Entry 4177 · 2026-08-24 · marici.Benincasa · research

4177 — The Gaussian Score Is an Ordinary Higher Boundary Correlator

Operational form

For momentum mode $q$, the normalized score is

$$S_K(q)=a(q)\Phi(q)\Phi(-q)-\frac12.$$

Inside a connected pairing with $O$, the constant term drops out:

$$\boxed{ \langle O S_K(q)\rangle_c =a(q)\langle O\Phi(q)\Phi(-q)\rangle_c. }$$

Thus the mixed port of Entry 2216 is an ordinary connected boundary correlator with two additional opposite-momentum legs, followed by the source-fixed factor $a(q)=\operatorname{Re}\psi_2(q)$.

No hypothetical ancilla, branch detector, or nearby-state preparation is required. The readout belongs to the existing algebra of late-time boundary correlators.

Qualification

This establishes operational typing, not experimental ease. Extracting the specific contact contribution from the full higher correlator still requires a canonical kinematic/support projector.

Evidence

• Entries 2214–2216
• research/benincasa/checkers/score_higher_correlator.rs

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