{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:S3QOGOWAAZD2WLCGLU6LNK2LEM","short_pith_number":"pith:S3QOGOWA","schema_version":"1.0","canonical_sha256":"96e0e33ac00647ab2c465d3cb6ab4b2316cc30fcb6a91fbef6db19091413660e","source":{"kind":"arxiv","id":"2608.12410","version":1},"attestation_state":"computed","paper":{"title":"Finding all cospectral mates over a number field","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.SP"],"primary_cat":"math.NT","authors_text":"Alexander Van Werde","submitted_at":"2026-08-11T18:00:54Z","abstract_excerpt":"We investigate a notion of cospectrality for integer matrices that is parameterized by algebraic number fields. Given a number field and a symmetric integer matrix, we wonder when conjugating the integer matrix by an orthogonal matrix with entries in the given field can produce new integer matrices.\n  Our results concern sufficient conditions for the associated notion of spectral determination, and we give constraints on the orthogonal matrices when the conditions are not applicable. The results use the discriminant of the characteristic polynomial and properties of Krylov subspaces. We levera"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.12410","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-08-11T18:00:54Z","cross_cats_sorted":["math.CO","math.SP"],"title_canon_sha256":"e3ba7292471857c13d6b222b9f1cd2ce4add71b34ec3bd2cef5a19fd1d4cfdd3","abstract_canon_sha256":"29803612c4295fde0f5c009a8ae79b8b53282f51a09e68ef64ff9e1c57805d9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-14T00:42:46.629501Z","signature_b64":"V4h1Cg93N+ktIZTOR+VTNyV/FE3kUgyuvZAHXgxzmRUyR+Yl4sOVnSPNvchF5HbzSHeTnARxeeeugeGWAxMUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96e0e33ac00647ab2c465d3cb6ab4b2316cc30fcb6a91fbef6db19091413660e","last_reissued_at":"2026-08-14T00:42:46.626527Z","signature_status":"signed_v1","first_computed_at":"2026-08-14T00:42:46.626527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finding all cospectral mates over a number field","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.SP"],"primary_cat":"math.NT","authors_text":"Alexander Van Werde","submitted_at":"2026-08-11T18:00:54Z","abstract_excerpt":"We investigate a notion of cospectrality for integer matrices that is parameterized by algebraic number fields. Given a number field and a symmetric integer matrix, we wonder when conjugating the integer matrix by an orthogonal matrix with entries in the given field can produce new integer matrices.\n  Our results concern sufficient conditions for the associated notion of spectral determination, and we give constraints on the orthogonal matrices when the conditions are not applicable. The results use the discriminant of the characteristic polynomial and properties of Krylov subspaces. We levera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12410","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.12410/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.12410","created_at":"2026-08-14T00:42:46.628306+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.12410v1","created_at":"2026-08-14T00:42:46.628306+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.12410","created_at":"2026-08-14T00:42:46.628306+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3QOGOWAAZD2","created_at":"2026-08-14T00:42:46.628306+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3QOGOWAAZD2WLCG","created_at":"2026-08-14T00:42:46.628306+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3QOGOWA","created_at":"2026-08-14T00:42:46.628306+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S3QOGOWAAZD2WLCGLU6LNK2LEM","json":"https://pith.science/pith/S3QOGOWAAZD2WLCGLU6LNK2LEM.json","graph_json":"https://pith.science/api/pith-number/S3QOGOWAAZD2WLCGLU6LNK2LEM/graph.json","events_json":"https://pith.science/api/pith-number/S3QOGOWAAZD2WLCGLU6LNK2LEM/events.json","paper":"https://pith.science/paper/S3QOGOWA"},"agent_actions":{"view_html":"https://pith.science/pith/S3QOGOWAAZD2WLCGLU6LNK2LEM","download_json":"https://pith.science/pith/S3QOGOWAAZD2WLCGLU6LNK2LEM.json","view_paper":"https://pith.science/paper/S3QOGOWA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.12410&json=true","fetch_graph":"https://pith.science/api/pith-number/S3QOGOWAAZD2WLCGLU6LNK2LEM/graph.json","fetch_events":"https://pith.science/api/pith-number/S3QOGOWAAZD2WLCGLU6LNK2LEM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3QOGOWAAZD2WLCGLU6LNK2LEM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3QOGOWAAZD2WLCGLU6LNK2LEM/action/storage_attestation","attest_author":"https://pith.science/pith/S3QOGOWAAZD2WLCGLU6LNK2LEM/action/author_attestation","sign_citation":"https://pith.science/pith/S3QOGOWAAZD2WLCGLU6LNK2LEM/action/citation_signature","submit_replication":"https://pith.science/pith/S3QOGOWAAZD2WLCGLU6LNK2LEM/action/replication_record"}},"created_at":"2026-08-14T00:42:46.628306+00:00","updated_at":"2026-08-14T00:42:46.628306+00:00"}