Cross-Sheet Anchor No-Go and the Six Bridge Correspondence Gate
Exact obstruction after the local Boolean repair
Entry339 constructs the full eight-state Boolean packet on each of the six literal half-galleries. This does not yet construct the six cross-sheet two-cones of the full-log toric source.
Index a toric ray by a road and a sheet sign, ((D,epsilon)). Associate to it the two literal anchors of the corresponding half-gallery: its endpoint triangulation and its road-center triangulation. Exhaustive comparison gives:
- the six admissible sheetwise pairs share exactly one endpoint anchor;
- all six admissible cross-sheet pairs, which have different roads and opposite signs, have no common anchor; and
- the three opposite-sign pairs that do share a center belong to the same road and are precisely the forbidden opposite rays, so they are not cones of the product fan.
Consequently an admissible cross-sheet toric edge cannot be realized by concatenating two already constructed half-gallery arms. This failure is before coefficients, normal signs, Tor grades, or Smith reduction.
Scoped no-go
Within the literal K6 half-gallery objects of entries 334, 339, the cross-sheet part of the full-log source has no edge image. Hence the eight maximal-cone compatibility equations cannot yet be written in one literal entry143 mapping complex.
This does not prohibit an extraordinary/log correspondence. It proves that the existing half-gallery anchors do not supply it.
Minimal additional datum
For each of the six cross-sheet two-cones one must construct a bridge object (W_{(D,+),(D',-)}) with support-typed maps to both full Boolean half-gallery packets. Its proper/excess-Gysin image must be a literal entry143 chain joining the two middle triangulations, carry the occurrence and normal-circle lines and both Tor grades, and specify the Beck--Chevalley homotopy on its two endpoint restrictions. Rotation and reflection may transport one seed only after its stabilizer square is proved.
Only after these six bridges exist can the 24 local rows of entry339 be assembled around the eight maximal cones and tested by an integral SNF.
Evidence
research/voevodsky/check_full_log_cross_sheet_anchor_no_go.rs- entries 143, 259--260, 334, 338, and 262.
{
"status": "falsified_scoped_existing_half_gallery_cross_sheet_gluing",
"toric_two_cones": 12,
"sheetwise_two_cones": 6,
"sheetwise_shared_anchor": 6,
"cross_sheet_two_cones": 6,
"cross_sheet_shared_anchor": 0,
"forbidden_opposite_ray_pairs": 3,
"forbidden_pairs_shared_center": 3,
"existing_half_gallery_concatenation_constructs_cross_sheet_edges": false,
"new_cross_sheet_bridge_correspondences_required": 6,
"global_maximal_cone_gluing_constructed": false,
"mapping_fiber_instantiated": false,
"physical_p_defined": false,
"physical_bockstein_defined": false,
"D8_Jordan_tested": false,
"graph_admission_claimed": false
}