{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:QRSCADH7CY6GLVKOL6P3SVPYQD","short_pith_number":"pith:QRSCADH7","schema_version":"1.0","canonical_sha256":"8464200cff163c65d54e5f9fb955f880f161946b888418af5c8ecf2017187bb0","source":{"kind":"arxiv","id":"math/0508171","version":2},"attestation_state":"computed","paper":{"title":"Matrices of Forests and the Analysis of Digraphs","license":"","headline":"","cross_cats":["cs.CV","cs.NI"],"primary_cat":"math.CO","authors_text":"Pavel Chebotarev, Rafig Agaev","submitted_at":"2005-08-09T20:11:27Z","abstract_excerpt":"The matrices of spanning rooted forests are studied as a tool for analysing the structure of digraphs and measuring their characteristics. The problems of revealing the basis bicomponents, measuring vertex proximity, and ranking from preference relations / sports competitions are considered. It is shown that the vertex accessibility measure based on spanning forests has a number of desirable properties. An interpretation for the normalized matrix of out-forests in terms of information dissemination is given.\n  Keywords: Laplacian matrix, spanning forest, matrix-forest theorem, proximity measur"},"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":"math/0508171","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2005-08-09T20:11:27Z","cross_cats_sorted":["cs.CV","cs.NI"],"title_canon_sha256":"8b31feab3c5845ed583d212763c1e8d1d81f7c40d4182133a1fc706d7166f552","abstract_canon_sha256":"681da3c3219ab669447596a414e9860accc9731c66ed6fd436aab0aa9ea64683"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:50:36.486695Z","signature_b64":"wh08b8VASOFjbQCCpJSx/FG8YTyaoAQZEzdMThuBm/Kgnn0Ga9L6M9UW87qppayjMhllcLC4anZqwHW/s79rAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8464200cff163c65d54e5f9fb955f880f161946b888418af5c8ecf2017187bb0","last_reissued_at":"2026-07-04T14:50:36.486285Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:50:36.486285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrices of Forests and the Analysis of Digraphs","license":"","headline":"","cross_cats":["cs.CV","cs.NI"],"primary_cat":"math.CO","authors_text":"Pavel Chebotarev, Rafig Agaev","submitted_at":"2005-08-09T20:11:27Z","abstract_excerpt":"The matrices of spanning rooted forests are studied as a tool for analysing the structure of digraphs and measuring their characteristics. The problems of revealing the basis bicomponents, measuring vertex proximity, and ranking from preference relations / sports competitions are considered. It is shown that the vertex accessibility measure based on spanning forests has a number of desirable properties. An interpretation for the normalized matrix of out-forests in terms of information dissemination is given.\n  Keywords: Laplacian matrix, spanning forest, matrix-forest theorem, proximity measur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508171","kind":"arxiv","version":2},"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/math/0508171/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":"math/0508171","created_at":"2026-07-04T14:50:36.486340+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0508171v2","created_at":"2026-07-04T14:50:36.486340+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508171","created_at":"2026-07-04T14:50:36.486340+00:00"},{"alias_kind":"pith_short_12","alias_value":"QRSCADH7CY6G","created_at":"2026-07-04T14:50:36.486340+00:00"},{"alias_kind":"pith_short_16","alias_value":"QRSCADH7CY6GLVKO","created_at":"2026-07-04T14:50:36.486340+00:00"},{"alias_kind":"pith_short_8","alias_value":"QRSCADH7","created_at":"2026-07-04T14:50:36.486340+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/QRSCADH7CY6GLVKOL6P3SVPYQD","json":"https://pith.science/pith/QRSCADH7CY6GLVKOL6P3SVPYQD.json","graph_json":"https://pith.science/api/pith-number/QRSCADH7CY6GLVKOL6P3SVPYQD/graph.json","events_json":"https://pith.science/api/pith-number/QRSCADH7CY6GLVKOL6P3SVPYQD/events.json","paper":"https://pith.science/paper/QRSCADH7"},"agent_actions":{"view_html":"https://pith.science/pith/QRSCADH7CY6GLVKOL6P3SVPYQD","download_json":"https://pith.science/pith/QRSCADH7CY6GLVKOL6P3SVPYQD.json","view_paper":"https://pith.science/paper/QRSCADH7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0508171&json=true","fetch_graph":"https://pith.science/api/pith-number/QRSCADH7CY6GLVKOL6P3SVPYQD/graph.json","fetch_events":"https://pith.science/api/pith-number/QRSCADH7CY6GLVKOL6P3SVPYQD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QRSCADH7CY6GLVKOL6P3SVPYQD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QRSCADH7CY6GLVKOL6P3SVPYQD/action/storage_attestation","attest_author":"https://pith.science/pith/QRSCADH7CY6GLVKOL6P3SVPYQD/action/author_attestation","sign_citation":"https://pith.science/pith/QRSCADH7CY6GLVKOL6P3SVPYQD/action/citation_signature","submit_replication":"https://pith.science/pith/QRSCADH7CY6GLVKOL6P3SVPYQD/action/replication_record"}},"created_at":"2026-07-04T14:50:36.486340+00:00","updated_at":"2026-07-04T14:50:36.486340+00:00"}