{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:476TIVS43LFEK7A4T6UARYY4YS","short_pith_number":"pith:476TIVS4","schema_version":"1.0","canonical_sha256":"e7fd34565cdaca457c1c9fa808e31cc4a6806d29c46d79e2cda336721a972437","source":{"kind":"arxiv","id":"1506.02855","version":1},"attestation_state":"computed","paper":{"title":"Spectral properties of weighted line digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"E. Segawa","submitted_at":"2015-06-09T10:42:37Z","abstract_excerpt":"In this paper, we treat some weighted line digraphs which are induced by a connected and undirected graph. For a given graph $G$, the adjacency matrix of the weighted line digraph $W$ is determined by a boundary operator from an arc-based space to a vertex-based space. We see that depending on the boundary operator and the Hilbert spaces, $W$ has different kind of an underlying stochastic transition operator. As an application, we obtain the spectrum of the positive support of cube of the Grover matrix in a large girth of the graph."},"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":"1506.02855","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-09T10:42:37Z","cross_cats_sorted":[],"title_canon_sha256":"53d46a184639026ae78505796e9296763fdbae57c91d125db1c1bc50cb09986f","abstract_canon_sha256":"ef75f3d71e266296ce1a2cd67f0e6a98fcd96c3ff53ae62762592f4cd76848d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:40.702417Z","signature_b64":"5QNqxMln4nFnshOa5FSfldX2oK+/RIujprfB3+baC5+pC557RIUXuts+aQBkNhYe8g6G4G2KjRotsJZNpPZNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7fd34565cdaca457c1c9fa808e31cc4a6806d29c46d79e2cda336721a972437","last_reissued_at":"2026-05-18T01:55:40.701744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:40.701744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral properties of weighted line digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"E. Segawa","submitted_at":"2015-06-09T10:42:37Z","abstract_excerpt":"In this paper, we treat some weighted line digraphs which are induced by a connected and undirected graph. For a given graph $G$, the adjacency matrix of the weighted line digraph $W$ is determined by a boundary operator from an arc-based space to a vertex-based space. We see that depending on the boundary operator and the Hilbert spaces, $W$ has different kind of an underlying stochastic transition operator. As an application, we obtain the spectrum of the positive support of cube of the Grover matrix in a large girth of the graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02855","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":""},"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":"1506.02855","created_at":"2026-05-18T01:55:40.701837+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.02855v1","created_at":"2026-05-18T01:55:40.701837+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02855","created_at":"2026-05-18T01:55:40.701837+00:00"},{"alias_kind":"pith_short_12","alias_value":"476TIVS43LFE","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"476TIVS43LFEK7A4","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"476TIVS4","created_at":"2026-05-18T12:29:05.191682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.19134","citing_title":"Arc search in graphs via Szegedy walks","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/476TIVS43LFEK7A4T6UARYY4YS","json":"https://pith.science/pith/476TIVS43LFEK7A4T6UARYY4YS.json","graph_json":"https://pith.science/api/pith-number/476TIVS43LFEK7A4T6UARYY4YS/graph.json","events_json":"https://pith.science/api/pith-number/476TIVS43LFEK7A4T6UARYY4YS/events.json","paper":"https://pith.science/paper/476TIVS4"},"agent_actions":{"view_html":"https://pith.science/pith/476TIVS43LFEK7A4T6UARYY4YS","download_json":"https://pith.science/pith/476TIVS43LFEK7A4T6UARYY4YS.json","view_paper":"https://pith.science/paper/476TIVS4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.02855&json=true","fetch_graph":"https://pith.science/api/pith-number/476TIVS43LFEK7A4T6UARYY4YS/graph.json","fetch_events":"https://pith.science/api/pith-number/476TIVS43LFEK7A4T6UARYY4YS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/476TIVS43LFEK7A4T6UARYY4YS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/476TIVS43LFEK7A4T6UARYY4YS/action/storage_attestation","attest_author":"https://pith.science/pith/476TIVS43LFEK7A4T6UARYY4YS/action/author_attestation","sign_citation":"https://pith.science/pith/476TIVS43LFEK7A4T6UARYY4YS/action/citation_signature","submit_replication":"https://pith.science/pith/476TIVS43LFEK7A4T6UARYY4YS/action/replication_record"}},"created_at":"2026-05-18T01:55:40.701837+00:00","updated_at":"2026-05-18T01:55:40.701837+00:00"}