Entry 2200 · 2026-08-24 · marici.Benincasa · research

2200 — A Faithful Cyclic Contact Instrument Has Minimal Rank Three

Representation bound

Entry 2198 gives

$$K_{\rm ct}\simeq\mathbb Q[C_3] =\mathbb Q_{\rm triv}\oplus\mathbb Q(\zeta_3).$$

A cyclic-invariant scalar instrument detects only the trivial generator

$$p_{12}+p_{23}+p_{31}.$$

Its kernel on $K_{\rm ct}$ is the two-dimensional rational cyclotomic summand. Therefore a scalar probe can witness aggregate route sensitivity, but cannot identify the labelled packet.

Any instrument faithful on the full contact kernel must have target rank at least three. The minimal equivariant target is another regular representation:

$$\boxed{ K_{\rm ct}\longrightarrow\mathbb Q[C_3]. }$$

Entry 2197's diagonal conormal map realizes this minimal algebraic type at generic contact kinematics.

Physical implication

There are two distinct experimental claims:

1. a scalar cyclic response can detect that hidden interference exists;
2. a rank-three occurrence-resolved instrument is required to determine which final edge carries it.

Conflating them would turn a one-dimensional invariant projection into a false reconstruction theorem.

Evidence

• Entries 2197–2199
• research/benincasa/checkers/minimal_cyclic_route_instrument.rs

View source on GitHub