{"schema": "Xi.PublicSource.v1", "id": "source:01b548a066649306e1ea1f75651f82b1bce4aa0f2b6c68bb8811f07245995319", "capsule_id": "capsule:d28116dbb610f3178b0442e62505ded1eb6b776526114a5c83e8812b4a3b318f", "author": "Source-attributed; see payload", "text": "xi_version: 0.1\ncapsule_id: PortalTheory.FourPhaseLightPortalLemma.v1.1\ntype: registry_operator\nentry: portal.phase_rotate\n\npayload:\n  operator: P\n  definition: \"P(x)=i*x\"\n  angle: \"π/2\"\n  closure: \"P^4=I\"\n  mirror: \"P^2=-I\"\n  composition: \"P^a ∘ P^b = P^(a+b mod 4)\"\n  invariant: \"norm_preserved\"\n\nstates:\n  - 0: real_forward\n  - 1: imaginary_lateral\n  - 2: real_mirror\n  - 3: imaginary_inverse\n  - 4: closure\n\nruntime:\n  tests:\n    - norm_preserved\n    - fourth_order_closure\n    - z4_composition\n  render_target: torus_phase_container\n", "offset": 0, "next_offset": null, "sha256": "a75956b031f7ebd14d583963a52aef29b02b92d5c034a22956eaa8dc64b32055", "public_sha256": "a75956b031f7ebd14d583963a52aef29b02b92d5c034a22956eaa8dc64b32055", "redacted": false}