{ "date": "2026-10-08", "script_sha256": "3b719cbc0cc7e69021c6743ce4ae5273e1dcebd211fca0face2bd2fb6de0137d", "input_sha256": { "additional-tiles.json": "820b62ff155e3e81f2b628ec813ecb903b5aea50644bbddbaa32e8b358139ffc", "compute_modes.py": "53fc1319ab02cdcf7a71031ac0284ba625500277417586f1ad71a6edcbcb1943", "compute.py": "acce24c8905fa13f4a5c1ede9cd6327acabd64e0153986337346f120e29e0ec3" }, "method": "Conforming P1 FEM with consistent mass, nested levels 2 and 3. Dirichlet trace imposed strongly; Neumann zero flux imposed naturally in the weak form.", "limitations": "Uncertified continuum estimates. The boundary operators do not encode the matching rules or select a tiling. Pointwise P1 normal derivatives need not vanish on Neumann edges.", "domains": [ { "id": "sphinx", "label": "Sphinx", "polygon": [ [ 0.0, 0.0 ], [ 3.0, 0.0 ], [ 2.5, 0.8660254037844386 ], [ 1.5, 0.8660254037844386 ], [ 1.0, 1.7320508075688772 ] ], "area": 2.598076211353316, "tiling_status": "The Sphinx admits hierarchical nonperiodic substitution tilings and also other tilings. Goodman\u2013Strauss gives a marked tile system enforcing its substitution; the bare hexiamond is not claimed to force aperiodicity.", "source_url": "https://arxiv.org/abs/2304.14388", "spectra": [ { "bc": "D", "label": "Dirichlet", "boundary_edges": [ "D", "D", "D", "D", "D" ], "fine_level": 3, "previous_level": 2, "checks": { "nodes": 12741, "triangles": 25024, "free_nodes": 12285, "fixed_nodes": 456, "area": 2.598076211353316, "maximum_fixed_trace": 0.0, "max_mass_orthogonality_error": 7.882583474838611e-15, "max_positive_relative_residual": 2.420702829302126e-13, "constant_mode_check": null }, "atlas": { "file": "modes-sphinx-D-0.png", "start_index": 0, "mode_count": 60, "rows": 6, "sha256": "44177e505a3df442f9fc7040edbc1893a54218d6d192e7a62d6ac771c36595f0", "cell_size": 320, "columns": 10, "bbox": [ -0.18000000000000016, -0.8139745962155616, 3.18, 2.546025403784439 ], "pages": [ { "file": "modes-sphinx-D-0.png", "start_index": 0, "mode_count": 60, "rows": 6, "sha256": 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