{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6DDGNFHIXGJYCAQWPIAFIVDRUD","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":"fe23c73f63d36929cb8b5aff1ab50ceaa68a4ff033760dd4325e07e197be7ffe","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-11T16:52:12Z","title_canon_sha256":"a5b06a23d17463416e8e8b5a5f84f336afdd584e0364994851af8fb5e84334a9"},"schema_version":"1.0","source":{"id":"1312.3236","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3236","created_at":"2026-05-18T02:53:29Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3236v2","created_at":"2026-05-18T02:53:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3236","created_at":"2026-05-18T02:53:29Z"},{"alias_kind":"pith_short_12","alias_value":"6DDGNFHIXGJY","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6DDGNFHIXGJYCAQW","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6DDGNFHI","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:e7f651280af885136d8707452c2f17232a0e8a24d4cc4f75ddd402ea9a80fb34","target":"graph","created_at":"2026-05-18T02:53:29Z","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":"We study the connection between mutually unbiased bases and mutually orthogonal extraordinary supersquares, a wider class of squares which does not contain only the Latin squares. We show that there are four types of complete sets of mutually orthogonal extraordinary supersquares for the dimension $d=8$. We introduce the concept of physical striation and show that this is equivalent to the extraordinary supersquare. The general algorithm for obtaining the mutually unbiased bases and the physical striations is constructed and it is shown that the complete set of mutually unbiased physical stria","authors_text":"Cristian Ghiu, Iulia Ghiu","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-11T16:52:12Z","title":"The correspondence between mutually unbiased bases and mutually orthogonal extraordinary supersquares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3236","kind":"arxiv","version":2},"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:af4e4e019b0b969f2c4981f85efd0ad26afe5dd937d9c525b2718434abe54a09","target":"record","created_at":"2026-05-18T02:53:29Z","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":"fe23c73f63d36929cb8b5aff1ab50ceaa68a4ff033760dd4325e07e197be7ffe","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-12-11T16:52:12Z","title_canon_sha256":"a5b06a23d17463416e8e8b5a5f84f336afdd584e0364994851af8fb5e84334a9"},"schema_version":"1.0","source":{"id":"1312.3236","kind":"arxiv","version":2}},"canonical_sha256":"f0c66694e8b9938102167a00545471a0ff71ba2b662d22497a00793b5d102836","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0c66694e8b9938102167a00545471a0ff71ba2b662d22497a00793b5d102836","first_computed_at":"2026-05-18T02:53:29.863448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:29.863448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LjZTEhXDlKq95BbtuOuo6TP/qgUJeL+8rAY2xmijfZpdas4YDqBJLExXIJthTqKfBxLwz8i1jVusdJk9nY7GDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:29.864094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3236","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af4e4e019b0b969f2c4981f85efd0ad26afe5dd937d9c525b2718434abe54a09","sha256:e7f651280af885136d8707452c2f17232a0e8a24d4cc4f75ddd402ea9a80fb34"],"state_sha256":"1dbc74224ce05da2ad5403a766bd9bafee79e9a2dccd892a601d3b4f0ff943e6"}