Established in scope
Genuine D4 orbifold branch has unique irreducible v117 class
In the question: Common clock sectors, quartic geometry and operational reconstruction
Complete theorem in exactly specified genuine D4 class. Same abstract matrix class does not identify different marked base paths. Do not infer full D4 connection symmetry from C4 rotation. No physical P1 origin.
Read the exact result, assumptions and evidence
Result
J_D4=1/2-(x⁴+x^-4)/4 generates C(x)^D4. For genuine unitary SU3 descent on(infinity,2,4), c=diag(1,i,-i), regular cubic M=a², four half-meridian branches have traces0,2,2omega,2omega². Trace2 is impossible; complex branches are reducible. Unique survivor is a³=1,p=(1/2,1/4,1/4), the v117 matrix orbit. For genuinely linearized stable parabolic object canonical MS descent follows from uniqueness of adapted metric. Treat concrete A0* connection separately.
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.
- Genuine stable unitary D4 orbifold descent
The expressly specified stable determinant-trivial parabolic rank3 branch has genuine mark-preserving D4 linearization with Coxeter fiber c=diag(1,i,-i) and regular cubic meridian M=a². Apply Mehta Seshadri to this object. Do NOT identify the concrete A0* ODE with it merely from C4 rotation.
- 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
- D4-ORBIFOLD-RIGIDITY.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/D4-ORBIFOLD-RIGIDITY.txt
167d26868e5f1c0a09420a8e51168893fd8341e595fb06e964e0053cb88859e4
- D4-ORBIFOLD-RIGIDITY.txt lines 181–360
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/D4-ORBIFOLD-RIGIDITY.txt
167d26868e5f1c0a09420a8e51168893fd8341e595fb06e964e0053cb88859e4
- D4-ORBIFOLD-RIGIDITY.txt lines 361–504
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/D4-ORBIFOLD-RIGIDITY.txt
167d26868e5f1c0a09420a8e51168893fd8341e595fb06e964e0053cb88859e4
- D4-RIGIDITY-INDEPENDENT-REVIEW.txt lines 1–180
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/D4-RIGIDITY-INDEPENDENT-REVIEW.txt
a4c9114146fdeb4bf325a12f1a48b68d5d64814c57e789906a07d5ed9ccc750d
- D4-RIGIDITY-INDEPENDENT-REVIEW.txt lines 181–244
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/D4-RIGIDITY-INDEPENDENT-REVIEW.txt
a4c9114146fdeb4bf325a12f1a48b68d5d64814c57e789906a07d5ed9ccc750d
- INDEPENDENT-BOUNDARY-REVIEW.txt lines 1–154
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/INDEPENDENT-BOUNDARY-REVIEW.txt
7fac8804f89364125b2970eed9c937e7eb5dad2edf7253ffa8e9cc25f3d429fc
finding:genuine-d4-orbifold-branch-has-unique-irreducible-v117-class