Established within the stated premises
Raw NS pullbacks yield the spin central commutator and quarter descent
finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent
For the untwisted NS NS line and raw complex-linear coefficient pullbacks,U_delta²=chi(1+i)=+I and U_rho U_delta=−U_delta U_rho,because universal lifts differ by the A cycle. The glide g=delta_E rho=−bar z+T has g²=z+i and U_g²=−I. With fixed sigma_s²=I,A=sigma_s U_g is Dirac covariant,A²=−I,and has c=±i spaces with involutive c^−1 A descent. Anti-linear Real j_g is distinct:(sigma_s j_g)²=+I and has no complex ±i eigenspaces. Q invariance allows only(+,+),(−,−);a genuine transported A4 Spin/Pin relation forces(−,−),without a separate no-zero-mode rule.
Scope: Raw flat spin pullbacks with explicit Clifford convention. Additional spin minimality requires genuine Spin/Pin bundle transport up to real central sign;an arbitrary projective U1 phase is another linearization. Do not identify Q,half translation,Pin operator and OS Real structure.
Required premises and original source excerpts
- 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.
premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks - 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.
premise:original-p1-seed-boundary-and-local-restriction-definitions - 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.
premise:typed-source-structures
- experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/GEOMETRY.txt, lines 240–393
Source SHA256: be6dca12fe366f6aeba7953dd7ba1c100ddfe40d5faca43d8ea1a883fe85c4ce
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- experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/INDEPENDENT-REVIEW.txt, lines 1–190
Source SHA256: 70ad3761cf9165538022baf5c65af259bf89bef344758d779936dccc5e7aea75
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- experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/INDEPENDENT-REVIEW.txt, lines 191–360
Source SHA256: 70ad3761cf9165538022baf5c65af259bf89bef344758d779936dccc5e7aea75
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- experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/check_elliptic_moebius_review.py, lines 91–225
Source SHA256: 980cf9a8a6638cf1940e8969800bc61cd000e00916834bef9227547a16db4deb
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- experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/elliptic-review-results.txt, lines 1–2
Source SHA256: e64e17ff8f2c7ccf01ca2697329703ceee5227b5bb186bcb1d70b107662eba23
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