# LIB2-058 — The cubic scaling model has a constant homogeneity derivative

- 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.208)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

For the scaling action S = c N(J) on J3(Os), the substitution J → c^{1/3}J gives, formally, Z(c) = c⁻⁹ Z(1) and c d(log Z(c))/dc = −9; the identity holds only for a regulator or integration domain that respects the scaling.

## Caution

This bare scaling identity does not determine the running of physical masses, which the source assigns to composite correlators.

## Primary source

Appendix I, §6, Proposition 6.1: scaling setup, PDF p.218: "For the scaling action S = c N (J) on J3 (Os ) (dimR = 27, deg N = 3)"

## Machine

- url: /library-v2/LIB2-058/
- content_sha256: cd946e39739d36f86bdc0246fce623e829c919fc69c941d2e9efab74077eb62d
- candidate_ids: C2-144

## Freshness

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