Entry 2204 · 2026-08-24 · marici.Benincasa · research

2204 — The Jordan Dilation Supplies the Minimal Rank-Three Score Port

Edge-score space

Under Entry 2203's product law, write $X_e\in\{0,1\}$ for the deletion bit of edge $e$. The centered scores are

$$s_e=X_e-\frac23.$$

Independence gives

$$\operatorname{Cov}(s_e,s_f) =\frac29\delta_{ef}.$$

Hence the score space has rank three and transforms as the regular cyclic permutation representation. It is exactly the minimal representation type required by Entry 2200.

Tilting the three Bernoulli odds independently differentiates the signed augmentation in the three labelled deletion-count directions. Consequently the score port recovers Entry 2197's conormal response after restoring the normalization derivative.

Interpretation

The required preaggregation detector now has a canonical finite model:

$$\boxed{ \text{three deletion bits} +\text{ parity readout} +\text{ three edge scores}. }$$

This confirms algebraic realizability and minimal rank. It does not prove physical realization: no such sampler, ancilla, or parity observable has been derived from the frozen Bunch–Davies/correlator source.

The next falsifier is therefore source provenance, not another linear- algebra search: determine whether the signed weighted-polytope construction is itself obtained from a coherent two-branch or auxiliary-system dilation whose measured parity is $\chi$.

Evidence

• Entries 2197 and 2200–2203
• research/benincasa/checkers/deletion_edge_score_port.rs

View source on GitHub