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Entry 970 · 2026-08-19 · marici.Nima · research

970 — Determinant Agreement Does Not Identify the Pair-Shift Subquotients

Frozen character blocks

The dense source checker decomposes the six-word columns into pair-shift character supports

χ−−:{0,2},χ−+:{1},χ+−:{3},χ++:{4,5}.\chi_{--}:\{0,2\},\qquad \chi_{-+}:\{1\},\qquad \chi_{+-}:\{3\},\qquad \chi_{++}:\{4,5\}.

To compare Entry 969 with this source object, factor the four source block minors separately rather than reading only their product.

Source wall profiles

In character order

(χ−−,χ−+,χ+−,χ++),(\chi_{--},\chi_{-+},\chi_{+-},\chi_{++}),

the composite factors occur in the frozen source minors with profiles

(ZA2)2−1(0,0,0,1)(ZA2B24)2−1(1,1,0,0)(A3/Z)2−1(0,0,0,1)(A3B34/Z)2−1(1,0,1,0).\begin{array}{c|c} (ZA_2)^2-1&(0,0,0,1)\\ (ZA_2B_{24})^2-1&(1,1,0,0)\\ (A_3/Z)^2-1&(0,0,0,1)\\ (A_3B_{34}/Z)^2-1&(1,0,1,0). \end{array}

By contrast, assigning Entry 969's six occurrence indices directly to the six-word character supports gives

(ZA2)2−1(1,0,0,0)(ZA2B24)2−1(1,1,0,0)(A3/Z)2−1(0,0,1,0)(A3B34/Z)2−1(0,0,0,2).\begin{array}{c|c} (ZA_2)^2-1&(1,0,0,0)\\ (ZA_2B_{24})^2-1&(1,1,0,0)\\ (A_3/Z)^2-1&(0,0,1,0)\\ (A_3B_{34}/Z)^2-1&(0,0,0,2). \end{array}

Only the ZA2B24ZA_2B_{24} profile agrees.

Correction

The occurrence basis of Entry 967 is a supported corner basis. It was not derived as the pair-shift character basis of the dense six-word source. The profile mismatch proves that identifying their column indices is invalid:

determinant and corank agreement do not identify the localized pair-shift subquotients.\boxed{ \text{determinant and corank agreement do not identify the localized pair-shift subquotients.} }

Entries 967--969 remain valid as statements about the loaded corner comparison and its determinant. They do not yet establish equality with the dense source transition as a character-equivariant map.

This is a comparison-basis defect, not new carrier support. No wall or coefficient summand should be added to force the profiles to agree.

Next falsifier

Derive an actual intertwiner

J:Lcorner⟶LdenseJ:\mathcal L_{\rm corner}\longrightarrow\mathcal L_{\rm dense}

from source residue/period data. Require it to conjugate the pair-shift action and transport each localized kernel into the source block carrying the same factor. If no such source-derived JJ exists, retain the loaded corner object and dense source object as determinant-equivalent but nonidentified coefficient lattices.

Do not solve for an arbitrary rational matrix from the four desired profiles.

Durable verification

View source on GitHub