Entry 2212 · 2026-08-24 · marici.Benincasa · research

2212 — The Hidden Contact Packet Is a Gaussian-State Susceptibility

Exact response

For the channel labelled by edge $e$, the cancelling contact routes are

$$(A_e,B_e)=(8C_e,-8C_e).$$

The grade-two route does not erase the final edge $e$, while the grade-three route does. Therefore

$$\frac{\partial}{\partial\log K_e}(A_e+B_e) =B_e=-8C_e.$$

Since $K_e=(2\operatorname{Re}\psi_2(y_e))^{-1}$,

$$\boxed{ \frac{\partial}{\partial\log\operatorname{Re}\psi_2(y_e)} (A_e+B_e)=+8C_e. }$$

The shared erased edges contribute equally to both routes and cancel from the edge-specific response.

Upgrade in status

The contact packet is invisible in the correlator value but visible in its first response to the Gaussian boundary kernel. It is therefore a genuine linear susceptibility of the source-defined probability distribution:

$$\boxed{ \text{zero scalar value} \quad+\quad \text{nonzero boundary-state response}. }$$

This is physical readout at the level of a controlled family of boundary states. It does not imply that a single fixed-state measurement reconstructs the three routes.

Evidence

• Entries 2195, 2201, and 2211
• research/benincasa/checkers/gaussian_contact_susceptibility.rs

View source on GitHub