Established in scope
Joint clock relations have exactly one native Clifford gauge class
In the question: Common clock sectors, quartic geometry and operational reconstruction
Finite matrix construction with fixed central character. Geometric bridge for Wq is now separately proved by finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package. Conjugacy class is not automatically physical gauge;P1/P2 anchors,state and readout excluded.
Read the exact result, assumptions and evidence
Result
Joint clock relations have exactly one native Clifford gauge class. Under explicit module condition beta->J=iI,no matrix in any64-element G31 fiber over the9 admissible Q actions squares to+iI;in zeta8 G31 each fiber has8. Original relation alpha sigma alpha^(-1)=sigma^(-1) leaves exactly alpha and−alpha. Explicit alpha=zeta8(XI)U has alpha²=J,alpha⁴=−I,and joint group order24. Actual C_G31(sigma) has order72 and is transitive on all9 sign classes. Thus one gauge class remains for fixed sigma,J,Pauli system.
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
- PAULI-SPIN-CENTRAL-LIFT.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/PAULI-SPIN-CENTRAL-LIFT.txt
e5ef50c899eba80dca03e1b7023edf816df3b45a669534fccf2fef215b0ae8e6
- PAULI-SPIN-CENTRAL-LIFT.txt lines 181–262
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/PAULI-SPIN-CENTRAL-LIFT.txt
e5ef50c899eba80dca03e1b7023edf816df3b45a669534fccf2fef215b0ae8e6
- PAULI-SPIN-CENTRAL-LIFT-INDEPENDENT-REVIEW.txt lines 1–115
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/PAULI-SPIN-CENTRAL-LIFT-INDEPENDENT-REVIEW.txt
81b238c1ff40cbd5804fc13841d0762fcb4ece53a8cc0189719aea4f3fc3632f
- PAULI-VERSUS-CODE-SOURCE-TARGET.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/PAULI-VERSUS-CODE-SOURCE-TARGET.txt
618a48566f2a1ad1be9b7f09aa1b2892f43b52644d9d8883db94fd6a75be699d
- PAULI-VERSUS-CODE-SOURCE-TARGET.txt lines 181–265
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/PAULI-VERSUS-CODE-SOURCE-TARGET.txt
618a48566f2a1ad1be9b7f09aa1b2892f43b52644d9d8883db94fd6a75be699d
- 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:joint-source-clock-relations-have-one-native-clifford-gauge-class