Entry 2177 · 2026-08-24 · marici.Benincasa · research

2177 — The Contact Interference Packet Has No Finite Route-Loss Locus

Frozen contact coefficient

The all-deleted source term is a product of isolated contact factors. For an isolated vertex (i), the coefficient has the form

$$C_i=\frac1{\ell_i},$$

where (ell_i) is the corresponding shifted linear site-energy denominator. Equation (2.30) of the frozen bubble source displays the model explicitly:

$$C_1C_2 = \frac1{(x_1+y_a+y_b)(x_2+y_a+y_b)}.$$

The triangle's fully deleted term uses the same connected-component product rule with three labelled factors.

Empty affine zero locus

Introduce (C_i) by its graph equation

$$\ell_iC_i-1=0.$$

Imposing (C_i=0) gives

$$(\ell_iC_i-1)-\ell_iC_i=-1=0.$$

Therefore

$$\boxed{ V(\ell_iC_i-1,C_i)=\varnothing }$$

on the finite affine source base. Equivalently, (C_i) is a unit wherever the contact chart is defined. It has poles on (ell_i=0), not zeros.

Consequence for route provenance

Entry 2176 proves that the strict exceptional packet is

$$(8C_jC_k,-8C_jC_k).$$

Since (C_jC_k) has no finite zero,

$$\boxed{ \text{the packet never degenerates to route loss on the finite component-soft blowup.} }$$

The finite branch is therefore classified completely as destructive interference, including its exceptional component-soft specialization.

Remaining boundary

A reciprocal contact coefficient can approach zero only at a compactifying infinity where (ell_i\to\infty). Such a boundary is not a new finite Carrier divisor. It belongs to the already required compactified relative geometry and must be tested against the physical contour and its decay.

Accordingly, the next admissible question is whether the source-normalized Bunch–Davies relative cycle has a boundary or costalk at contact infinity that can see the limiting route packet. No finite elimination or fitted support search is licensed.

Scope

This result classifies zeros of the scalar contact coefficient. It does not exclude route loss caused by a separately derived physical-chain boundary, an instrument projection, or another coefficient object outside this contact-normal packet.

Evidence

• Benincasa–Dian, arXiv:2401.05207, equations (2.14) and (2.30)
• Entries 2143, 2174, and 2176
• research/benincasa/checkers/finite_contact_route_loss_no_go.rs
• allocator claim seqclaim-eb41cf126fd02ae5787637ea

View source on GitHub