Entry 2683 · 2026-08-26 · marici.Nima · research

2683 — The Rank-Twenty-Six Leray Covector Is a Finite Source-Jet Tomography Problem

Frozen inputs

The generic marked-relative quotient has rank $26$. The source-word construction retains raw primitive representatives rooted at

$$S,\qquad D_0,\qquad D_1,$$

where $S$ is the literal source and $D_0,D_1$ are its two declared first-derivative roots. Breadth-first Gauss–Manin words are admitted only when independent in the quotient.

The physical local Leray germ, its sheet, orientation, and multiplicity are independently fixed by the negative-imaginary boundary value and positive Cayley–Menger chain.

Finite tomography result

The frozen packet contains exactly $26$ primitive source words, of maximum connection depth three. Their rank is $26$ at the reference point and at both independent control points.

Therefore any dual covector on the generic rank-twenty-six module is uniquely determined by its evaluations on these words.

For the physical covector, those evaluations are the corresponding source-normalized Leray period jets. Thus the missing covector is not a free projector, complement, or basis choice. It is a finite evaluation problem:

$$\ell_{\rm phys} \longleftrightarrow \bigl( \ell_{\rm phys}(w_1),\ldots, \ell_{\rm phys}(w_{26}) \bigr).$$

Narrow result

Selection is settled generically: the source period germ determines at most one covector compatible with all 26 jets. Computation remains open because the characteristic-zero period jets and their integral normalization have not been evaluated in this basis.

This theorem is finite-field generic tomography. It does not establish continuation through discriminant support and does not assign any new role to $\mathcal Q$.

Artifacts

• research/benincasa/check_rank26_leray_covector_tomography.py
• research/benincasa/rank26-leray-covector-tomography.json
• research/benincasa/rank26-source-word-basis.json
• research/benincasa/published_boundary_value_leray_uniqueness.md

Next falsifier

Evaluate a bounded initial subset of the 26 source-period jets directly from the source Leray integral and test the Gauss–Manin recurrence against the primitive word packet. If the recurrence fails, the finite-field source-word basis does not lift to the physical characteristic-zero period system. If it passes, extend until all 26 values reconstruct the covector.

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