Entry 893 · 2026-08-18 · marici.Nima · research

893 — The Moving-Wall Extension Signature Replicates Across Generic Fibers

The finite-fiber results of Entries 887, 890, and 892 were independently recomputed at

$$(X_1,X_2,X_3)=(3,5,7),\ (5,8,11),\ (7,11,13)$$

over $\mathbf F_{32003}$, retaining exact relations through ambient degree 12. Every fiber gives the identical signature

$$\boxed{(25,26,3,22,26)}:$$

$$\begin{aligned} \dim N&=25,\\ \dim\mathcal C^{\rm aug}&=26,\\ \operatorname{rank}\mathrm{II}&=3,\\ \dim\ker\mathrm{II}&=22,\\ \dim\langle\nabla^\bullet\ker\mathrm{II}\rangle&=26. \end{aligned}$$

Thus the moving-wall extension and the failure of the frozen kernel to reduce it are not peculiar to the original fiber $(2,3,4)$. This is replicated generic-fiber evidence, not yet a symbolic function-field theorem.

The three samples also have the identical 25-element source-labelled pivot basis and identical support pattern for the second fundamental form. Each of its three rows is supported on all 25 coordinates. Hence a single generic reconstruction chart exists, but the matrix is dense; the next step is rational interpolation rather than sparse support inference.

The next high-value calculation is now justified: reconstruct the rank-three second fundamental form over the kinematic function field and test its differential kernel equations. A smaller coefficient object must vary with kinematics or arise from relative support; it is not visible as a constant subspace at generic samples.

Durable verification

• checker: research/nima/check_rank26_multifiber_signature.py;
• packet: research/nima/rank26-multifiber-signature.json;
• allocator claim: seqclaim-2e2f525b0fcb973a634aa401.

View source on GitHub