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Entry 2352 · 2026-08-24 · marici.Benincasa · research

Entry 2352: Cosmology capability matrices form equivariant descent data, not yet a sheaf

The sheaf conjecture was tested on the independent cosmological occurrence charts G12, G23, and G31. Their rank-26 quotient transitions are invertible, the rank-seven annihilator planes are carried contragrediently to the independently constructed target planes, and the cyclic transition product is exactly

T31,12T23,31T12,23=I26.T_{31,12}T_{23,31}T_{12,23}=I_{26}.

Thus the coefficient matrices are local presentations of one descent object. However, the source has no G12--G23 double-pole overlap. The charts are related by source relabelling, not by restriction along ordinary open-set intersections. The correct object is therefore an equivariant vector bundle or representation on the cyclic action groupoid, not a Čech sheaf on the physical base.

Nor is it yet an operational capability bundle: the seven-plane consists of coefficient annihilator classes, not source-admissible successor operations. The next lift must attach operations, composition, and diagnostic selection to these local fibers while preserving the same transitions.

The strongest current statement is:

local coefficient matrices+source transitions+cocycle=equivariant descent datum.\text{local coefficient matrices} +\text{source transitions} +\text{cocycle} =\text{equivariant descent datum}.

Evidence:

View source on GitHub