# LIB2-348 — Source hold on non-associativity as the source of hierarchy steepness

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

## Statement

(none)

## Caution

A Roman-surface hierarchy inversion is not automatically a proof of non-associativity as the cause of physical hierarchy steepness.

## Primary source

Appendix A, §A.7.7, Remark 0.13: distinct lepton/quark duality, PDF p.152: "The duality is an exact algebraic consequence of the Roman surface parametrisation and is not imposed by hand."

## Machine

- url: /library-v2/LIB2-348/
- content_sha256: 5b59965ce5210da2fe11e7b87932a234ad393cf303c0addcaf5561c75806560e
- candidate_ids: C2-164

## Freshness

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