{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:37BRGH2P5IXAIZWFV3NDR26SQ7","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":"62495ea4e4436a92b1b30a83c7fe253c8fd2613a2abd07d0b8ed50d8f619b81c","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-14T22:47:27Z","title_canon_sha256":"8b88b5b422d7bdbf2ed9db089da71735256e0fb1e67b2300d86295d0a79563db"},"schema_version":"1.0","source":{"id":"1104.2940","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2940","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2940v1","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2940","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"37BRGH2P5IXA","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"37BRGH2P5IXAIZWF","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"37BRGH2P","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:24cd95b0c32f10238dfe6e31f980adf29628100efc6794226e5c1293fe36c160","target":"graph","created_at":"2026-05-18T04:24:04Z","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":"In this paper we give a new construction of parametric families of complex Hadamard matrices of square orders, and connect them to equiangular tight frames. The results presented here generalize some of the recent ideas of Bodmann et al. and extend the list of known equiangular tight frames. In particular, a (36,21) frame coming from a nontrivial cube root signature matrix is obtained for the first time.","authors_text":"Ferenc Sz\\\"oll\\H{o}si","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-14T22:47:27Z","title":"Complex Hadamard matrices and Equiangular Tight Frames"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2940","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:b65970bab8a6c2a42168f6b98b09a99a0716daa671074e6c2bc5eb80ab526830","target":"record","created_at":"2026-05-18T04:24:04Z","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":"62495ea4e4436a92b1b30a83c7fe253c8fd2613a2abd07d0b8ed50d8f619b81c","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-04-14T22:47:27Z","title_canon_sha256":"8b88b5b422d7bdbf2ed9db089da71735256e0fb1e67b2300d86295d0a79563db"},"schema_version":"1.0","source":{"id":"1104.2940","kind":"arxiv","version":1}},"canonical_sha256":"dfc3131f4fea2e0466c5aeda38ebd287da735aee8bbc9e07e09401c5c6e3e619","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfc3131f4fea2e0466c5aeda38ebd287da735aee8bbc9e07e09401c5c6e3e619","first_computed_at":"2026-05-18T04:24:04.661205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:04.661205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OiGLDFM+bY37q8Hn/esKEuS7nogixv9i+PEmFJ7g52gWWnfuOVcXjVJ2qgaK+6z8zBTm5VDN7roHmThHi4qACw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:04.661857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2940","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b65970bab8a6c2a42168f6b98b09a99a0716daa671074e6c2bc5eb80ab526830","sha256:24cd95b0c32f10238dfe6e31f980adf29628100efc6794226e5c1293fe36c160"],"state_sha256":"e1e0848cbfc4840204b22f5f6a61b1c72bb90cd7864e21c715c449496c721412"}