Conditional result
Even cover degree removes topology and selects neither C12 nor connection
finding:even-degree-pullback-removes-cartan-topology-without-selecting-clock-cover
An actually supplied degreeq pullback to the same normal base sends class2 to2q mod4. Every even degree removes this topological obstruction,smallest positive degree2;on compact S2 only branched or as a general degree map. Existing C2,C6,C12 do this only with proved same base and bundle map. Parity does not select C12. A given nonflat smooth connection remains nonflat under branched pullback. Sequence1 to Z4 to pi1(K/N) to N to1 explains why trivial N or G31 monodromy can hide class2.
Scope: Conditional repair with existing covers. Identity of normal S2 and original punctured source base is unproved. No freely chosen double cover as P1 selection. Full relative C12 monodromy retains its own global criterion.
Required premises and original source excerpts
- Native Cartan four in whole conjugated source
Given original Cartan h_C,H+=ker(J-i),and whole native clock chat with chat^9=Jhat,chat^4=sigmahat. Existing inner conjugacy transports the entire tuple and Cartan to kappa. H+ is not identified with SU4 family factor. In current W_m orientation,+i64 is its dual branch. No preferred conjugator is selected.
premise:native-cartan-four-in-full-clock-conjugate-source - Old joint class2 bundle on the same normal sphere
Given natural lift iota_m,sum m=-2,acts over the old common normal S2 with(c1(E3),c1(E2))=(0,1). For every m,its K=(Spin10 x SU4)/Z4 principal bundle has class2 in pi1(K)=Z4. Proposed choice is an everywhere smooth whole Cartan subspace in its fixed kappa sector. No identity with separate punctured flavor base is assumed.
premise:primitive-normal-sphere-joint-k-bundle-class-two - Actual degree pullback to precisely the same normal base
Conditional cover connection assumes an actual degreeq map f:Sigma to S2 from a closed oriented surface,pulling back exactly the joint K bundle. Connection statement assumes a smooth branched cover. Existing C2,C6,C12 qualify only after proving identity of base and bundle map.
premise:given-same-normal-base-degree-pullback - Existing marked cyclic cover tower and compact elliptic images
Use only existing C_n:u_n^n=x^4-1 with fixed x base,deck Delta_n and already forced compiler clock R12=Q12 Delta12^4=(ix,omega s),Q12=(ix,s). Compare compact algebraic curves over C and pullback function fields. A comparison of punctured local systems must retain its removed points,peripheral loops,spin and field transports.
premise:existing-marked-cyclic-cover-tower-with-compact-elliptic-images - 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.
premise:typed-source-structures
- experiments/theory-contracts/original-admissible-source-closure-20261025/CARTAN-FAMILY-DICTIONARY.txt, lines 220–253
Source SHA256: 7b16a69ded0088bfe7a1fad8e1d8bdd79f49d4b00ff5bcb581a8ba260c45e864
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/e-series-compiler-closure-20261023/COVERS.txt, lines 13–65
Source SHA256: cdd04f5f38819b60ddd8488eb1c3c316c6849829387205e78ec5e4bf767f80bf
bounded-excerpt · current-at-snapshot