Degree-Two Full-Log Carrier and the Central Exceptional Primitive Repair
Oriented degree
The coherently oriented maximal-cone fillers of entry266 sum to twice the primitive K6 fundamental sphere. The full-log carrier therefore reaches the generic target top with coefficient two, not one.
This factor is derived from the signed-ray determinant orientations and all nine facet coefficients. It is not the unsigned fact that every facet occurs twice.
Primitive exceptional repair
Entry176 independently proves that the central exceptional relative cap has normalized coefficient +1. Adjoining it to the degree-two carrier gives the top/framing row
[2, 1].
Its Smith form is [1], so the row is saturated and has zero cokernel. With the certified central value k=1, the primitive top equation
2 a + k = 1
has carrier coordinate a=0. The corresponding finite local top parity is zero.
This is the exact integral mechanism that repairs the global degree-two carrier without division by two.
Remaining support gate
The calculation does not identify the central exceptional generator with the literal entry143 generic-top/endpoint-Q defect. Entry176 explicitly leaves that spatial comparison unconstructed. Therefore the zero computed here is a local augmented-top coordinate, not the physical p_partial_Q.
The next required arrow is a support-typed proper/log-excess comparison that simultaneously realizes the facet lift of entry343 and transports the central exceptional unit into the literal generic-Q top. Only then can the pointed endpoint/Q mapping fiber be instantiated.
Evidence
- research/voevodsky/check_full_log_maximal_cone_k6_fillers.rs
- research/voevodsky/check_degree_two_central_exceptional_repair.rs
- entries 143, 176, 266, and 267.
{
"status": "proved_scoped_degree_two_central_exceptional_repair",
"carrier_degree": 2,
"central_coefficient": 1,
"augmented_row": [2, 1],
"smith_factors": [1],
"cokernel": 0,
"normalized_central_k": 1,
"carrier_coordinate": 0,
"local_top_parity": 0,
"spatial_central_to_entry143_top_map_constructed": false,
"mapping_fiber_instantiated": false,
"physical_p_defined": false,
"physical_bockstein_defined": false,
"D8_Jordan_tested": false,
"graph_admission_claimed": false
}