{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2PORGTUQFNWYZJPXPDBK266S2X","short_pith_number":"pith:2PORGTUQ","schema_version":"1.0","canonical_sha256":"d3dd134e902b6d8ca5f778c2ad7bd2d5e63e2720b224dc434ce83baf947df987","source":{"kind":"arxiv","id":"1207.7033","version":2},"attestation_state":"computed","paper":{"title":"A Beginner's Guide to Counting Spanning Trees in a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.SP"],"primary_cat":"cs.DM","authors_text":"Saad Quader","submitted_at":"2012-07-30T18:36:25Z","abstract_excerpt":"(DRAFT VERSION) In this article we present a proof of the famous Kirchoff's Matrix-Tree theorem, which relates the number of spanning trees in a connected graph with the cofactors (and eigenvalues) of its combinatorial Laplacian matrix. This is a 165 year old result in graph theory and the proof is conceptually simple. However, the elegance of this result is it connects many apparently unrelated concepts in linear algebra and graph theory. Our motivation behind this work was to make the proof accessible to anyone with beginner\\slash intermediate grasp of linear algebra. Therefore in this paper"},"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":"1207.7033","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-07-30T18:36:25Z","cross_cats_sorted":["math.CO","math.SP"],"title_canon_sha256":"9bd1b437b079409415015fd8bae91dda7519d9e0db5f82dd07c2143f248d47b5","abstract_canon_sha256":"bb846cafd1749b49780b0db71a7dfa036533e88913bf1b7e8b7d23c22109d6da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:35.650734Z","signature_b64":"XkON4L+OKNRoTMFozH9QestWQeSHkmh70Daw6lbyGR2vj1/kNctCkPJJK3zYBu9AwpaoRC1Dfzx+YoZdaoz6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3dd134e902b6d8ca5f778c2ad7bd2d5e63e2720b224dc434ce83baf947df987","last_reissued_at":"2026-05-18T03:49:35.650087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:35.650087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Beginner's Guide to Counting Spanning Trees in a Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.SP"],"primary_cat":"cs.DM","authors_text":"Saad Quader","submitted_at":"2012-07-30T18:36:25Z","abstract_excerpt":"(DRAFT VERSION) In this article we present a proof of the famous Kirchoff's Matrix-Tree theorem, which relates the number of spanning trees in a connected graph with the cofactors (and eigenvalues) of its combinatorial Laplacian matrix. This is a 165 year old result in graph theory and the proof is conceptually simple. However, the elegance of this result is it connects many apparently unrelated concepts in linear algebra and graph theory. Our motivation behind this work was to make the proof accessible to anyone with beginner\\slash intermediate grasp of linear algebra. Therefore in this paper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.7033","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":""},"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":"1207.7033","created_at":"2026-05-18T03:49:35.650179+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.7033v2","created_at":"2026-05-18T03:49:35.650179+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.7033","created_at":"2026-05-18T03:49:35.650179+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PORGTUQFNWY","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PORGTUQFNWYZJPX","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PORGTUQ","created_at":"2026-05-18T12:26:50.516681+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/2PORGTUQFNWYZJPXPDBK266S2X","json":"https://pith.science/pith/2PORGTUQFNWYZJPXPDBK266S2X.json","graph_json":"https://pith.science/api/pith-number/2PORGTUQFNWYZJPXPDBK266S2X/graph.json","events_json":"https://pith.science/api/pith-number/2PORGTUQFNWYZJPXPDBK266S2X/events.json","paper":"https://pith.science/paper/2PORGTUQ"},"agent_actions":{"view_html":"https://pith.science/pith/2PORGTUQFNWYZJPXPDBK266S2X","download_json":"https://pith.science/pith/2PORGTUQFNWYZJPXPDBK266S2X.json","view_paper":"https://pith.science/paper/2PORGTUQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.7033&json=true","fetch_graph":"https://pith.science/api/pith-number/2PORGTUQFNWYZJPXPDBK266S2X/graph.json","fetch_events":"https://pith.science/api/pith-number/2PORGTUQFNWYZJPXPDBK266S2X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PORGTUQFNWYZJPXPDBK266S2X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PORGTUQFNWYZJPXPDBK266S2X/action/storage_attestation","attest_author":"https://pith.science/pith/2PORGTUQFNWYZJPXPDBK266S2X/action/author_attestation","sign_citation":"https://pith.science/pith/2PORGTUQFNWYZJPXPDBK266S2X/action/citation_signature","submit_replication":"https://pith.science/pith/2PORGTUQFNWYZJPXPDBK266S2X/action/replication_record"}},"created_at":"2026-05-18T03:49:35.650179+00:00","updated_at":"2026-05-18T03:49:35.650179+00:00"}