Established in scope
Complete elliptic NS spin kernel splits globally into quarter pair
In the question: Common clock sectors, quartic geometry and operational reconstruction
Exact holomorphic half-form Green kernel on named four-mark C2 source. Uniqueness concerns underlying spin-line class,not an extra Q linearization phase. No automatic positive equal-time CAR covariance,smooth quarter circle or physical time/action normalization. Raw coefficient monodromy remains order2.
Read the exact result, assumptions and evidence
Result
Partition{1,−1}|{i,−i} is exactly the supplied Q fixed nontrivial spin-line class by divisor D_A and H0 test. With g⁴=(x²−1)/(x²+1),S_alpha=sqrt(dx dz)[g(x)/g(z)+g(z)/g(x)]/[2(x−z)] is the actual normalized Szego kernel. Its complete two-sheet matrix has constant unitary diagonalization to diag(g(x)/g(z),g(z)/g(x))/(x−z),without an undetermined elliptic remainder. dlogg=x dx/(x⁴−1) has alternating residues±1/4;four central spin meridians square to−I and multiply toI. Q exchanges both character lines. Pole,spin divisor,conjugate-sheet cancellation and H0(alpha)0 prove the global identity;theta3 numerical checks are only diagnostics.
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.
- 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
- GLOBAL-SPIN-KERNEL.txt lines 1–190
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/GLOBAL-SPIN-KERNEL.txt
2f8a165804067b7522b2689239e2bcef8b58d925e3db2d09b2d8e50caabdecc8
- GLOBAL-SPIN-KERNEL.txt lines 191–279
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/GLOBAL-SPIN-KERNEL.txt
2f8a165804067b7522b2689239e2bcef8b58d925e3db2d09b2d8e50caabdecc8
- SPIN-TRACE-LOCAL-KERNEL.txt lines 1–190
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/SPIN-TRACE-LOCAL-KERNEL.txt
591051be956f8bb3c464d039dca502ba66b1274b8faf84c73c411be10c84d0f7
- SPIN-TRACE-LOCAL-KERNEL.txt lines 191–274
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/SPIN-TRACE-LOCAL-KERNEL.txt
591051be956f8bb3c464d039dca502ba66b1274b8faf84c73c411be10c84d0f7
- UPDATE-SPIN-KERNEL-AND-MODULAR-C3.txt lines 1–181
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/UPDATE-SPIN-KERNEL-AND-MODULAR-C3.txt
c45a2af3cdfb9f7c4a80a3a83b843cbf1d4d0cf53c2c6386f6b3325d129be71e
- INDEPENDENT-FINAL-REVIEW.txt lines 1–168
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/INDEPENDENT-FINAL-REVIEW.txt
e9de361910ef0018fad5aaeae2831244ed23094990a8a6827ff45848c32f17eb
- check_spin_transport_and_cusp.py lines 1–144
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/check_spin_transport_and_cusp.py
590c83f4347957009aca9ccbbd5eefe848425f0b5c26b0a7ba0e5fbf99eaac6a
- spin-transport-cusp-results.json lines 1–33
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/spin-transport-cusp-results.json
0630c3c9ca65d10b083c4ea891f3f294e1e7f78bd31c3b2e6ad207767aeb06ce
finding:elliptic-ns-spin-trace-has-complete-global-quarter-kernel