Established in scope
Modular theta-square pair reconstructs v117 with a different geometric Q mark
In the question: Common clock sectors, quartic geometry and operational reconstruction
Exact joint representation equivalence after expressly named phases. No original P1/P2 origin proof or identification of spatial with moduli monodromy. New moduli path is an additional changed premise and specifically does not repair the fixed Q identification.
Read the exact result, assumptions and evidence
Result
Standard theta squares give raw group96,central mu4 and projective PSL2(Z4)=S4. Spin labels alone see onlyS3. For UTheta=−i A_T,MTheta=i A_S A_T, X=[[-1−i,0,0],[0,i,−i],[0,1,1]]/sqrt2 satisfies exactly XUThetaX*=U_v117 and XMThetaX*=M0_EXACT. Same X intertwines both generators;normalized group has24elements. Geometric Q:z->iz at tau=i is modularS with projective order2 and eigenmultiplicity1+2,whereas U_v117=T has order4 and three distinct eigenvalues. Isotrivial v493 supplies no elliptic T path. Origin needs an actual level4 family/sewing transport with distinct spatial mark and derived phase section.
Required assumptions
- Original P2 order-three cusp class and stable bundle anchor
Target the original P2 Deligne class with cusp weights0,1/3,2/3 and holomorphic anchor O(-2)+O(-1)^2. Exact v117 M0_EXACT has polynomiallambda³−1,trace0,order3;its joint representation with U is irreducible. Keep these exact matrix properties distinct from the numerical ODE identification there. Test whether the natural scalar/spin pushforward of existing C2 realizes this actual connection;physical selection of the direct sum as flavor module is not presumed.
- Theta-square modular action with distinct geometric Q
Test standard S/T action on three theta squares as a representation of a marked elliptic family, retaining weight and central phases. Geometric Q:z->iz at fixed tau=i is the S homology change, not an already supplied T moduli path. Do not assume this family action has the same origin as spatial monodromy of fixed four-punctured P2.
- 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
- MODULAR-C3-SOURCE-TEST.txt lines 1–190
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/MODULAR-C3-SOURCE-TEST.txt
cf2fc1a89b7582ed4986b71c7a9e243525cd4ea2333cdd1cd4c86dce107b3993
- MODULAR-C3-SOURCE-TEST.txt lines 191–345
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/MODULAR-C3-SOURCE-TEST.txt
cf2fc1a89b7582ed4986b71c7a9e243525cd4ea2333cdd1cd4c86dce107b3993
- INDEPENDENT-FINAL-REVIEW.txt lines 1–168
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/INDEPENDENT-FINAL-REVIEW.txt
e9de361910ef0018fad5aaeae2831244ed23094990a8a6827ff45848c32f17eb
- check_spin_transport_and_cusp.py lines 1–144
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/check_spin_transport_and_cusp.py
590c83f4347957009aca9ccbbd5eefe848425f0b5c26b0a7ba0e5fbf99eaac6a
- spin-transport-cusp-results.json lines 1–33
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/spin-transport-cusp-results.json
0630c3c9ca65d10b083c4ea891f3f294e1e7f78bd31c3b2e6ad207767aeb06ce
finding:theta-square-modular-pair-reconstructs-v117-with-distinct-geometric-q