{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ZVV5LUZPV6E2LEAMXA35GTYXWS","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":"ddcad68df5a72d7bcee619094e191b755731ab85d1b60be4a7f1d2f8f39cc327","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2023-11-01T08:03:11Z","title_canon_sha256":"7a70b623373a6667275b7fcee059ee7fa154f9cb0224665c91e831c642516c8a"},"schema_version":"1.0","source":{"id":"2311.00354","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.00354","created_at":"2026-07-05T07:07:45Z"},{"alias_kind":"arxiv_version","alias_value":"2311.00354v1","created_at":"2026-07-05T07:07:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.00354","created_at":"2026-07-05T07:07:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZVV5LUZPV6E2","created_at":"2026-07-05T07:07:45Z"},{"alias_kind":"pith_short_16","alias_value":"ZVV5LUZPV6E2LEAM","created_at":"2026-07-05T07:07:45Z"},{"alias_kind":"pith_short_8","alias_value":"ZVV5LUZP","created_at":"2026-07-05T07:07:45Z"}],"graph_snapshots":[{"event_id":"sha256:c9c1a03e35f40621e4987a5c812a76d34e6b04db2f9cb2a34ccb64fd3ec2664b","target":"graph","created_at":"2026-07-05T07:07:45Z","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/2311.00354/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explore a notion of bent sequence attached to the data consisting of an Hadamard matrix of order $n$ defined over the complex $q^{th}$ roots of unity, an eigenvalue of that matrix, and a Galois automorphism from the cyclotomic field of order $q.$ In particular we construct self-dual bent sequences for various $q\\le 60$ and lengths $n\\le 21.$ Computational construction methods comprise the resolution of polynomial systems by Groebner bases and eigenspace computations. Infinite families can be constructed from regular Hadamard matrices, Bush-type Hadamard matrices, and generalized Boolean ben","authors_text":"Andr\\'es Armario, Danni Lu, Ferruh Ozbudak, Minjia Shi, Patrick Sol\\'e, Ronan Egan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2023-11-01T08:03:11Z","title":"Butson Hadamard matrices, bent sequences, and spherical codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.00354","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:e017d547c138e1cfa3038a4d38182d60ce65685bb7e1b1a1b6b8ff6f44d34d12","target":"record","created_at":"2026-07-05T07:07:45Z","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":"ddcad68df5a72d7bcee619094e191b755731ab85d1b60be4a7f1d2f8f39cc327","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2023-11-01T08:03:11Z","title_canon_sha256":"7a70b623373a6667275b7fcee059ee7fa154f9cb0224665c91e831c642516c8a"},"schema_version":"1.0","source":{"id":"2311.00354","kind":"arxiv","version":1}},"canonical_sha256":"cd6bd5d32faf89a5900cb837d34f17b48160bd1a43c8bcaa3c2ca11bca6df230","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd6bd5d32faf89a5900cb837d34f17b48160bd1a43c8bcaa3c2ca11bca6df230","first_computed_at":"2026-07-05T07:07:45.981442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:07:45.981442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FdUmIQzggnrmQpR9O/LvgRUosHLzc/ikS8Iz+YtI52dWrrMlUR3B9WVVe7DSWuFkxVCtbPmkorcJurG6k5qDCg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:07:45.981936Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.00354","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e017d547c138e1cfa3038a4d38182d60ce65685bb7e1b1a1b6b8ff6f44d34d12","sha256:c9c1a03e35f40621e4987a5c812a76d34e6b04db2f9cb2a34ccb64fd3ec2664b"],"state_sha256":"1cb3388999878ff610be1e948f7a17f3bba1e7e67271e6110da2fe8a31ef9a01"}