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There are exactly $72$, 1786763, and $167776$ such matrices, up to monomial equivalence. Additionally, we show an example of a $\\mathrm{BH}(14,10)$ matrix for the first time, and show the nonexistence of $\\mathrm{BH}(8,15)$, $\\mathrm{BH}(11,q)$ for $q\\in\\{10,12,14,15\\}$, and $\\mathrm{BH}(13,10)$ matrices."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.02287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-07T17:58:29Z","cross_cats_sorted":[],"title_canon_sha256":"53bf015a4d1ea2f305ef077ebdfcc1750246a21edc9fef58052951b7c7749f6a","abstract_canon_sha256":"0d1bc2b5dcbfe034564909bc3d7c24173954fd44859879e43addf6db074897c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:42.385563Z","signature_b64":"3o/wKLri6e5HHBNslQWtkBZEmW1caHn+D+lmQff3Vy+Xxktx62sp8PqgbTNiHxRnSRXYxNhn2tgKyzSCKHyrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7354f7d67249494b73eccd68a3224fec0da7dac3919728ceff5de36f44586169","last_reissued_at":"2026-05-18T00:40:42.384832Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:42.384832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orderly generation of Butson Hadamard matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"F. 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Additionally, we show an example of a $\\mathrm{BH}(14,10)$ matrix for the first time, and show the nonexistence of $\\mathrm{BH}(8,15)$, $\\mathrm{BH}(11,q)$ for $q\\in\\{10,12,14,15\\}$, and $\\mathrm{BH}(13,10)$ matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02287","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.02287","created_at":"2026-05-18T00:40:42.384957+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.02287v1","created_at":"2026-05-18T00:40:42.384957+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02287","created_at":"2026-05-18T00:40:42.384957+00:00"},{"alias_kind":"pith_short_12","alias_value":"ONKPPVTSJFEU","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"ONKPPVTSJFEUW47M","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"ONKPPVTS","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ONKPPVTSJFEUW47MZVUKGISP5Q","json":"https://pith.science/pith/ONKPPVTSJFEUW47MZVUKGISP5Q.json","graph_json":"https://pith.science/api/pith-number/ONKPPVTSJFEUW47MZVUKGISP5Q/graph.json","events_json":"https://pith.science/api/pith-number/ONKPPVTSJFEUW47MZVUKGISP5Q/events.json","paper":"https://pith.science/paper/ONKPPVTS"},"agent_actions":{"view_html":"https://pith.science/pith/ONKPPVTSJFEUW47MZVUKGISP5Q","download_json":"https://pith.science/pith/ONKPPVTSJFEUW47MZVUKGISP5Q.json","view_paper":"https://pith.science/paper/ONKPPVTS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.02287&json=true","fetch_graph":"https://pith.science/api/pith-number/ONKPPVTSJFEUW47MZVUKGISP5Q/graph.json","fetch_events":"https://pith.science/api/pith-number/ONKPPVTSJFEUW47MZVUKGISP5Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ONKPPVTSJFEUW47MZVUKGISP5Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ONKPPVTSJFEUW47MZVUKGISP5Q/action/storage_attestation","attest_author":"https://pith.science/pith/ONKPPVTSJFEUW47MZVUKGISP5Q/action/author_attestation","sign_citation":"https://pith.science/pith/ONKPPVTSJFEUW47MZVUKGISP5Q/action/citation_signature","submit_replication":"https://pith.science/pith/ONKPPVTSJFEUW47MZVUKGISP5Q/action/replication_record"}},"created_at":"2026-05-18T00:40:42.384957+00:00","updated_at":"2026-05-18T00:40:42.384957+00:00"}