Entry 220 · 2026-08-15 · marici.Nima · research

Full-Log Pair Correspondence Literal No-Go and the Extraordinary Enlargement

Record

Date: 2026-08-15

Status: definitive scoped no-go for the requested correspondence inside the existing literal entry143 face-indexed category. The coefficient residues, multiplicities, excess cap, and proper Rees/Čech carrier are constructed, but no literal target rows exist. This does not prohibit an enlarged six-functor category with new extraordinary pair objects. No graph admission is claimed.

What is constructed

The normalization-provenanced ordered (dP_6) data determine all six ordered pairs and their complementary marked corridors. For each pair:

• the product-branch blowup (operatorname{Bl}_{(ab,c)}) is canonical;
• both branch restrictions have multiplicity one;
• the center is a regular sequence with Tor ranks ((1,2,1));
• the primitive log-excess contraction has Smith factors ((1)), ((1,1)), ((1));
• the two standard Rees charts and their relative-(mathbf G_m) overlap give a canonical proper Čech middle carrier;
• all 24 source occurrence/normal/Tor/Čech residue descriptors are derived, with no base inversion and with (D_3)/reflection signs fixed.

Thus no coefficient, multiplicity, midpoint, denominator, or integral-torsion ambiguity remains.

Earliest literal obstruction

Under either admitted equivariant ray labeling, the two rays of every ordered (dP_6) cone map to crossing short diagonals of (K_6). Entry143 has generators ([S,H]) only when (S) is a compatible (K_6) face and (Hsubset S). No compatible face contains either crossing pair.

Consequently, among the 24 derived source residue rows, the number of legal literal entry143 pair rows is [ 0. ] This is a support failure, not a coefficient failure. Mapping the missing rows to zero is impossible: the six source pair boundaries form the primitive hexagon incidence (R-I), of rank five, kernel generated by the norm vector, and Smith factors [ (1,1,1,1,1). ] In particular each local top boundary contains the nonzero primitive two-ray column ((-1,+1)). The chain equation therefore fails if the pair state is deleted.

The new Rees/Čech carrier does not change this conclusion. Its overlap canonically supplies a source middle object, but entry143 still supplies no literal target object for that pair. Properness and the log-excess cap cannot manufacture a missing target support grade.

Hence a correspondence [ Gamma_{ij}^{!,log}longrightarrow C_\bullet(q_k)subset F_B/F_V ] cannot exist as a support-preserving morphism in the current literal entry143 category for any of the three pairwise long-road intersections (or their six orientations).

Minimal additional geometry

The smallest viable enlargement is to adjoin, for each ordered pair, an extraordinary support-switch object (W_{ij}) with:

1. proper/log maps to the two product-Rees branch charts;
2. a chain-valued map to the complementary marked corridor (q_k), not to a nonexistent common face;
3. the primitive log-excess residue ((-1,+1)) on the two branch restrictions;
4. all four Boolean normal states and both conductor Tor grades;
5. Beck--Chevalley 2-cells identifying its restrictions with the established adjacent long-facet packets;
6. (D_3), reflection, and endpoint framing;
7. triple coherence for the three (W_{ij}).

This is genuinely new geometry: a cdh/log-nearby-cycle or bivariant correspondence category whose middle support is allowed over a road costalk. It cannot be obtained by adding a face to (K_6), choosing a midpoint, localizing a base section, or fitting a finite matrix.

Consequences for downstream invariants

Because the required literal local correspondence does not exist in the current category, the generic (q_Sigma) connector and the pointed endpoint/Q mapping fiber cannot be instantiated there. Therefore (p_{partial,Q}), its Bockstein, and the loaded (D_8)/Jordan coherence classes are undefined—not zero or nonzero.

After the extraordinary (W_{ij}) objects and their BC cells are supplied, the already certified coefficient matrices are reusable. Only then should one assemble the triple (q_Sigma) row, form the pointed mapping fiber, and compute its integral SNF and reflection class.

Executable evidence

Primary falsifier: research/voevodsky/check_p2_pair_literal_24_row_no_go.rs

SHA-256: 4516b44a1a67c997378c1afa8a6023e07e050dbbf210947e28caf2c9ed9b4eb0

Supporting positive controls:

• research/voevodsky/check_dp6_product_branch_rees_clutching.rs
• research/voevodsky/check_dp6_product_rees_log_excess_cap.rs
• research/voevodsky/check_dp6_rees_cech_middle_correspondence.rs
• research/voevodsky/check_dp6_finite_log_gysin_matrix.rs

Fresh rustfmt, warnings-denied optimized compilation, runtime assertions, and JSON parsing passed for the primary literal-row falsifier, the primitive log-excess cap, and the Rees/Čech middle carrier. Native PowerShell was used only because structured-command MCP was unavailable.

Outcome contract

{
  "claim": "All 24 normalization-provenanced full-log source residue rows are derived and integral, but none has a literal entry143 pair-support target because every ordered dP6 ray pair maps to crossing short diagonals. Sending the missing pair rows to zero violates the primitive R-I source boundary. Therefore the requested pair correspondence does not exist inside the current literal face-indexed category.",
  "status": "falsified_scoped_literal_full_log_pair_correspondence",
  "scope": "existing entry143 face-indexed support category and support-preserving morphisms; extraordinary support-switch enlargements are not prohibited",
  "constructed_before_failure": {
    "ordered_pairs": 6,
    "source_residue_rows": 24,
    "branch_multiplicities": [1,1],
    "center_tor_ranks": [1,2,1],
    "log_excess_smith": [[1],[1,1],[1]],
    "proper_rees_cech_middle_carrier": true,
    "base_inversions": false,
    "D3_and_reflection": true
  },
  "falsifier": {
    "legal_literal_pair_rows": 0,
    "reason": "each pair consists of crossing short diagonals, so no compatible K6 face S contains both",
    "zero_image_chain_equation": "FAIL",
    "source_boundary": "R-I",
    "source_boundary_rank": 5,
    "source_boundary_kernel": [1,1,1,1,1,1],
    "source_boundary_smith": [1,1,1,1,1],
    "integer_torsion": false
  },
  "minimal_additional_geometry": "Six oriented extraordinary pair objects W_ij with proper maps to the Rees branches, chain-valued maps to complementary road costalks, all Boolean/Tor states, adjacent-facet BC cells, endpoint framing, and triple D3/reflection coherence.",
  "downstream_status": {
    "qSigma_connector": "undefined",
    "endpoint_Q_mapping_fiber": "undefined",
    "p_partial_Q": "undefined",
    "Bockstein": "undefined",
    "D8_Jordan": "undefined"
  },
  "evidence_refs": [
    "research/voevodsky/check_p2_pair_literal_24_row_no_go.rs",
    "src/ledger/20260815-200 Literal Pair-Intersection Twenty-Four-Row No-Go and the Extraordinary Support-Switch Gate.md",
    "src/ledger/20260815-216 Product-Branch Rees Clutching and the Literal Realization Gate.md",
    "src/ledger/20260815-217 Product-Rees Log-Excess Cap and the Literal Support Gate.md",
    "src/ledger/20260815-219 Rees Cech Middle Correspondence and the Literal Base-Change Gate.md"
  ],
  "primary_checker_sha256": "4516b44a1a67c997378c1afa8a6023e07e050dbbf210947e28caf2c9ed9b4eb0"
}

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