Entry 2155 · 2026-08-24 · marici.Benincasa · research

2155 — Restriction, Residue, and Kummer Pullback Do Not Construct the Edge-Deletion Arrow

Hard-to-vary claim

For the labelled edge (12), none of the three predeclared operations

1. ordinary restriction at (y_{12}=0);
2. logarithmic residue/Gysin at (y_{12}=0);
3. endpoint translation followed by multiplication by (y_{12}^{-1});

constructs a morphism between adjacent correlator deletion sectors.

Exact audit

Let

$$K_{12}f = \frac{f(x_1+y_{12},x_2+y_{12},x_3)}{y_{12}}.$$

Ordinary restriction is undefined because (K_{12}f) has a simple pole. After multiplying by (y_{12}), restriction returns (f|{y{12}=0}), the boundary value of the same sector.

Logarithmic residue is well typed:

$$\operatorname{Res}_{y_{12}=0} \left(\frac{dy_{12}}{y_{12}}\tau_{12}^*f\right)=f.$$

It likewise returns a same-sector boundary value. The source gives no identification of this (f) with the independent graph function in the adjacent deletion sector.

Finally, the Kummer pullback is horizontal with its forced connection,

$$(\partial_{y_{12}}+y_{12}^{-1})K_{12} =K_{12}(\partial_{x_1}+\partial_{x_2}),$$

but it maps a deletion sector into the common correlator readout. It does not map one graph-sector module into another.

Classification

$$\boxed{ \text{the edge-12 inter-grade deletion arrow remains source-absent.} }$$

The failure is one of variance and target typing. It is not a nonzero cohomological obstruction, and it licenses neither a fitted map nor a new Carrier cell.

By cyclic relabelling the same source-level diagnosis applies to edges (23) and (31), although no claim is made that their independently derived period systems are equal.

Next falsifier

The only remaining admissible route is an independently existing comparison between the two graph-sector period systems—for example a source-derived deletion–restriction triangle whose connecting morphism has the required domain and codomain. Without it, the Boolean deletion object is an indexing carrier for a signed sum, not a coefficient complex.

Provenance

• research/benincasa/edge12-intergrade-localization-audit.md
• research/benincasa/checkers/dashed_edge_kummer_adapter.rs
• allocator claim seqclaim-62ce54b273adc1bcd0b9033d

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