{
  "date": "2026-10-09",
  "status": "passed",
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  "number_of_field_states": 22,
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  "allowed_placements": "Integer translations and four quarter-turn rotations; no reflections; fixed amplitudes.",
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      {
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      {
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      },
      {
        "left": 10,
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      {
        "left": 10,
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      },
      {
        "left": 10,
        "right": 10,
        "turn": 0,
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        ]
      },
      {
        "left": 10,
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        "turn": 0,
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        ]
      },
      {
        "left": 10,
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        "turn": 0,
        "shift": [
          0,
          2
        ]
      },
      {
        "left": 10,
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        "turn": 0,
        "shift": [
          3,
          0
        ]
      },
      {
        "left": 11,
        "right": 1,
        "turn": 0,
        "shift": [
          0,
          -2
        ]
      },
      {
        "left": 11,
        "right": 2,
        "turn": 0,
        "shift": [
          0,
          2
        ]
      },
      {
        "left": 11,
        "right": 3,
        "turn": 0,
        "shift": [
          0,
          2
        ]
      },
      {
        "left": 11,
        "right": 5,
        "turn": 0,
        "shift": [
          0,
          2
        ]
      },
      {
        "left": 11,
        "right": 8,
        "turn": 0,
        "shift": [
          0,
          2
        ]
      },
      {
        "left": 11,
        "right": 10,
        "turn": 0,
        "shift": [
          -3,
          0
        ]
      },
      {
        "left": 11,
        "right": 10,
        "turn": 0,
        "shift": [
          0,
          -2
        ]
      },
      {
        "left": 11,
        "right": 10,
        "turn": 0,
        "shift": [
          3,
          0
        ]
      },
      {
        "left": 11,
        "right": 11,
        "turn": 0,
        "shift": [
          -3,
          0
        ]
      },
      {
        "left": 11,
        "right": 11,
        "turn": 0,
        "shift": [
          3,
          0
        ]
      }
    ],
    "legal_contact_count": 136,
    "rotated_or_staggered_legal_contacts": 0,
    "conclusion": "Each L state has a unique opposite-role partner. Every pair is a 3-by-2 rectangle. Legal rectangle contacts are exactly aligned Jeandel--Rao neighbors with the same orientation."
  },
  "infinite_claim": "Exact forced-pair reduction to the cited aperiodic set: every legal infinite L tiling decodes to an aperiodic Wang tiling. Every Wang tiling expands to a legal L tiling. Infinite existence and no translation periods use the source theorem.",
  "limitations": [
    "Boundary conditions alone do not force aperiodicity; the finite allowed field palette is essential.",
    "The palette has finitely many states, but each state uses infinitely many Neumann modes.",
    "The total fields are static and not single-eigenvalue Helmholtz solutions.",
    "No claim of forcing the chair substitution; the hierarchy is inherited from the encoded Wang system.",
    "Reflections and noninteger placements are excluded. No minimality claim.",
    "No GCTS search engine or finite-patch aperiodicity inference."
  ],
  "figures": [
    {
      "file": "l-boundary-palette.png",
      "sha256": "b70f322bd6cd4e94e41047d15f88077e742405828c47353a67371e7a0372b937"
    },
    {
      "file": "l-boundary-forced-pair.png",
      "sha256": "31043e409020274acc73a56881b61f75c153a4972fb2f8ea5a00e3e2b3fc6306"
    }
  ]
}