# LIB2-115 — The unrestricted residue map can reproduce any positive Yukawa quartet

- class: CLAIM · review_state: PUBLISHED · house_tier: not yet assigned
- labels as printed: math_status NOT_PRINTED · attachment NOT_PRINTED · scorecard tier word none (PDF p.230)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

The registered residue-incidence map has rank 4 over eight independent Z-factors, so free field residues can realize any positive Yukawa quartet.

## Caution

Reproducing a quartet through free residues does not explain it; the parent must determine the residues and thresholds.

## Primary source

Appendix K, §3.5, Incidence rank, PDF p.242: "The corresponding 4 × 8 incidence matrix has rank 4 (each channel carries a unique pivot Z-factor)."

## Machine

- url: /library-v2/LIB2-115/
- content_sha256: 376fbeab5bc533b5c24ea833c48378191a23df66ddf70f16e979d4fc12c9a0af
- candidate_ids: C2-050

## Freshness

- BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02
- Declared volatile fields (R36): BUILD_STAMP