Scoped exclusion
Primitive class2 sphere prevents global whole Cartan-subspace choice
In the question: Common clock sectors, quartic geometry and operational reconstruction
Topological exclusion only for whole Cartan-subspace choice in fixed quarter sector over precisely the same primitive normal base. Needs no connection. Does not exclude single vectors,arbitrary rank4 carriers,punctured bases or allowed defect and degeneration sites. Previous parallel-clock theorem remains valid. No splitting of old sign-lift extension claimed.
Read the exact result, assumptions and evidence
Result
Pointwise centralizer of whole Cartan four is T^J=F2^4;setwise normalizer N has order16*46080=737280. An everywhere smooth Cartan-subspace choice reduces the K_C bundle to N. On simply connected S2 this would trivialize it,contradicting old class2 in Z4 for every natural m. Separately,a whole Cartan four parallel under the same K connection forces curvature0.
Required assumptions
- 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.
- 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.
- Existing natural joint lift with given split connection
Assume a GIVEN unitary E=E3+E2 and GIVEN block U3xU2 connection A_E. Use only the natural iota_m with sum m=-2 completely classified on22September and their derived connection A_Wm=rho_LambdaEven(A_E)+M_m tr A_E. This does not select A_E from P1;an independent nonabelian family connection is not silently 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
- CARTAN-FAMILY-DICTIONARY.txt lines 172–219
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/CARTAN-FAMILY-DICTIONARY.txt
7b16a69ded0088bfe7a1fad8e1d8bdd79f49d4b00ff5bcb581a8ba260c45e864
- check_cartan_family_dictionary.py lines 50–85
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/check_cartan_family_dictionary.py
91344d5d71b4fd7c163b7648460ab5127d5c026cd1927faa4510c126f3a02c4b
- PROOF.md lines 80–99
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/source-joint-spin-family-lift-20260922/PROOF.md
d3ae02543e90d840879808554816f923cc36cab52268a032d1ce29c2569f5bd2
finding:primitive-class-two-sphere-obstructs-global-cartan-subspace-choice