{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:QDGKUEPDZLE3Y2GNWTOAL55F7Z","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":"6ea4bfcc362d2af494ba694647bfc5236a76da55a7039348c73d68a7d9c405fc","cross_cats_sorted":["cs.IT","math.IT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-06-11T00:29:49Z","title_canon_sha256":"b6792f9f80afe6dc49d66aa2ae3163aa7a90e8b32e120ac29757e3f9c37c15e1"},"schema_version":"1.0","source":{"id":"2006.06126","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.06126","created_at":"2026-07-05T12:00:25Z"},{"alias_kind":"arxiv_version","alias_value":"2006.06126v3","created_at":"2026-07-05T12:00:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.06126","created_at":"2026-07-05T12:00:25Z"},{"alias_kind":"pith_short_12","alias_value":"QDGKUEPDZLE3","created_at":"2026-07-05T12:00:25Z"},{"alias_kind":"pith_short_16","alias_value":"QDGKUEPDZLE3Y2GN","created_at":"2026-07-05T12:00:25Z"},{"alias_kind":"pith_short_8","alias_value":"QDGKUEPD","created_at":"2026-07-05T12:00:25Z"}],"graph_snapshots":[{"event_id":"sha256:dd3c8c6cf6febd8d6af1fd15ec99523ab4b34d3a8876963f1d897c2dae6060ee","target":"graph","created_at":"2026-07-05T12:00:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2006.06126/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that much of the theory of finite tight frames can be generalised to vector spaces over the quaternions. This includes the variational characterisation, group frames, and the characterisations of projective and unitary equivalence. We are particularly interested in sets of equiangular lines (equi-isoclinic subspaces) and the groups associated with them, and how to move them between the spaces $\\Rd$, $\\Cd$ and $\\Hd$. We discuss what the analogue of Zauner's conjecture for equiangular lines in $\\Hd$ might be.","authors_text":"Shayne Waldron","cross_cats":["cs.IT","math.IT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-06-11T00:29:49Z","title":"Tight frames over the quaternions and equiangular lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.06126","kind":"arxiv","version":3},"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":"sha256:1a336359968be340c721f75a85a761793133c276404a9810e904e77c1766d8cf","target":"record","created_at":"2026-07-05T12:00:25Z","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":"6ea4bfcc362d2af494ba694647bfc5236a76da55a7039348c73d68a7d9c405fc","cross_cats_sorted":["cs.IT","math.IT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-06-11T00:29:49Z","title_canon_sha256":"b6792f9f80afe6dc49d66aa2ae3163aa7a90e8b32e120ac29757e3f9c37c15e1"},"schema_version":"1.0","source":{"id":"2006.06126","kind":"arxiv","version":3}},"canonical_sha256":"80ccaa11e3cac9bc68cdb4dc05f7a5fe6f21c06462f2e6f7694a3bf2595dffae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80ccaa11e3cac9bc68cdb4dc05f7a5fe6f21c06462f2e6f7694a3bf2595dffae","first_computed_at":"2026-07-05T12:00:25.034002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:00:25.034002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8VzJxfoOnHpqluPwnZfw7sCgbhKkg+UBLp3LojPe6W59BDNDzg9qefMY0NCFLhrkwAgcueGc/0zyxvYrW3lwDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:00:25.034631Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.06126","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a336359968be340c721f75a85a761793133c276404a9810e904e77c1766d8cf","sha256:dd3c8c6cf6febd8d6af1fd15ec99523ab4b34d3a8876963f1d897c2dae6060ee"],"state_sha256":"1eab754bbd72f94736eefbcb1a36c697e89516e2ca33cd9532ef67c36ddbbc76"}