. . . . "COD spacegroup count endpoint queried for one representative space group per Bravais lattice in the spellings the COD uses; a lattice counts as realised at 100 or more entries." . . "Measured: 14 Bravais lattices with at least 100 COD entries in a representative space group (of 14) (n = 14). Interpretation: Completeness (exactly fourteen) is a theorem and is not tested; what is tested is the empirical half, that all fourteen occur in real crystals. The count is of database entries, not distinct substances, and a lattice realised only by a handful of entries would still count as realised under the mixed rule." . "Claim test of bravais1850-03: supports, confidence 0.9" . . . "Planned datasets: cod-search-api" . "claim-test/0.1.0" . "physical" . "Any lattice whose every spelling returns 0: refutes (that mode is not realised). Any lattice between 1 and 99: mixed. Any query that errors or times out after three attempts: inconclusive." . "Completeness (no fifteenth lattice) is a theorem and is not what this tests." . "Counts are of database entries, not distinct substances." . "One representative space group per lattice; counts understate how often each lattice occurs." . "For each of the 14 Bravais lattices, the COD spacegroup count for a representative space group (aP P-1; mP P21/c; mC C2/c; oP Pnma; oC Cmcm; oI Imma; oF Fddd; tP P4/mmm; tI I4/mmm; hR R-3m; hP P63/mmc; cP Pm-3m; cI Im-3m; cF Fm-3m), trying the COD spellings of the Hermann-Mauguin symbol (with or without the full-setting 1s, e.g. 'P 1 21/c 1' and 'P 21/c'), is at least 100: supports." . "Any lattice whose every spelling returns 0: refutes (that mode is not realised). Any lattice between 1 and 99: mixed. Any query that errors or times out after three attempts: inconclusive." . "0.9"^^ . . "supports" . "If there are fourteen lattice modes and nature realises them, every one of the fourteen Bravais lattices is the lattice of at least one experimentally determined crystal structure." . "COD spacegroup count endpoint queried for one representative space group per Bravais lattice in the spellings the COD uses; a lattice counts as realised at 100 or more entries." . "For each of the 14 Bravais lattices, the COD spacegroup count for a representative space group (aP P-1; mP P21/c; mC C2/c; oP Pnma; oC Cmcm; oI Imma; oF Fddd; tP P4/mmm; tI I4/mmm; hR R-3m; hP P63/mmc; cP Pm-3m; cI Im-3m; cF Fm-3m), trying the COD spellings of the Hermann-Mauguin symbol (with or without the full-setting 1s, e.g. 'P 1 21/c 1' and 'P 21/c'), is at least 100: supports." . "true"^^ . . "" . "CC0 (COD data are public domain)" . . "Location (not a URL): https://www.crystallography.net/cod/result?spacegroup=&format=count" . "Dataset: Crystallography Open Database (COD) search API and CIF files" . . . "delphisci claim tester (claude-fable-5.1; crystals-and-form-tests-1)" . . . "claude-fable-5.1" . . . . . . . . . "2026-11-08T16:24:31.804Z"^^ . . . . . "Claim test of bravais1850-03: supports, confidence 0.9" . . "RSA" . "MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAyFHtPB6p0mCjDozxlOY9CmO3nBm7Te3jFbXyLmM+G1tGe47Da0jYIbhkl9Oo1ZjxmCa3LCwlEqK8gj6hEIcL4ahW30JXh9HycfKVk1bugkzMEV15tJdTzAU3sGMFnbNsn43xY2LFLy45tApkRm5byEiM7oRRrooIdwoQKnP4Wzq/bfAoJ9qvW+MGkelyOTd1jbSt+KfmT7xKmDfWzAHddUlWwMX2QJOLxDaffOteTop6ZRgPiNmPJKA/S62Gac9XtSYT3oDkZ6/nr5cxxNLpOyxTf5FPISiCe11xYO/unYjY+mwnOfA8yhJIyx1l0O9I0vpOpn+E5TvyHJV+oSTrvwIDAQAB" . "s1TtioMBqx0memhCcVd5AkmpvO7uQpGAnNBTDC7I+iLnx/u317MAH49RILo+R+mQaeYKR9rgXXFr09UbsVRMUBu4+NWZnghBxM1B33uv4ArsjMSo3W94Bz/TVTFrFX5ISLm+OTyOR6Y7gzLi7JdIltDX7W8DXSdep4GuehhmT0qQgQovnUqtZFAeGNdawlDgYY/lVqoYSsiVlwN53jsmHVWg82gIFrJfj7GaYTesEHVrhb61Ufx3W4wrqDcgjizjVMuTZaIBR5jXU4an/TCH8HS5Hu8OXt8g8CoG/4ZngLcoWHwYFxNQltZpi3Ml2jmTjw1/speZH8OLo8Wvj3QhZg==" . . .