Established in scope
Original cubic and quarter select spin line and half-turn lift
In the question: Common clock sectors, quartic geometry and operational reconstruction
Spin bundle of actual genus2 source,not honest C2 linearization. Subsequent finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package closes complex module bridge for Wq. Physical choice of inverse point norm and state remains open.
Read the exact result, assumptions and evidence
Result
Original cubic and quarter select spin line and half-turn lift. S0=O(q0+q1+q2−K_C) is even,S0²=K_C,and equivalent to p definition. c has no nonzero fixed vector on Jac(C)[2],so S0 is unique c-invariant theta characteristic among16. Q preserves S0;at marked fixed point q0,Q*eta=i eta. Any compatible spin lift alpha has alpha^4=−I,order8. beta=alpha composed Q*alpha is order4 lift of h=Q²,independent of alpha->−alpha,with local phase+i. Previously open S0,beta selection is closed by existing data.
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.
- 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
- SOURCE-SELECTED-THETA-SPIN.txt lines 1–174
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/SOURCE-SELECTED-THETA-SPIN.txt
cf4478191ccd75d62a2f049a54193541009bed24877df9cbe0ed9f942d07d717
- SOURCE-SELECTED-THETA-SPIN-INDEPENDENT-REVIEW.txt lines 1–84
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/SOURCE-SELECTED-THETA-SPIN-INDEPENDENT-REVIEW.txt
ab9a1e2a12a2b25175834f2140d3e17664e470c59ca55da204264f5ebb9cb54c
- HYPERELLIPTIC-SPIN-QUARTER.txt lines 1–137
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/HYPERELLIPTIC-SPIN-QUARTER.txt
68163e1664b76d9cbd2b28ffe8314acb9fefec78a14a4ce9b557d4e8240138eb
- HYPERELLIPTIC-SPIN-QUARTER-INDEPENDENT-REVIEW.txt lines 1–41
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/HYPERELLIPTIC-SPIN-QUARTER-INDEPENDENT-REVIEW.txt
67b28753483b4472cf0e8cb672a9a2624cb61b89b5f6712d0c40bf9fed66afe0
- 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:source-cubic-and-quarter-select-even-theta-and-spin-half-turn-lift