{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TXOQNGSUXLDSDHSQ2TN5VTSUCX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"92c3d3afb601303b52c97eaa1204e011e4cc4e7cf9c50caeab3f731635fd7233","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-10T10:36:38Z","title_canon_sha256":"266c36495a2e11922ec0e10aae34a6367ffb182d84e18711603ed8d27015894e"},"schema_version":"1.0","source":{"id":"1610.02839","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02839","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02839v1","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02839","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"TXOQNGSUXLDS","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TXOQNGSUXLDSDHSQ","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TXOQNGSU","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:d4fa0fc69df79f25f41e5a12321c6131d405c4ce395a9af7fd1040e07671eb3d","target":"graph","created_at":"2026-05-18T01:02:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The notion of type of quadruples of rows is proven to be useful in the classification of Hadamard matrices. In this paper, we investigate Hadamard matrices with few distinct types. Among other results, the Sylvester Hadamard matrices are shown to be characterized by their spectrum of types.","authors_text":"A. Mohammadian, B. Tayfeh-Rezaie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-10T10:36:38Z","title":"Hadamard matrices with few distinct types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02839","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3d561e15cb9bae79e28005124686a2de8bafab81d3781349b716628e62f7628a","target":"record","created_at":"2026-05-18T01:02:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"92c3d3afb601303b52c97eaa1204e011e4cc4e7cf9c50caeab3f731635fd7233","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-10T10:36:38Z","title_canon_sha256":"266c36495a2e11922ec0e10aae34a6367ffb182d84e18711603ed8d27015894e"},"schema_version":"1.0","source":{"id":"1610.02839","kind":"arxiv","version":1}},"canonical_sha256":"9ddd069a54bac7219e50d4dbdace5415c844919397ce0640bf9964aa80c929cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ddd069a54bac7219e50d4dbdace5415c844919397ce0640bf9964aa80c929cb","first_computed_at":"2026-05-18T01:02:50.588780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:50.588780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hHgJFDQx8Vx/d9qadKHq5HlwtQlGSImakWktwDhKMGuN4Y6VvGXX5CbmJXqSsPMNY8MQ18s2vzNV7l/IJhl/Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:50.589166Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02839","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d561e15cb9bae79e28005124686a2de8bafab81d3781349b716628e62f7628a","sha256:d4fa0fc69df79f25f41e5a12321c6131d405c4ce395a9af7fd1040e07671eb3d"],"state_sha256":"4b783b52fda120ddc362cf3bd162ea4c0561f27c777f7fb112a6b271685476f3"}