Scoped exclusion
Natural elliptic anchor connection is not the original P2 cusp connection
In the question: Common clock sectors, quartic geometry and operational reconstruction
Excludes only the natural scalar/spin direct connection as the actual original P2 connection,including scalar-twist repairs. Does not exclude other originally derived nonabelian connections on the common bundle. Separate exact v117 matrix properties from numerical ODE identification.
Read the exact result, assumptions and evidence
Result
Natural induced connection on Vell has residues0,1/2,1/2 at each ramification mark,monodromy1,−1,−1,polynomial(lambda−1)(lambda+1)^2,order2,trace−1. Original P2 target has residues0,1/3,2/3,spectrum1,omega,omega²,polynomiallambda³−1,order3,trace0. Thus no local connection intertwiner exists. Nonzero scalar twists preserve the repeated eigenvalue and cannot repair it. Natural direct sum is also reducible,while stated original <U,M0> is irreducible. v499 already separates the Z2 pillowcase from the Z3 weight cover. Another connection on the same bundle remains additional data to derive.
Required assumptions
- Existing C2 group with untwisted raw flat spin pullbacks
On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed.
- 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.
- 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
- PUSHFORWARD-ANCHOR.txt lines 1–190
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/PUSHFORWARD-ANCHOR.txt
cbe5383c9df7b8f1b1095566f909ce3a357d10e9b3cd1bd15c89b8c72af870a2
- PUSHFORWARD-ANCHOR.txt lines 191–224
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/PUSHFORWARD-ANCHOR.txt
cbe5383c9df7b8f1b1095566f909ce3a357d10e9b3cd1bd15c89b8c72af870a2
- check_pushforward_anchor.py lines 1–41
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/check_pushforward_anchor.py
16784bcf6b852244c7bbd1d161266e1b6dd3f31d0268c7645d3c9623375a99f7
- pushforward-anchor-results.json lines 1–18
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/pushforward-anchor-results.json
349eecee55bb0e505d86c172c9092dc22d0d2b886fd001d17664d33c190626d6
finding:natural-elliptic-anchor-connection-is-not-original-p2-cusp-connection