Ordered dP6 Log Links and the Marked Half-Corridor Support Switch
Date: 2026-08-15
Status: proved in the finite labelled log-link and carrier dictionary. The
line-valued extraordinary Gysin transformation and literal six-functor stalk
map remain unconstructed. No graph admission is claimed.
Result
The two toric contractions of entry 165 label the six maximal cones of (dP_6) by
[ (pi,pi_{ m Cr})= (0,1),(0,2),(1,2),(1,0),(2,0),(2,1). ]
These are exactly the six ordered pairs of distinct physical roads. Polarity sends cone (i) to cone (i+3) and reverses its ordered pair. The omitted road is therefore intrinsic and selects the complementary marked corridor (q_k). The cyclicly ordered pairs select its positive marked half; their reversals select the negative marked half.
This removes a previously unresolved carrier-level choice. It uses the actual two toric contractions, not a fitted pairing between cones and roads.
For every ordered cone, the selected half-corridor consists of the two literal entry-143 edges obtained from entry 99's marked half-gallery. Both edge supports are compatible (K_6) faces of size two. Transporting the four Boolean masks to (Hsubseteq S) on each edge gives:
[ 6 ext{ cones} imes4 ext{ masks}=24 ]
source columns and (48) legal target edge-state terms. For every term the Čech denominator support is exactly (Ssetminus H). The normal-removal differential has the entry-143 signs
[ \varnothing,\qquad {a}mapsto-\varnothing,\qquad {b}mapsto-\varnothing,\qquad {a,b}mapsto-{b}+{a}, ]
and squares to zero. Rotation by two fan cones rotates both ordered road labels, the complementary marked corridor, and its ordered Boolean basis. Each corridor's two halves meet at the certified marked central vertex.
The two Tor grades remain spectator grades on each source column. They are not the factor producing the number 24.
Scope boundary
The checker derives a canonical target support dictionary. It does not yet construct the morphism of coefficient or sheaf objects. In particular it does not prove:
- the occurrence-line map from the crossing cone labels to the legal corridor edge labels;
- the multiplicity-sensitive excess-Gysin evaluation on those lines;
- the two adjacent-facet Beck--Chevalley coefficient squares;
- the literal six-functor costalk/corestriction realization;
- the strict reflection comparison 2-cell.
Accordingly this result does not instantiate the endpoint/Q mapping fiber or determine (p_{partial,Q}).
Next gate
On one seed cone, for example ((D_{14},D_{03}) o q_{25}^{+}), construct the line-valued transformation
[ operatorname{or}{log}otimes I{14}^{\vee}otimes I_{03}^{\vee}otimes K_{ m Tor/Cech} longrightarrow E_{143}|{q{25}^{+}} ]
and prove that its two log-boundary restrictions equal the certified (D_{14}) and (D_{03}) facet packets. The present theorem fixes every target support and Boolean sign of that transformation. Rotation and polarity then fix the other five ordered cones.
Certificate
research/voevodsky/check_dp6_ordered_pair_log_link_to_marked_corridor.rs- SHA-256:
1866dd8deca29f30c9e302419ce88c2c74678d33e7fe41691736a5e4b303ff9a
Validation:
rustfmt --edition 2021 --check: passed after formatting;rustc --edition=2021 -D warnings -O: passed;- linked runtime assertions and JSON emission: passed;
- temporary executable removed.
Outcome contract
{
"claim": "The two actual dP6 toric contractions canonically label its six cones by all ordered pairs of distinct roads. Pair reversal is polarity, the omitted road selects the complementary marked q_k corridor, and orientation selects its positive or negative marked half. This derives 24 source Boolean columns and 48 legal literal entry143 target edge-state terms with the exact normal and Cech signs.",
"status": "proved_scoped_ordered_dp6_log_link_to_marked_half_corridor_dictionary",
"scope": "finite labelled toric/log-link and entry143 carrier support dictionary; no line-valued extraordinary Gysin or literal six-functor realization",
"evidence": {
"ordered_cone_road_pairs": [[0,1],[0,2],[1,2],[1,0],[2,0],[2,1]],
"polarity_reverses_ordered_pair": true,
"complementary_corridors_each": 2,
"plus_half_cones": 3,
"minus_half_cones": 3,
"source_boolean_columns": 24,
"legal_target_boolean_terms": 48,
"normal_d_squared": 0,
"target_label_order": "moving_then_persistent",
"D3_rotation_exact_on_ordered_boolean_basis": true,
"retained_tor_grades": [0,1],
"occurrence_line_map": "unconstructed",
"adjacent_facet_BC": "unconstructed",
"literal_six_functor_stalk_map": "unconstructed",
"physical_mapping_fiber": "unconstructed"
},
"checker_sha256": "1866dd8deca29f30c9e302419ce88c2c74678d33e7fe41691736a5e4b303ff9a",
"next_required_map": "Construct the occurrence-line/excess-Gysin transformation on one ordered cone and prove its two boundary restrictions equal the adjacent long-facet packets."
}