Established in scope
Actual equatorial trace fixes orthogonal Hardy range
In the question: Common clock sectors, quartic geometry and operational reconstruction
Actual full equatorial trace for supplied metric. No equality with old quarter state, positive annulus KMS state or physical time. Preserve smooth annulus results and original W8 Hardy comparison.
Read the exact result, assumptions and evidence
Result
Actual measure is |dz|=|dx|/(|c||y|). Closed half-form trace is L2 unitary to |dx|. The two bounded Cauchy idempotents gP_Hg^-1 and g^-1P_Hg, |g|²=|tan(theta)|^1/2, have exactly closed range H² by outer cyclic factors. Their orthogonal range projector is P_H⊕P_H. Integrable branch singularities do not remove H1 vertex coupling. Intrinsic boundary generator has variable speed 4K(-1)sqrt(|sin2theta|), failing constant base-winding Ward relation.
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
- check_real_boundary_and_modular.py lines 1–165
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/check_real_boundary_and_modular.py
03fe91a722026292a2e7a5e59f5fe70ca57cb4fb5d8ad417da3bb17d8268ef05
finding:actual-equatorial-half-form-trace-fixes-orthogonal-hardy-range