked equator
Retain supplied square elliptic curve, flat metric and NS spin line. On the full ramified equator sqrt(dz/dx) transports actual L2 norm to |dx|. Keep holomorphic kernel, orthogonal analytic range, positive CAR covariance and H1 vertex domain distinct. No new channel metric or free vertex condition.
- 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
- GRAPH-CUT-REFLECTION-TEST.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/GRAPH-CUT-REFLECTION-TEST.txt
badd09c2ee1d16493341e4375d32a0db55f47097d9f35634cd43489a08237696
- GRAPH-CUT-REFLECTION-TEST.txt lines 181–215
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/GRAPH-CUT-REFLECTION-TEST.txt
badd09c2ee1d16493341e4375d32a0db55f47097d9f35634cd43489a08237696
- REFLECTION-INDEPENDENT-REVIEW.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/REFLECTION-INDEPENDENT-REVIEW.txt
2731432207346c866b7ab7eeea925f2adef902152031c62b9a7f2d0d4bb11e18
- REFLECTION-INDEPENDENT-REVIEW.txt lines 181–212
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/REFLECTION-INDEPENDENT-REVIEW.txt
2731432207346c866b7ab7eeea925f2adef902152031c62b9a7f2d0d4bb11e18
finding:full-equatorial-checkerboard-free-algebra-fails-fixed-reflection-positivity