{
  "id": "tl-walsh-diagonal-phase",
  "source_ids": [
    "zylberman-debbasch-2024-walsh",
    "pellini-ferrari-dacrema-2025-comment"
  ],
  "statement": "An explicit real Walsh expansion supplies a commuting diagonal phase circuit; the controlled circuit must include its constant coefficient. The amplitude-loading consumer is a separate obligation.",
  "lean_decl": [],
  "lean_status": "obligation",
  "used_by": [
    "spw-walsh",
    "spw-diagonal",
    "spw-controlled"
  ],
  "dependencies": [
    "family:matrix-contract",
    "family:charged-access"
  ],
  "next_action": "Prove a bit-order-aware single Walsh-string matrix action, with j=0 and its controlled version, before proving truncation or loader complexity.",
  "tags": [
    "Walsh",
    "zero-order",
    "controlled-phase",
    "planned-formalization"
  ],
  "failure_modes": [
    "Deleting a global phase before controlling the circuit changes interference.",
    "Identifying Walsh integer order with physical little-endian wire order without the source adapter.",
    "Inferring polynomial loading of arbitrary data from a sparse phase expansion.",
    "Treating shared Walsh terminology as a checked reuse of the UCRY backend."
  ]
}