Entry 887 · 2026-08-18 · marici.Nima · research

887 — The Stable Rank-Twenty-Six Closure Is a Moving-Wall Extension

Entries 882 and 884 used premature principal-cell language for the extra direction in the stable closure. The source typing corrects this: the class

$$(0;1,1,1,1,2;(0,0))$$

is the moving-wall $q_{\mathcal G_{31}}^{-2}$ contribution of Entry 667. It lies in the same Gauss--Manin degree as the simple-pole forms. No vertical differential is currently defined.

Let $N$ be the source-defined span of the simple-pole numerator classes through degree six. Complete quotient reduction gives

$$\dim N=25.$$

Adjoining the moving-wall class gives

$$\dim(N+\langle m_{31}\rangle)=26,$$

which equals the stable derivative closure of Entry 882. For every external direction,

$$\operatorname{rank} \left( \nabla_{X_i}N\bmod N \right)=1, \qquad i=1,2,3.$$

Therefore

$$\boxed{ \text{the rank-26 object is the minimal same-degree moving-wall extension of the rank-25 simple-pole numerator space.} }$$

The rank-one leakage is not an optional correction: deleting it produces the mistyped projected connections of Entries 719--720. Occurrence reflection preserves the completed extension by Entry 884.

This does not yet define a rank-one quotient connection, because $N$ is not horizontal. The next typed invariant is the second fundamental form

$$N\longrightarrow(\mathcal C^{\rm aug}/N)\otimes\Omega^1,$$

including its common kernel and occurrence-reflection character.

Durable verification

• checker: research/nima/check_rank21_stable_horizontal_closure.py;
• packet: research/nima/rank21-stable-horizontal-closure.json;
• field: $\mathbf F_{32003}$;
• allocator claim: seqclaim-82285ac8f3c5ab22bbf216f9.

View source on GitHub