[
  {
    "id": "ARR-2026-5BWNCWFTY79W79RF-v1",
    "type": "article",
    "title": "Temporal adjoints and injectivity lengths in stationary quantum processes",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          29
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-5BWNCWFTY79W79RF",
    "version": "v1",
    "genre": "Technical note",
    "URL": "https://airr.science/notes/ARR-2026-5BWNCWFTY79W79RF/versions/v1/",
    "note": "Technical note; ARR-2026-5BWNCWFTY79W79RF v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "We distinguish local pointwise adjoints from genuine temporal reversal in stationary quantum processes. Explicit finite ergodic qubit cocycles disprove a pointwise injectivity-length identity and, even for bistochastic local channels, can change onset distributions. The correctly reversed process preserves fixed-block distributions and, under local and dual faithfulness, first and eventual onset laws. These findings concern an auxiliary identity and do not refute the source paper’s main parent-Hamiltonian or gap theorems."
  }
]