Established in scope
Marked negative-point norm carries exactly missing central character
In the question: Common clock sectors, quartic geometry and operational reconstruction
Point norm and central character proved. Full family and complex module intertwiner are closed in following spin-rigidification findings. Original boundary selection of one inverse norm remains open. One complex four-space with scalar J does not also carry s exchange of conjugate characters.
Read the exact result, assumptions and evidence
Result
Marked negative-point norm carries exactly missing central character. For Nq=tensor_a S0|q_a,beta on each fiber is+i,so beta_Nq=−i and beta_Nq^(-1)=+i. c acts trivially on Nq. Hence H0(2Theta) tensor Nq^(-1) has alpha²=+iI,alpha⁴=−I without fitted phase. Determinant of three fibers and norm line differ under Q only by transposition sign. p partner has conjugate−i character;s exchanges both. Using exactly one inverse point norm in actual field space remains candidate bridge.
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.
- 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
- MARKED-Q-DIVISOR-CENTRAL-TWIST.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/MARKED-Q-DIVISOR-CENTRAL-TWIST.txt
da1f75831a46a0c0662f931486b77e6e2085126df452b009d1a90351d413d904
- MARKED-Q-DIVISOR-CENTRAL-TWIST.txt lines 181–340
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/MARKED-Q-DIVISOR-CENTRAL-TWIST.txt
da1f75831a46a0c0662f931486b77e6e2085126df452b009d1a90351d413d904
- MARKED-Q-DIVISOR-CENTRAL-TWIST-INDEPENDENT-REVIEW.txt lines 1–130
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/MARKED-Q-DIVISOR-CENTRAL-TWIST-INDEPENDENT-REVIEW.txt
f2b4f084ace7506fd9e5ea90f293082d6ad7149fbba1ac8d830159aeb80eda8f
- SPIN-RIGIDIFIED-THETA-MODULE.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/SPIN-RIGIDIFIED-THETA-MODULE.txt
4bd17ffbb2be4b31c4eb7a4efe9cd8a1191c9065655889ce189f3b1f6c2499d2
- SPIN-RIGIDIFIED-THETA-MODULE.txt lines 181–276
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/SPIN-RIGIDIFIED-THETA-MODULE.txt
4bd17ffbb2be4b31c4eb7a4efe9cd8a1191c9065655889ce189f3b1f6c2499d2
- SPIN-RIGIDIFIED-THETA-MODULE-INDEPENDENT-REVIEW.txt lines 1–130
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/SPIN-RIGIDIFIED-THETA-MODULE-INDEPENDENT-REVIEW.txt
fadd56e04d9e10af0d0f7e9cd94010a35563ee3dc092659499502e410dbb23f8
finding:marked-negative-point-norm-restores-required-spin-central-character