Full-Log Maximal-Cone BC Backbone and the Literal Row-Assignment Gate
Derived 24-row backbone
Every maximal cone of the full-log toric bundle in entry 259 selects one signed ray in each of the three conductor-normal directions. Its three unordered pairs of directions give three two-step Gysin contractions. Therefore the eight maximal cones canonically produce
Beck--Chevalley relations. Reversing the contraction order reverses the exterior sign, while both paths carry exactly the same multiplicity monomial. The cancellation is integral and never divides a road multiplicity.
After orienting the two composites, every relation has primitive row . Their block matrix has rank 24 and 24 unit Smith factors. Rotation and reflection permute the complete set.
Exact scope boundary
This derives the multiplicity-sensitive source-side 24-row BC backbone. It does not assign those rows to literal entry143 generators. Such an assignment cannot be an ordinary face-poset map by entry 258: the mixed two-cones have empty common K6 support and every maximal cone has empty triple support.
The remaining datum is a single mixed-variance realization functor whose local maps identify:
- each two-step source contraction with the corresponding occurrence and normal-circle differential in entry143;
- its two conductor Tor grades with the literal target Tor rows;
- its localization comparison with the target Cech corestriction; and
- the oriented sum of the eight maximal-cone homotopies with the six short-facet terms in the generic-top defect.
Without these vertical maps, the 24 unit relations are not yet the requested 24 literal rows, and the endpoint/Q mapping fiber remains untyped.
Evidence
research/voevodsky/check_full_log_maximal_cone_bc_rows.rs- entries 143, 251, 258, 333, and 259.
{
"status": "proved_scoped_full_log_maximal_cone_BC_backbone",
"maximal_cones": 8,
"pairwise_contractions_per_cone": 3,
"BC_rows": 24,
"opposite_exterior_signs": true,
"multiplicity_monomials_retained": true,
"rank": 24,
"smith_unit_factors": 24,
"integer_torsion": false,
"D3": true,
"reflection": true,
"literal_entry143_row_assignment_constructed": false,
"mapping_fiber_instantiated": false,
"physical_p_defined": false,
"physical_bockstein_defined": false,
"D8_Jordan_tested": false,
"graph_admission_claimed": false
}