Scoped exclusion
Holomorphic quarter Cauchy idempotents are not positive CAR covariances
In the question: Common clock sectors, quartic geometry and operational reconstruction
Excludes only unchanged oblique idempotents as CAR covariance in actually induced measure. Orthogonal analytic range is constructively fixed; no general exclusion of positive elliptic sources.
Read the exact result, assumptions and evidence
Result
In actual L2 measure gP_Hg^-1 and g^-1P_Hg are not self-adjoint. Range and kernel have exact nonzero overlap integral |tan(theta)|^1/2 exp(-2i theta)dtheta/(2pi)=-1/sqrt2. An additionally chosen channel metric could orthogonalize them but would change the source.
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
- TRACE-METRIC-AND-DOMAIN.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/TRACE-METRIC-AND-DOMAIN.txt
fb696ebe6c3e531c0773eab309083dc4407c68011c6a08221abb433bdf39ad45
- TRACE-METRIC-AND-DOMAIN.txt lines 181–353
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/TRACE-METRIC-AND-DOMAIN.txt
fb696ebe6c3e531c0773eab309083dc4407c68011c6a08221abb433bdf39ad45
- INDEPENDENT-BOUNDARY-REVIEW.txt lines 1–154
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/INDEPENDENT-BOUNDARY-REVIEW.txt
7fac8804f89364125b2970eed9c937e7eb5dad2edf7253ffa8e9cc25f3d429fc
- real-boundary-modular-results.json lines 1–40
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/real-boundary-modular-results.json
d17c4687ad401f2d8b83629235c4b2750f96cd25cb0bd29f8a9353ed42a7ff93
finding:actual-holomorphic-quarter-cauchy-idempotents-are-not-positive-car-covariances