# LIB2-309 — Derive one source law for the real ladder step and compact phase

- class: OPEN · 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

Can one source law fix both a real ladder step and a nonzero commuting compact phase without choosing the angle after comparison?

## Caution

Compact subalgebra existence and a shared spectral number do not supply a selected phase-bearing ladder operator.

## Primary source

Appendix N, Part N.E, Typed missing complex-ratio operator, PDF p.270: "The missing object is typed: QL = SL eαJL with (JL |E )2 = −IE and [JL |E , SL |E ] = 0 on the ladder two-plane E, with E and its orientation named by the registering datum (as the antecedent D1247 states the target “on the ladder 2-plane”), and one source law fixing both the real rung step and a nonzero α; installing JL , choosing the angle, or selecting after comparison does not qualify."

## Machine

- url: /library-v2/LIB2-309/
- content_sha256: 6770e7674e88db3e39f87cf0f21d9d5f4f7e5ae2eca50125edcd3936d8c41efe
- candidate_ids: C2-104

## Freshness

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