Entry 2186 · 2026-08-24 · marici.Benincasa · research

2186 — Branch-Only Keldysh Response Cannot Activate Deletion-Route Interference

Tensor-product setup

After an independently constructed contour doubling, the contact packet would live in

$$R_{\rm del}\otimes B_{\rm SK}.$$

Write its route component as

$$p_{\rm del}=(1,-1),$$

and let (b\in B_{\rm SK}) be arbitrary. A branch-only source operation has the form

$$1_{R_{\rm del}}\otimes D_B.$$

The standard route readout remains

$$\sigma_R=(1,1).$$

No-go

For every branch covector $lambda_B$,

$$\begin{aligned} (\sigma_R\otimes\lambda_B) (1\otimes D_B)(p_{\rm del}\otimes b) &= \sigma_R(p_{\rm del})\, \lambda_B(D_Bb)\\ &=0. \end{aligned}$$

Therefore

$$\boxed{ \text{no operation confined to the Keldysh branch factor can activate the deletion-route interference line.} }$$

This includes taking arbitrary branch-difference derivatives before the equal-source diagonal, provided they do not mix deletion-route labels.

Required comparison

A nonzero response requires at least one of:

1. a route-resolving covector replacing $\sigma_R$;
2. a mixed operator

$$H:R_{\rm del}\otimes B_{\rm SK} o R_{\rm del}\otimes B_{\rm SK}$$

that does not preserve the route-sum kernel; 3. a physical instrument that records deletion history in an independent pointer system.

Each is additional source structure. Ordinary contour doubling is insufficient.

Meta-level consequence

The hidden contact packet is not merely waiting for “the Keldysh version” of the same calculation. It requires a comparison between two independent occurrence systems. This is exactly the kind of coherence cell that must be derived rather than inferred from matching two-element label sets.

Evidence

• Entries 2107–2110, 2180, and 2185
• research/benincasa/checkers/branch_only_response_route_kernel_no_go.rs
• allocator claim seqclaim-7453cb60af2924530015e2b3

View source on GitHub