Literal Pair-Intersection Twenty-Four-Row No-Go and the Extraordinary Support-Switch Gate
Date: 2026-08-15
Status: falsified for ordinary literal entry143 face corestrictions.
Extraordinary log-Gysin/support-switch correspondences remain open. No graph
admission is claimed.
Exact earliest falsifier
The proposed pair-intersection source has six physical dP6 cones. Each cone has four Boolean normal states, hence the requested 24 occurrence/normal/Tor/ Čech incidences.
Under either admitted (D_3)- and polarity-equivariant ray labeling, the two rays of every cone map to crossing short diagonals of (K_6). Entry143 has a generator ([S,H]) only when (S) is a compatible (K_6) face and (Hsubseteq S). No compatible face contains either crossing pair. Therefore all 24 proposed literal target rows are absent before coefficients, Tor multiplicities, signs, or endpoint normalizations are chosen.
Mapping the unsupported source rows to zero is not a chain map. The six cone boundaries share six ray states and form the oriented hexagon incidence matrix (R-I). It has rank five, kernel generated by ((1,1,1,1,1,1)), Smith factors ((1,1,1,1,1)), and no torsion. Its nonzero primitive ray boundary cannot map to the zero literal target.
Rotation and reflection preserve the crossing obstruction. The norm kernel is the global SNC top relation; it does not create any of the missing individual ([S,H]) rows.
Scope
This is a no-go only for ordinary support-preserving maps in entry143's existing face-indexed category. It does not rule out a new derived, constructible, log, cdh, nearby-cycle, or bivariant correspondence.
The minimal additional datum is six branch-selected extraordinary pair objects (three per polarity side), each equipped with:
- two log-residue maps to the adjacent long-facet ray packets;
- a multiplicity-sensitive support-switch/Gysin comparison landing in the complementary marked corridor (C_\bullet(q_k)subset F_B/F_V);
- all four Boolean normal-state maps with the two Tor grades and Čech signs;
- endpoint-framed Beck-Chevalley cells and (D_3)/reflection covariance.
Only after those objects and maps exist can one form the literal 24-row matrix, test its SNF, instantiate the endpoint/Q mapping fiber, and compute (p_{partial,Q}), its Bockstein, (D_8), or Jordan coherence. Those downstream invariants remain undefined here.
Certificate
The focused source is:
research/voevodsky/check_p2_pair_literal_24_row_no_go.rs- SHA-256:
4516b44a1a67c997378c1afa8a6023e07e050dbbf210947e28caf2c9ed9b4eb0
It reconstructs the (K_6) face census ((1,9,21,14)), derives all 24 source residue descriptors from the (S minus H) localization rule and entry143 normal-removal signs, retains Tor grades zero and one, exhausts both equivariant labelings, verifies zero legal literal target rows, checks the primitive cone and double-Cech residues, constructs the global (R-I) boundary, proves a unit 5-by-5 minor, and checks rotation and reflection.
Worker MCP run run-db7c3be78cbc480ab123645c739c0c71 passed
rustfmt --edition 2021 --check and warnings-denied metadata compilation.
After the MSVC toolchain was initialized explicitly with vcvars64.bat, a
warnings-denied optimized linked build and runtime execution also passed; its
JSON parsed with the stated status, and the temporary executable was removed.
Outcome contract
{
"claim": "The 24 source residue descriptors are derived from S-minus-H localization, entry143 normal signs, primitive ray residues, and double-Cech cancellation. All 24 ordinary literal entry143 target rows are absent because every physical dP6 cone is supported on a crossing short-diagonal pair; the zero-image replacement violates the nonzero primitive R-I source boundary.",
"status": "falsified_scoped_literal_24_row_map__source_residues_derived",
"scope": "existing entry143 face-indexed generators and ordinary support-typed corestrictions only; extraordinary support-switch/log-Gysin correspondences remain open",
"evidence": {
"k6_face_census": [1, 9, 21, 14],
"physical_dp6_cones": 6,
"boolean_states_per_cone": 4,
"derived_source_residue_rows": 24,
"cech_denominators": "exactly S minus H",
"normal_removal_signs": {"empty": [], "left": [-1], "right": [-1], "top_to_right_left": [-1, 1]},
"normal_d_squared": 0,
"ray_residue": [-1, 1],
"forced_double_cech_correction": [-1, 1],
"retained_tor_grades": [0, 1],
"required_literal_rows": 24,
"legal_literal_rows": 0,
"both_equivariant_labelings_checked": true,
"source_boundary": "R-I on six shared ray states",
"source_boundary_rank": 5,
"source_boundary_kernel_rank": 1,
"source_boundary_smith": [1, 1, 1, 1, 1],
"source_norm_kernel": [1, 1, 1, 1, 1, 1],
"zero_image_chain_equation": "FAIL",
"D3_rotation": "preserves crossing obstruction",
"D3_reflection": "preserves crossing obstruction",
"integer_torsion": "none",
"endpoint_Q_mapping_fiber": "uninstantiated",
"physical_p_partial_Q": "undefined",
"physical_bockstein": "undefined",
"D8_and_Jordan": "untested because the mapping fiber is uninstantiated"
},
"checker_sha256": "4516b44a1a67c997378c1afa8a6023e07e050dbbf210947e28caf2c9ed9b4eb0",
"validation": {
"filesystem_mcp_full_reread": "PASS",
"rustfmt": "PASS via worker MCP run-db7c3be78cbc480ab123645c739c0c71",
"rustc_metadata": "PASS via worker MCP run-db7c3be78cbc480ab123645c739c0c71; empty compiler output",
"linked_rustc": "PASS after explicit vcvars64 initialization; rustc --edition=2021 -D warnings -O",
"runtime": "PASS; JSON parsed with status falsified_scoped_literal_24_row_map__source_residues_derived",
"cleanup": "PASS; temporary executable absent"
},
"minimal_additional_geometry": "Adjoin six branch-selected extraordinary pair objects with log residues to both adjacent rays and a chain-valued support-switch/Gysin comparison to the complementary marked corridor, including all Boolean, Tor, Cech, endpoint, reflection, and D3 Beck-Chevalley data."
}