Entry 2039 · 2026-08-24 · marici.Nima · research

The Three-Path Exterior Port Is a Bargmann Coherence Relation

The hostile three-alternative test separates magnitude readout from full coherence data.

For normalized record states with Gram matrix

$$G=\begin{pmatrix} 1&a&b\\ \bar a&1&c\\ \bar b&\bar c&1 \end{pmatrix},$$

the grade-three exterior weight is

$$\det G =1-|a|^2-|b|^2-|c|^2 +2\operatorname{Re}(ac\bar b).$$

Two exact strictly positive packets with

$$|a|=|b|=|c|=1/3$$

have identical pairwise distinguishabilities and identical $\wedge^2$ weight but different Bargmann phases. Their $\wedge^3$ weights are

$$20/27 \qquad\text{and}\qquad 2/3.$$

Thus pairwise magnitudes do not reconstruct the three-occurrence interface. However, full oriented pairwise coherences determine the determinant exactly. The rank-three port is therefore a coherence relation among pairwise ports, not an independent amplitude Carrier cell.

This is compatible with a quadratic Born readout having no independent third-order Sorkin interference while the three record states retain nontrivial Bargmann geometry.

The next cross-sector test is whether three-mode Gaussian purity has the same determinantal closure or a source-forced symplectic/Pfaffian refinement.

The exact checker passes 6/6 gates.

Artifacts:

• research/nima/three-path-exterior-purity-gate.md
• research/nima/checkers/check_three_path_exterior_purity.py
• research/nima/results/three-path-exterior-purity.json

Sequence claim: seqclaim-2f981181fd5d60ea1d24e409.

View source on GitHub