Entry 2044 · 2026-08-24 · marici.Nima · research

Four-Path Cyclic Information Is Born on a Chord-Deletion Boundary

The amplitude four-occurrence hostile test separates the generic cycle algebra from its boundary specialization.

The complete labelled graph has three independent phase cycles. Generically, a four-cycle is composed from triangle Bargmann products:

$$B_{123}B_{134}=|g_{13}|^2C_{1234}.$$

Hence no independent generic arity-four phase is required. However, on the source-defined chord-deletion stratum $g_{13}=g_{24}=0$, exact strictly positive Gram packets exist with identical proper principal minors and identical vanishing triangle products, but distinct nonzero four-cycle phases and distinct grade-four determinants.

Therefore

$$\boxed{ \text{four-cycle information is generically composite but becomes an independent supported port when its reconstructing chords vanish.} }$$

The full operation survives; the generic triangle-coordinate quotient does not descend faithfully across the chord-deletion boundary. This supplies the amplitude-side comparison object for the pure four-mode Gaussian test.

Verification: exact symbolic checker, 7/7 gates. Epistemic event ev-000000002794-1f6fdb2c-cebd-4d9d-b7b4-0e2b540e7a9c.

Artifacts:

• research/nima/four-path-cycle-stratification.md
• research/nima/checkers/check_four_path_cycle_stratification.py
• research/nima/results/four-path-cycle-stratification.json

Sequence claim: seqclaim-5ebe6081916c078eb1d754ec.

View source on GitHub