Admitted Log-Source Q Image Lattice and the Primitive Interior Correspondence Gate
Date: 2026-08-15
Status: superseded by entry 275. The original conclusion omitted the two
normalization-sheet hemispheres and was false. No graph admission is claimed.
Correction
Entry 275 proves that each octahedral sheet hemisphere has primitive relative
Q coefficient one. Their sum is the coefficient-two total. The corrected row
is [2,1,1,0,0,0,0,0,0], with Smith factor one. The 2Z conclusion below is
historical and must not be cited.
Exact source image
Project every currently support-typed source class to the primitive relative K6 top coordinate certified in entry 273. The full-log maximal-cone class has coefficient two. The six local oriented KN wall classes and entry 272's short hexagon filler lie in , hence have literal -coefficient zero. Thus the admitted row is
Its Smith factor is two, its image is , and its cokernel is . No integral combination has coefficient one.
Entry 198's projective-conductor Gysin is abstractly primitive, but it is not an admitted literal column: entry 271 proves that its two disjoint triangular pair-incidence components cannot identify with the connected six-corridor hexagon. Including that unit without a new correspondence would stipulate the missing map.
Minimal enlargement
A single independently constructed reflection-odd relative-interior column of coefficient changes the row to , Smith factor one. It must come from a proper support-typed normalization/log-BM or nearby-cycle object whose boundary is the literal connected hexagon, whose chart restrictions are the entry 219, 328 Rees/KN packets, and whose long boundary is the based entry143 row.
Until this column is geometric rather than declared, the endpoint/Q mapping fiber and all downstream invariants remain undefined.
Certificate
research/voevodsky/check_admitted_log_source_q_image_lattice.rs
{
"claim": "The currently admitted support-typed normalization/log source classes map to the literal relative Q coordinate with image lattice 2Z; local primitive Rees/KN walls and the short hexagon have Q-image zero.",
"status": "falsified_scoped_admitted_source_primitive_Q_surjectivity",
"scope": "currently admitted source classes only; enlarged proper log-BM/nearby-cycle interior correspondences remain open",
"matrix": {
"admitted_Q_row": [2,0,0,0,0,0,0,0],
"smith": [2],
"image": "2Z",
"cokernel": "Z/2",
"P2_unit_literal_column_admitted": false,
"minimal_new_column": 1
},
"minimal_repair": "Construct one proper support-typed reflection-odd relative-interior correspondence with literal Q coefficient +1 and boundary restrictions equal to the connected hexagon and all adjacent Rees/KN packets.",
"physical_mapping_fiber": "unconstructed",
"physical_p_partial_Q": "undefined",
"physical_Bockstein": "undefined"
}