# LIB2-181 — The local covariant odd response is one orbit with an unselected torsor

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- labels as printed: math_status NOT_PRINTED · attachment NOT_PRINTED · scorecard tier word none (PDF p.316)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

On the transported paired-shell space, HomS3(J−,sgn) has real dimension 4; its normalized sphere is one connected-covariance orbit, leaving the endpoint-exchange torsor τ = ±1 unselected.

## Caution

A single equivalence class is not a selected representative, endpoint orientation or physical response coefficient.

## Primary source

Appendix T, §15.2, Source-intertwiner space and covariance orbit, PDF p.334: "On the transported paired-shell generation space G6 , the source intertwiner space HomS3 (J− , sgn) has real dimension four, while its normalized sphere is a single orbit of the connected covariance group."

## Machine

- url: /library-v2/LIB2-181/
- content_sha256: 5881646a8c47d2549361508da35526323da880c02d5f5bd1ccbf59bf5a6c354f
- candidate_ids: C2-134

## Freshness

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