Established in scope
Spin-rigidified theta space is identified as complete complex Heisenberg and clock module
In the question: Common clock sectors, quartic geometry and operational reconstruction
Complex four-dimensional module closure for explicitly constructed Wq including full central action. Physical source selection of one inverse Nq copy remains open. Does not derive integral Gaussian E8 lattice,physical metric,W8 dynamics,or state rule.
Read the exact result, assumptions and evidence
Result
Spin-rigidified theta space is identified as complete complex Heisenberg and clock module. For L=O(2Theta),N={g in G(L):g⁴=1} is canonical order64 group with mu4 center. Every symplectic Phi lifts to N≅N64;Stone-von Neumann identifies Wq=H0(L) tensor Nq^(-1) with native C4 module. c lift has no remaining Pauli shift because1−Sigma invertible. alpha gamma alpha^(-1)=gamma^(-1) and trace(Ad gamma)=1 force trace(gamma)=1,hence exactly gamma->sigma without cube-root phase. Same intertwiner sends alpha to fully classified joint Clifford conjugacy class.
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
- 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:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package