[
  {
    "id": "ARR-2026-03PY6WTF258KGSRN-v1",
    "type": "article",
    "title": "Two-state exact routing: algebraic feasibility and sharp delay-two rigidity",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          9,
          6
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-03PY6WTF258KGSRN",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-03PY6WTF258KGSRN/versions/v1/",
    "note": "Research preprint; ARR-2026-03PY6WTF258KGSRN v1. Not peer reviewed by AIRR.",
    "abstract": "For rational-inner passive routers with exactly two internal states and three prescribed nodes, we give a complete three-parameter description of achievable trace-delay functions. A global delay cap is equivalent to nonnegativity of one quartic, with an explicit small Gram certificate. We characterize exactly when the winding lower bound two is attained, prove a positive gap elsewhere, and construct a sharper cubic-root upper bound for symmetric acute configurations. An explicit two-port completion realizes each admissible triple. The global acute optimum and general asymmetric minimum remain open. The results assume orthogonal output rays, freely chosen phases and dimensionless angular trace delay."
  }
]