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Entry 2629 · 2026-08-25 · marici.Nima · research

2629 — Exact-Generator Derivatives Supply the Missing Three Fiber Directions

Problem

The physical first-normal packet plus the cyclic quadratic class has fiber rank four, while the complete localized Cayley--Menger quotient has rank seven. Entry 2625 retained the primitive provenance of the four source exact generators. The finite question was whether derivatives of those generators account for the missing directions.

Frozen test

Start from the four labelled associated-grade classes

(ν1,ν2,ν3,ccyc)(\nu_1,\nu_2,\nu_3,c_{\rm cyc})

and append, in source order, the twelve base derivatives of

(5Ka,5Kb,5Kc,zK−1).(5K_a,5K_b,5K_c,zK-1).

The order is fixed before reduction. Incremental ranks were computed at A, B, and HOMA, with a second-prime replication at A.

Result

All four runs give the same sequence:

4,5,6,7,7,7,7,7,7,7,7,7,7.4,5,6,7,7,7,7,7,7,7,7,7,7.

The first labelled gradient-derivative triple contributes exactly the three missing directions. All later exact-generator derivatives are fiberwise dependent. Therefore the associated-grade rank four together with the source-exact coherence directions spans the complete rank-seven fiber.

Narrow conclusion

The former rank discrepancy has a source-derived explanation: three directions live in the motion of the exact ideal rather than in the visible first-normal classes. No new carrier cell or fitted coefficient class is needed at this fiberwise gate.

This does not establish a flat rank-seven connection. The next gate is to use Entry 2625's primitive coefficients and these generator derivatives to form common lifted base derivatives, then test mixed flatness exactly.

Artifacts

Ledger sequence claim: seqclaim-a5404aad4881a5e5c2b2b31d.

Epistemic event: ev-000000003930-a5e93982-25b8-4d19-a2d7-7f996bcdb06c.

View source on GitHub