Literal Maximal-Filler Facet Boolean Lift and the Spatial Pushforward Gate
Complete facet-state matrix
Entry266 pairs the 18 oriented facet occurrences into two copies of every one of the nine K6 facets. The literal entry143 packet on a facet labelled by one diagonal has two Boolean states and two retained Tor grades.
Lifting all occurrences therefore gives 72 assignment occurrences onto 36 distinct literal facet generators. Every target generator occurs exactly twice, so the 36 Beck--Chevalley equality rows are disjoint primitive [1,-1] rows. Their matrix has rank 36, 36 unit Smith factors, and no integer torsion.
The six short-diagonal facets are pentagons and the three long-diagonal facets are squares, giving 42 boundary edges. Across both occurrences, both Boolean states, and both Tor grades, the checker derives 336 literal radial Cech rows and 36 normal-removal rows. It verifies all 168 radial/normal mixed squares: the entry143 normal signs at support sizes one and two are opposite, so the two orders cancel integrally.
The complete two-dimensional finite literal lift is D3- and reflection-stable.
Remaining geometric realization
The cellular and BM-Cech matrices are now fixed through maximal-cone degree. What remains is not another finite incidence choice. It is the support-typed proper/log-excess transformation from the normalization-provenanced product-branch Rees Cech carrier into these literal entry143 generators.
That transformation must realize the already certified 336 radial rows, 36 normal rows, and 36 paired-facet BC equalities, restrict to the three-segment edge lift of entry342, and preserve endpoint framing. Until this pushforward is constructed, the generic Q top and pointed endpoint/Q mapping fiber remain uninstantiated.
Evidence
- research/voevodsky/check_maximal_fillers_literal_facet_boolean_lift.rs
- entries 143 and 259-266.
{
"status": "proved_scoped_literal_maximal_filler_facet_Boolean_lift",
"facets": 9,
"short_pentagons": 6,
"long_squares": 3,
"facet_boundary_edges": 42,
"facet_occurrences": 18,
"state_Tor_assignment_occurrences": 72,
"distinct_literal_facet_generators": 36,
"paired_facet_BC_equalities": 36,
"BC_matrix_rank": 36,
"BC_smith_unit_factors": 36,
"radial_Cech_rows": 336,
"normal_rows": 36,
"mixed_square_checks": 168,
"integer_torsion": false,
"D3": true,
"reflection": true,
"spatial_Rees_to_entry143_BC_constructed": false,
"global_endpoint_Q_map_constructed": false,
"mapping_fiber_instantiated": false,
"physical_p_defined": false,
"physical_bockstein_defined": false,
"D8_Jordan_tested": false,
"graph_admission_claimed": false
}