{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3HS7MGFFNE6XA55VII3PUVVOGU","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":"6c2ed4bcc543f42d8f1b98113546d134241789d5a65bf679c45f9d0f5f3b2e1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-04-08T16:27:41Z","title_canon_sha256":"9080bdd49c5b51e95b4f43cd332f5b3ee2e436d3eecdcbfca53dc2ac811188fb"},"schema_version":"1.0","source":{"id":"1904.04172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04172","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04172v1","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04172","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"3HS7MGFFNE6X","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3HS7MGFFNE6XA55V","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3HS7MGFF","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:a2e45f1b22db6f4e2c403a8a061159fc40e2fc051a74f659aa79f576d2465ca8","target":"graph","created_at":"2026-05-17T23:49:06Z","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":"A g-circulant matrix of order n is defined as a matrix of order n where each row is a right cyclic shift in g-places to the preceding row. Using number theory, certain nonnegative g-circulant real matrices are constructed. In particular, it is shown that spectra with sufficient conditions so that it can be the spectrum of a real g-circulant matrix is not a spectrum with sufficient conditions so that it can be the spectrum of a real circulant matrix of the same order. The obtained results are applied to Nonnegative Inverse Eigenvalue Problem to construct nonnegative, g-circulant matrices with g","authors_text":"Enide Andrade, Luis Arrieta, Mar\\'ia Robbiano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-04-08T16:27:41Z","title":"On the spectra of $g$-circulant matrices and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04172","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":"sha256:1cbe5e2eb3eb0d4ace21dd0c27d30d23bd56cb6d62da2566e2c022469fab87d6","target":"record","created_at":"2026-05-17T23:49:06Z","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":"6c2ed4bcc543f42d8f1b98113546d134241789d5a65bf679c45f9d0f5f3b2e1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-04-08T16:27:41Z","title_canon_sha256":"9080bdd49c5b51e95b4f43cd332f5b3ee2e436d3eecdcbfca53dc2ac811188fb"},"schema_version":"1.0","source":{"id":"1904.04172","kind":"arxiv","version":1}},"canonical_sha256":"d9e5f618a5693d7077b54236fa56ae353bd5fe82e2721c8da66e6b709d456ee2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9e5f618a5693d7077b54236fa56ae353bd5fe82e2721c8da66e6b709d456ee2","first_computed_at":"2026-05-17T23:49:06.873497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:06.873497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n/K9aeLCOXk7g+UaDT2eJvSfa+uuam0drDybNQGnydLSYFEONA9hd86hXanDrUxSL6UwDLTMf5yn2CYcvE/1BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:06.874075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.04172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cbe5e2eb3eb0d4ace21dd0c27d30d23bd56cb6d62da2566e2c022469fab87d6","sha256:a2e45f1b22db6f4e2c403a8a061159fc40e2fc051a74f659aa79f576d2465ca8"],"state_sha256":"17d0391e480f53587e837f2df531beb7473c7e6ddafc427fdee87b419c5c2b6b"}