Entry 2199 · 2026-08-24 · marici.Benincasa · research

2199 — Every Scalar-Factored Readout Annihilates the Contact Kernel

Factorization theorem

Let

$$V_{\rm ct}\xrightarrow{\epsilon_{\rm ct}}R_{\rm ct}$$

be Entry 2196's frozen contact augmentation, and let

$$K_{\rm ct}=\ker\epsilon_{\rm ct}.$$

Any further observable constructed only from the summed correlator has the form

$$V_{\rm ct}\xrightarrow{\epsilon_{\rm ct}}R_{\rm ct} \xrightarrow{\phi}O.$$

For every such $\phi$,

$$\boxed{(\phi\epsilon_{\rm ct})|_{K_{\rm ct}}=0.}$$

This is independent of whether $\phi$ is linear, differential, integral, or a supported restriction, provided it genuinely factors through the ordinary correlator object.

Consequence

No post-processing of the scalar correlator can recover the hidden route packet. A successful physical activation must fail to factor through $R_{\rm ct}$: it must retain, mark, condition on, or otherwise resolve a route before aggregation.

Thus the missing physical datum is not a more ingenious scalar functional. It is a lift of the physical readout to the labelled-port object.

Evidence

• Entries 2194 and 2196–2198
• research/benincasa/checkers/scalar_readout_factorization_no_go.rs

View source on GitHub