{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:T7SSZ2SKEU2NIRDMORAEHV4P6Q","short_pith_number":"pith:T7SSZ2SK","schema_version":"1.0","canonical_sha256":"9fe52cea4a2534d4446c744043d78ff4200f222ccda0ddb0f9f3ae14b97fb7ed","source":{"kind":"arxiv","id":"1209.4581","version":2},"attestation_state":"computed","paper":{"title":"On unit weighing matrices with small weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Darcy Best, Hadi Kharaghani, Hugh Ramp","submitted_at":"2012-09-20T16:44:00Z","abstract_excerpt":"We study the structure of unit weighing matrices of order n and weights 2, 3 and 4. We show that the number of inequivalent unit weighing matrices UW(n,4) depends on the number of decompositions of n into sums of non-negative multiples of some specific positive integers. We also show two interesting sporadic cases in order to show the complexities involved for weights larger than 4."},"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":"1209.4581","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-20T16:44:00Z","cross_cats_sorted":[],"title_canon_sha256":"a5e6c1c42c7bfe786d08e054968bcbf3436d9da7db50ed28802ebf975d93c102","abstract_canon_sha256":"6d278ca324990ce5c011911b143c575e4fd9388b567059d4b0ac9e272dd14dfc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:55.638717Z","signature_b64":"/s08mH4qZnSddVhLYoRn5rpScv76v+9pdaCd3AVDoV5d+faRAddrUY/+sHOP3UA2305Rr8Gw8aQA1LxGiVE8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fe52cea4a2534d4446c744043d78ff4200f222ccda0ddb0f9f3ae14b97fb7ed","last_reissued_at":"2026-05-18T03:38:55.638197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:55.638197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On unit weighing matrices with small weight","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Darcy Best, Hadi Kharaghani, Hugh Ramp","submitted_at":"2012-09-20T16:44:00Z","abstract_excerpt":"We study the structure of unit weighing matrices of order n and weights 2, 3 and 4. We show that the number of inequivalent unit weighing matrices UW(n,4) depends on the number of decompositions of n into sums of non-negative multiples of some specific positive integers. We also show two interesting sporadic cases in order to show the complexities involved for weights larger than 4."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4581","kind":"arxiv","version":2},"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":"1209.4581","created_at":"2026-05-18T03:38:55.638284+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.4581v2","created_at":"2026-05-18T03:38:55.638284+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4581","created_at":"2026-05-18T03:38:55.638284+00:00"},{"alias_kind":"pith_short_12","alias_value":"T7SSZ2SKEU2N","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"T7SSZ2SKEU2NIRDM","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"T7SSZ2SK","created_at":"2026-05-18T12:27:23.164592+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/T7SSZ2SKEU2NIRDMORAEHV4P6Q","json":"https://pith.science/pith/T7SSZ2SKEU2NIRDMORAEHV4P6Q.json","graph_json":"https://pith.science/api/pith-number/T7SSZ2SKEU2NIRDMORAEHV4P6Q/graph.json","events_json":"https://pith.science/api/pith-number/T7SSZ2SKEU2NIRDMORAEHV4P6Q/events.json","paper":"https://pith.science/paper/T7SSZ2SK"},"agent_actions":{"view_html":"https://pith.science/pith/T7SSZ2SKEU2NIRDMORAEHV4P6Q","download_json":"https://pith.science/pith/T7SSZ2SKEU2NIRDMORAEHV4P6Q.json","view_paper":"https://pith.science/paper/T7SSZ2SK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.4581&json=true","fetch_graph":"https://pith.science/api/pith-number/T7SSZ2SKEU2NIRDMORAEHV4P6Q/graph.json","fetch_events":"https://pith.science/api/pith-number/T7SSZ2SKEU2NIRDMORAEHV4P6Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T7SSZ2SKEU2NIRDMORAEHV4P6Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T7SSZ2SKEU2NIRDMORAEHV4P6Q/action/storage_attestation","attest_author":"https://pith.science/pith/T7SSZ2SKEU2NIRDMORAEHV4P6Q/action/author_attestation","sign_citation":"https://pith.science/pith/T7SSZ2SKEU2NIRDMORAEHV4P6Q/action/citation_signature","submit_replication":"https://pith.science/pith/T7SSZ2SKEU2NIRDMORAEHV4P6Q/action/replication_record"}},"created_at":"2026-05-18T03:38:55.638284+00:00","updated_at":"2026-05-18T03:38:55.638284+00:00"}