Scoped exclusion
With fixed q0 rigidification,direct point-norm correction does not preserve original cubic action
In the question: Common clock sectors, quartic geometry and operational reconstruction
Two explicitly defined q0-normalized variants. Following source-selected S0-relative normalization removes first family obstruction;boundary-first then square remains excluded. Not intrinsic obstruction of all Poincare families.
Read the exact result, assumptions and evidence
Result
With fixed q0 rigidification,direct point-norm correction does not preserve original cubic action. For E_L=S0 tensor L,evaluation line is Nq(S0) tensor P_delta,delta=Dq−3q0=q1−q2 nonzero in Vq. O(2Theta) tensor P_delta is a different marked line bundle. Since c has no nonzero fixed vector in Vq,c*delta differs from delta;no linear c lift exists on same theta line bundle. Imposing vanishing first on determinant line then performing usual squaring removes P_delta² but point phase becomes−1 rather than+i. Neither direct functor variant supplies required joint 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.
- 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
- 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:point-normalized-theta-family-correction-fails-original-cubic-action