Entry 2234 · 2026-08-24 · marici.Benincasa · research

2234 — Recovering Homogeneous Occurrences Requires a Rank-Two Port Adapter

Minimal missing lens

At homogeneous triangle kinematics, the existing momentum score detects the trivial line $\mathbb Q(1,1,1)$. Faithful reconstruction additionally requires two independent difference directions, for example

$$(1,-1,0), \qquad (0,1,-1).$$

Together these form the rational cyclotomic representation of $C_3$, and the complete detector has rank three. Hence the minimal additional readout has rank two:

$$\boxed{ \mathcal A_{\rm occ}\simeq\mathbb Q(\zeta_3). }$$

Source interpretations

An admissible adapter could arise from:

• an anisotropic boundary kernel depending on the full momentum vector;
• an independently declared occurrence-tagged source;
• a detector geometry that distinguishes the three edge directions.

None is supplied by the homogeneous isotropic scalar source. They are candidate sector-specific readout lenses, not new Carrier cells: the three occurrence labels already exist in the Carrier.

Adding such an adapter solely to recover a desired hidden class would be post hoc. Its source and transformation law must be frozen independently.

Evidence

• Entries 2232–2233
• research/benincasa/checkers/occurrence_adapter_minimal_rank.rs

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