{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2PTCU3LDW2TBHRCCIGLH6EYAAM","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":"9acb98e7b5fec5d597451b7b6d9395cfba574622bc5dc3d8c4ae33926bdeb26a","cross_cats_sorted":["math.NT","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-04T11:04:08Z","title_canon_sha256":"52ae1bf3c70524042e32a0e8289c0e06b395295c144b711250e23abd2c81bea0"},"schema_version":"1.0","source":{"id":"1503.05400","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05400","created_at":"2026-05-18T01:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05400v2","created_at":"2026-05-18T01:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05400","created_at":"2026-05-18T01:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"2PTCU3LDW2TB","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2PTCU3LDW2TBHRCC","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2PTCU3LD","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:69c8ac65a825a2b2e8badf797d8153f29283471b3d53214a891cec632d003429","target":"graph","created_at":"2026-05-18T01:19:12Z","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 obtain a general expression for the entries of the lth (l is integer) powers of even order (2k+1)-diagonal Toeplitz matrices. Additionally, we have the complex factorizations of Fibonacci polynomials.","authors_text":"Durmu\\c{s} Bozkurt, H. K\\\"ubra Duru","cross_cats":["math.NT","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-04T11:04:08Z","title":"Integer Powers of Certain Complex (2k+1)-diagonal Toeplitz Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05400","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":"sha256:31692e17053313cbd471c57f97e1b01481d18549001a75e21de660891067ab7b","target":"record","created_at":"2026-05-18T01:19:12Z","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":"9acb98e7b5fec5d597451b7b6d9395cfba574622bc5dc3d8c4ae33926bdeb26a","cross_cats_sorted":["math.NT","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-04T11:04:08Z","title_canon_sha256":"52ae1bf3c70524042e32a0e8289c0e06b395295c144b711250e23abd2c81bea0"},"schema_version":"1.0","source":{"id":"1503.05400","kind":"arxiv","version":2}},"canonical_sha256":"d3e62a6d63b6a613c44241967f1300030af82589f9e33add16ce9ab33b6b89cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3e62a6d63b6a613c44241967f1300030af82589f9e33add16ce9ab33b6b89cb","first_computed_at":"2026-05-18T01:19:12.336278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:12.336278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W0M54Qw5+REOKguimCT0vvsEGChgscCPMbmtTNgB5FsadlhwjJMKS+McQ2pPl7CafB2SLyjcWzHqv5P2IsqMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:12.337021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05400","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31692e17053313cbd471c57f97e1b01481d18549001a75e21de660891067ab7b","sha256:69c8ac65a825a2b2e8badf797d8153f29283471b3d53214a891cec632d003429"],"state_sha256":"cf23db2e1f441908d88bf9769ba113edb3da1fe2c9c1ad602bfff7a863a5f366"}