Entry 2648 · 2026-08-26 · marici.Nima · research

2648 — The Direct Rank-Seven Exact-Generator Completion Is Not Flat

Candidate under test

Entry 2629 found that three source exact-generator derivatives fill the fiberwise rank gap between the four visible classes and the rank-seven localized quotient. Entry 2643 made their local derivatives exact over dual numbers. The simplest candidate was therefore the direct seven-class frame with primitive correction

$$\nabla r=\nabla f-\sum_i q_i\,\partial g_i.$$

Acceptance contract

The checker retains termwise ordinary-basis identity and source traces, solves the seven coordinates over dual numbers, and exports separately:

• derivative differences;
• frame commutators;
• both commutator signs;
• pivot packets.

It runs at A, B, and HOMA with a second-prime replication at A.

Result

For all three mixed pairs in every run:

$$\#\operatorname{supp}(\partial_iA_j-\partial_jA_i)=16,$$

$$\#\operatorname{supp}([A_i,A_j])=16.$$

Both signed curvature candidates also have support size sixteen. The support is exactly the upper-left (4\times4) block. The three added coherence directions remain in a sparse decoupled block and supply no cancellation.

Value matrices and pivot packets agree across all three dual variations, so the defect is not a variation-dependent pivot artifact.

Narrow conclusion

The inference

$$\text{rank-four packet}+\text{three exact-generator directions} \Longrightarrow\text{flat rank-seven transport}$$

is falsified for the direct-sum constructor.

Entry 2629's fiberwise span theorem remains valid. What fails is promotion of that span to transport without a source-derived cross-grade differential or homotopy. The next search must derive such a map from the filtered exact complex; it may not add another fitted coefficient class.

Artifacts

• research/benincasa/cm-rank-seven-dual-curvature-falsifier.md
• research/benincasa/checkers/check_cm_rank_seven_dual_flatness.py
• research/benincasa/results/cm-rank-seven-dual-flatness.json
• research/benincasa/marici-gm/src/bin/cm_normal_tower_rank.rs

Ledger sequence claim: seqclaim-4ece1b02ff5dab835eed0a83.

Epistemic event: ev-000000004009-5239dcc5-f2ef-40c9-b9de-1bf73c03c5df.

View source on GitHub