{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ORWHDZIMT3WFXRXFE4EU4X4A5H","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":"c3c504423e97f6e147faff09e4a17c119ed8bce17412359e3f5f527d11b62b0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-23T19:45:26Z","title_canon_sha256":"d7cce0f650d54cce0064a78ce3bfc93986787dc1cfebfb13fdd76c9e79333c7a"},"schema_version":"1.0","source":{"id":"1204.5160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5160","created_at":"2026-05-18T03:57:14Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5160v1","created_at":"2026-05-18T03:57:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5160","created_at":"2026-05-18T03:57:14Z"},{"alias_kind":"pith_short_12","alias_value":"ORWHDZIMT3WF","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"ORWHDZIMT3WFXRXF","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"ORWHDZIM","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:9ec88cf9911cf4c16b4a94fc1cc86ba3864d0ddb59cb0c6fc7b8bfcbe8c2ab80","target":"graph","created_at":"2026-05-18T03:57:14Z","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":"One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete enumeration of the objects is possible, there is no apparent way how to study them in details, store them efficiently, or generate a particular one rapidly. In this paper we propose a novel method to deal with these difficulties, and illustrate it by presenting the classification of quaternary complex Hadamard matrices up to order 8. The obtained matrices are","authors_text":"Ferenc Sz\\\"oll\\H{o}si","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-23T19:45:26Z","title":"On quaternary complex Hadamard matrices of small orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5160","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":"sha256:4720c55dfda37a127900447ce4baf209fbcdfc20981f5e141c28eacc42d1de30","target":"record","created_at":"2026-05-18T03:57:14Z","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":"c3c504423e97f6e147faff09e4a17c119ed8bce17412359e3f5f527d11b62b0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-23T19:45:26Z","title_canon_sha256":"d7cce0f650d54cce0064a78ce3bfc93986787dc1cfebfb13fdd76c9e79333c7a"},"schema_version":"1.0","source":{"id":"1204.5160","kind":"arxiv","version":1}},"canonical_sha256":"746c71e50c9eec5bc6e527094e5f80e9d1074ae01cd56b916d93861c6d27cc86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"746c71e50c9eec5bc6e527094e5f80e9d1074ae01cd56b916d93861c6d27cc86","first_computed_at":"2026-05-18T03:57:14.577856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:14.577856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xq/7yyGS0IYjeWM9ux5/5VPGuLFB8+zNi5PLjNMz+vcAkVM5aHla1Cbw49bcU3yb9r4ld9eMnQWC7DWahT5pCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:14.578567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4720c55dfda37a127900447ce4baf209fbcdfc20981f5e141c28eacc42d1de30","sha256:9ec88cf9911cf4c16b4a94fc1cc86ba3864d0ddb59cb0c6fc7b8bfcbe8c2ab80"],"state_sha256":"1176daca57816dade41d549645e858108cfe6aed5cd316a315b0e55eccfb53b2"}