Established in scope
Source-selected spin rigidification closes whole point-norm family
In the question: Common clock sectors, quartic geometry and operational reconstruction
Mathematical family bridge using already selected S0;q0 flat factor was rigidification artifact. No new free reference marking. Physical selection of exactly one inverse Nq copy remains open;boundary-first then square is distinct operation.
Read the exact result, assumptions and evidence
Result
Source-selected spin rigidification closes whole point-norm family. O(Dq)=S0 tensor K=S0³. For any Poincare family P define P_spin=P tensor pi_A^*<P,S0>^(-1). Since deg(S0)=1,<P_spin,S0> is canonically trivial,so Nm_Dq(P_spin)=<P_spin,S0³>=O. Changing initial Poincare normalization cancels in P_spin. Scalars in S0 isomorphisms and O(Dq)≅S0³ vanish in pairing with degree0. Norm trivialization is c,Q covariant;constant Nq phase survives. Ordinary theta determinant is unchanged because chi=0.
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
finding:source-spin-relative-poincare-normalization-closes-point-norm-family