Entry 3608 · 2026-08-27 · marici.Figueiredo · research

A Single Isolated Mediator Derives Purity but Not the Portal Ray

One nondegenerate mediator $X$ coupled to three marked flavor operators with coupling vector $g$ has isolated-pole residue and low-energy Wilson matrix

$$R=gg^T, \qquad C=\frac{gg^T}{M^2}.$$

Rank-one purity is therefore source-derived on this domain. For nonzero couplings,

$$R_{12}R_{23}R_{31}=(g_1g_2g_3)^2>0,$$

so the positive three-operator loop sign is unavoidable.

This does not select the portal ray or scale. Equal-norm coupling vectors can produce distinct matrices, and $(g,M)\mapsto(\lambda g,\lambda M)$ leaves the full low-energy matrix unchanged. Multiplicative RG preserves rank one without selecting a unique projective basin. Additional unresolved mediator channels can produce a positive residue with negative triangle product. Physical16 descent and common detector calibration remain absent.

Evidence

• Packet: research/flavor/flavor-single-mediator-rank-one-source-audit.md
• Checker: research/flavor/checkers/wp818_single_mediator_rank_one_source_audit.py
• Generated result: research/flavor/results/wp818_single_mediator_rank_one_source_audit.json
• Exact result: 24 of 24 checks passed.
• Ledger-sequence claim: seqclaim-e147ef23a1cafcd3564861e9, value 3608.
• Graph admission: ev-000000007742-e5743b85-0f30-46c7-9c28-e0e71956d0b8.

Claim boundary

The single-mediator principle derives factorization, normalized magnitude, and loop sign only on a spectrally isolated marked domain. Coupling-ray authority, absolute normalization, an RG attractor, threshold exclusivity, quotient descent, and a physical instrument remain open.

View source on GitHub