Scoped exclusion
Ordinary theta determinant functor erases selected spin character
In the question: Common clock sectors, quartic geometry and operational reconstruction
Only ordinary rigidified determinant and Kummer functor. Finite Clifford construction remains valid under explicitly required central character. Refinements and additional lines from marked source data are not excluded.
Read the exact result, assumptions and evidence
Result
Ordinary theta determinant functor erases selected spin character. Every E_L=S0 tensor L has chi=1+1−2=0. Scalar lambda acts on det RΓ(E_L) by lambda^chi=1. Thus beta²=−I becomes beta_D²=+I,and alpha⁴=−I becomes alpha_D⁴=+I. Dualizing or squaring cannot restore lost phase. All four standard H0(2Theta) functions are even;inversion acts+I. Direct untwisted functor therefore does not give beta->J=iI.
Required assumptions
- Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
- Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
- Native Pauli translations and frozen Gaussian phase class
Native theta-translation target is P_nat=N64/mu4 from v783 in frozen four-component frame,with actual sigma and J=iI. Code quotient L/(1+i)L is the distinct duality-twisted context module. G31 has center mu4;full Clifford matrix group has center mu8 and additional coset zeta8 G31. Retain these concrete actions and phases.
- Ordinary rigidified theta determinant functor
A=Jac(C), E_L=S0 tensor L of degree1 on genus2. D_L=det H0(E_L) tensor det H1(E_L)^(-1),or dual convention;Poincare family rigidified at marked q0. Then O(2Theta) and four holomorphic sections with standard symmetric linearization. No additional Pfaffian,metaplectic factor,or marked-point determinant.
- 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
- THETA-FUNCTOR-SPIN-SIGN-TEST.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/THETA-FUNCTOR-SPIN-SIGN-TEST.txt
a5128ab5c2b1602bd64a7b6610ba9282707d6ec65c839051ecb42ccc50bfb910
- THETA-FUNCTOR-SPIN-SIGN-TEST.txt lines 181–212
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/THETA-FUNCTOR-SPIN-SIGN-TEST.txt
a5128ab5c2b1602bd64a7b6610ba9282707d6ec65c839051ecb42ccc50bfb910
- THETA-FUNCTOR-SPIN-SIGN-INDEPENDENT-REVIEW.txt lines 1–67
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/THETA-FUNCTOR-SPIN-SIGN-INDEPENDENT-REVIEW.txt
9390dd8aba4e1429bc00568de0f9985ad3862c2d05f5b70f930dc81ecdfa3eb0
finding:ordinary-theta-determinant-erases-selected-spin-central-character