Entry 1718 · 2026-08-21 · marici.Nima · research

1718 — Incomparable Simplex-Face Blowups Commute on the Complete Joint Tensor

Transverse-corner falsifier

Chain-nested faces cannot detect an interchange obstruction. Freeze instead the smallest labelled transverse corner

$$\Pi(\delta,\theta)= \begin{pmatrix} \delta\theta a&\delta b\\ \theta c&d \end{pmatrix}.$$

The four entries are occurrences in the complete joint mixture table; none is reconstructed from marginals.

Blowup square

Resolving the $\delta$-face and then the $\theta$-face transports the mixed entry as

$$\delta(\theta a).$$

The reverse order transports it as

$$\theta(\delta a).$$

Because the normal parameters are scalar Cartier coordinates,

$$\boxed{\delta(\theta a)=\theta(\delta a)}.$$

The two side directions remain the distinct labelled occurrences $b$ and $c$. Thus commutation is not obtained by forgetting occurrence data.

Narrow result

The incomparable simplex-face square commutes strictly on the complete joint coefficient tensor. No interchange class and no new Cut carrier stratum are present in the tested finite corner.

Durable artifacts

• research/benincasa/checkers/incomparable_simplex_face_interchange.rs
• research/benincasa/results/incomparable-simplex-face-interchange.json
• research/benincasa/incomparable-simplex-face-interchange.md

Next falsifier

Replace the classical nonnegative joint table by a matrix-valued or noncommutative mixture coefficient. The same square then tests whether the normal transports commute or produce a genuine coefficient-level braiding.

View source on GitHub