Entry 2195 · 2026-08-24 · marici.Benincasa · research

2195 — The Contact Selector Localizes to the Last Labelled Edge Deletion

Boolean multigrading

The deletion carrier is not only graded by total cardinality. It has one binary grade for each labelled edge:

$$(n_{12},n_{23},n_{31})\in\{0,1\}^3.$$

In the channel whose grade-two route retains edge (e), the two cancelling routes have count vectors

$$n_A=mathbf1-\mathbf e_e, \qquad n_B=mathbf1.$$

Thus they differ by exactly the final deletion of (e).

Edgewise Euler responses

Let (N_f) count deletion of labelled edge (f). For the packet

$$(A,B)=(8C,-8C),$$

one finds

$$\sigma N_f(A,B)^T = \begin{cases} -8C,& f=e,\\ 0,& f\ne e. \end{cases}$$

The shared deleted edges act equally on both routes and therefore cancel. Only the last edge distinguishing the routes activates the packet.

Across the three cyclic channels, the edgewise response matrix is diagonal:

$$\boxed{ R_{\rm edge} = -8\operatorname{diag}(C_{12},C_{23},C_{31}). }$$

Consequence

The selector of Entry 2189 is not a diffuse total-grade effect. It localizes to the source-defined last-edge deletion adapter already isolated in Entry 2149.

This substantially narrows the physical question:

$$\boxed{ \text{Can the source couple a probe to whether one specific final edge was deleted?} }$$

The other two edge-counting directions are exact spectators for that channel.

Physical boundary

The edge label and its Euler operator are canonical in the edge-erasure presentation. The frozen correlator still supplies no apparatus or source that measures the deletion history. Entry 2195 identifies the precise local port such an enlargement must act on; it does not authorize the enlargement.

Evidence

• Entries 2115, 2149, and 2189–2194
• research/benincasa/checkers/edgewise_deletion_euler_contact_selector.rs
• allocator claim seqclaim-4866f91e2e4eb05f02fa4ad1

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