Read the result in its research context.

Result

Unitary theta=2pi s identifies domains and actual operators:B_Sigma/(2pi)=Bcov=2(B1/4 direct_sum B3/4),V=T_pi,u_cov=[[0,u_base],[I,0]]. Q rotates cut charts and is not V. At canonical width W=1/2,the second chiral Calderon compression is C_A=(1+exp(2pi Bcov))^−1,hence geometric beta_angle=2pi without fitting. C_A is a mixed traceclass perturbation of the Hardy sea at distance<0.086590;relative covariance/Fredholm factor remains1−z,and(1−z)² for double winding. Known two-boundary graph reconstruction is specialized to the actual existing C2 cut. The old full flat Moebius test has modulus1,this one1/2;units cannot identify their full Dirac problems.

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.

• Free chiral Cauchy quantization of the canonical elliptic annulus

  Treat the dividing half of the given square curve in its canonical flat conformal representative as a product collar. Compute the Cauchy graph of Dplus=partial_t+B_Sigma,B_Sigma=−i partial_s with NS boundary,then interpret it using the expressly free chiral CAR construction as a quasifree two-boundary state. The labelled second-face compression is the covariance;the other is complementary. This Gaussian interpretation does not derive the original relative spectral-action measure,P1 time or EM/Quillen response.

• Original quarter CAR source with fixed fold and current dictionary

  The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.

• Original P1, boundary, seed and local restriction definitions

  Reviewed originals: P1 declares oriented seam, reflection-positive kernel, unit winding and c3; stronger T_boundary includes A_+ as data; operational seed takes A_loc, time, reflection, state, seam class and collar operator as inputs. A_adm(O) is A/A*-invariant restriction of supplied local insertions. Compare without P2/E8/target spinor assumptions and without presuming an original gauge/microscopic localization intertwiner.

• 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

• BOUNDARY-SOURCE.txt lines 1–190

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/BOUNDARY-SOURCE.txt

  a12e7b7566734e26ef9c53c6ee910638a77f20412085943d6cd30b255b7e9251

• BOUNDARY-SOURCE.txt lines 191–380

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/BOUNDARY-SOURCE.txt

  a12e7b7566734e26ef9c53c6ee910638a77f20412085943d6cd30b255b7e9251

• BOUNDARY-SOURCE.txt lines 381–570

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/BOUNDARY-SOURCE.txt

  a12e7b7566734e26ef9c53c6ee910638a77f20412085943d6cd30b255b7e9251

• BOUNDARY-SOURCE.txt lines 571–594

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/BOUNDARY-SOURCE.txt

  a12e7b7566734e26ef9c53c6ee910638a77f20412085943d6cd30b255b7e9251

• INDEPENDENT-REVIEW.txt lines 191–360

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/INDEPENDENT-REVIEW.txt

  70ad3761cf9165538022baf5c65af259bf89bef344758d779936dccc5e7aea75

• check_boundary_source.py lines 1–74

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/check_boundary_source.py

  1ce6a612aae1190204dcbb44cb4c71b5c330c0efd01643d3d1d3b261567fe6bd

• boundary-source-results.json lines 1–69

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/boundary-source-results.json

  00932f60621d41dbe1b3545d7691b00f71b322f0daaf788269b6baec9756dd3a

• UPDATE-REAL-SLOTS-AND-SOURCE.txt lines 1–115

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/UPDATE-REAL-SLOTS-AND-SOURCE.txt

  c2d8461181fdd54a61cfcd68617a1905964e76b50cb5737e404a75b42717fc9e

finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms