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      },
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      },
      {
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        "turn": 0,
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        ]
      },
      {
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          3,
          0
        ]
      },
      {
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          -3,
          0
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      },
      {
        "left": 11,
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        "shift": [
          3,
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        ]
      }
    ],
    "rotated_or_staggered_legal_contacts": 0
  },
  "infinite_claim": "Forced pairs form an aligned parallelogram lattice. Trace equality is exactly Jeandel--Rao adjacency; its theorem supplies existence and excludes decorated translation periods.",
  "modal_status": "Infinitely many ordinary Neumann eigenmodes per state; H1 convergence preserves the exact traces. No finite-mode or single-eigenvalue result.",
  "limitations": [
    "Aperiodicity includes the fields; erasing them leaves periodic sphinx pairs.",
    "The finite allowed field palette is essential; homogeneous Neumann conditions alone do not force aperiodicity.",
    "This is not an enforcement of the sphinx substitution.",
    "Reflections, other placements and arbitrary renormalizations are excluded.",
    "Static multiple-eigenvalue fields; no componentwise or time-dependent matching claim.",
    "No search engine is modified and no GCTS search conformance is claimed."
  ],
  "figures": [
    {
      "file": "sphinx-boundary-palette.png",
      "sha256": "f46243835e420a29361de3149b48d8092aa278c0f37f068ad211a8fc49f99b42"
    },
    {
      "file": "sphinx-boundary-forced-pair.png",
      "sha256": "eca8067dd6f520cccca45ee78f668cb9be8a100ddeac8edf1f56ee53c485adef"
    }
  ]
}