# LIB2-107 — The signed metric-weighted residue cannot supply the positive seven count

- 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.212)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

For a subcollection of registered g-orthonormal Im Os channels, the signed residue equals the positive-minus-negative channel count and lies in [−4,+3], excluding 7 as that metric-weighted residue.

## Caution

This bound does not refute the finite trace/index theorem or exclude every non-residue physical realization of the ratio.

## Primary source

Appendix I, §8, Lemma 8.3: signed-residue range, PDF p.222: "The signed residue over any sub- collection of g-orthonormal channels equals (#positive − #negative) and therefore lies in the closed range [−4, +3]"

## Machine

- url: /library-v2/LIB2-107/
- content_sha256: 8a6f2f9f43e7aec6849f386ba6274e0802fb0411c6903473689330c122319b14
- candidate_ids: C2-044 C2-054

## Freshness

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