{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:32GDRDD3NHE2KH3FFLLGRE4G5N","short_pith_number":"pith:32GDRDD3","schema_version":"1.0","canonical_sha256":"de8c388c7b69c9a51f652ad6689386eb47dd76d234df91aac93d2e0daee86fdb","source":{"kind":"arxiv","id":"1705.10925","version":2},"attestation_state":"computed","paper":{"title":"A combinatorial proof of a formula of Biane and Chapuy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"math.CO","authors_text":"Sinho Chewi, Venkat Anantharam","submitted_at":"2017-05-31T02:48:01Z","abstract_excerpt":"Let $G$ be a simple strongly connected weighted directed graph. Let $\\mathcal{G}$ denote the spanning tree graph of $G$. That is, the vertices of $\\mathcal{G}$ consist of the directed rooted spanning trees on $G$, and the edges of $\\mathcal{G}$ consist of pairs of trees $(t_i, t_j)$ such that $t_j$ can be obtained from $t_i$ by adding the edge from the root of $t_i$ to the root of $t_j$ and deleting the outgoing edge from the root of $t_j$. A formula for the ratio of the sum of the weights of the directed rooted spanning trees on $\\mathcal{G}$ to the sum of the weights of the directed rooted s"},"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":"1705.10925","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-31T02:48:01Z","cross_cats_sorted":["cs.DM","math.PR"],"title_canon_sha256":"005cb54f5405d8cd497fc6d557de0e58309ca9e030c468ee8195f2c4ae991008","abstract_canon_sha256":"01602df9849e2ca6a66cf3da5934b97065092c5d55282028cdb7763684e3c325"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:17.159622Z","signature_b64":"4pV286axMyBlqS7VtH6u4bexho9ZvIlSYQwvJSPrLoOOVG/+5uc16xgroiCU/fHGLUqrIGAExUgVUw4zgyzFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de8c388c7b69c9a51f652ad6689386eb47dd76d234df91aac93d2e0daee86fdb","last_reissued_at":"2026-05-18T00:20:17.159064Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:17.159064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A combinatorial proof of a formula of Biane and Chapuy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"math.CO","authors_text":"Sinho Chewi, Venkat Anantharam","submitted_at":"2017-05-31T02:48:01Z","abstract_excerpt":"Let $G$ be a simple strongly connected weighted directed graph. Let $\\mathcal{G}$ denote the spanning tree graph of $G$. That is, the vertices of $\\mathcal{G}$ consist of the directed rooted spanning trees on $G$, and the edges of $\\mathcal{G}$ consist of pairs of trees $(t_i, t_j)$ such that $t_j$ can be obtained from $t_i$ by adding the edge from the root of $t_i$ to the root of $t_j$ and deleting the outgoing edge from the root of $t_j$. A formula for the ratio of the sum of the weights of the directed rooted spanning trees on $\\mathcal{G}$ to the sum of the weights of the directed rooted s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10925","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":"1705.10925","created_at":"2026-05-18T00:20:17.159167+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.10925v2","created_at":"2026-05-18T00:20:17.159167+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10925","created_at":"2026-05-18T00:20:17.159167+00:00"},{"alias_kind":"pith_short_12","alias_value":"32GDRDD3NHE2","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"32GDRDD3NHE2KH3F","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"32GDRDD3","created_at":"2026-05-18T12:30:55.937587+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/32GDRDD3NHE2KH3FFLLGRE4G5N","json":"https://pith.science/pith/32GDRDD3NHE2KH3FFLLGRE4G5N.json","graph_json":"https://pith.science/api/pith-number/32GDRDD3NHE2KH3FFLLGRE4G5N/graph.json","events_json":"https://pith.science/api/pith-number/32GDRDD3NHE2KH3FFLLGRE4G5N/events.json","paper":"https://pith.science/paper/32GDRDD3"},"agent_actions":{"view_html":"https://pith.science/pith/32GDRDD3NHE2KH3FFLLGRE4G5N","download_json":"https://pith.science/pith/32GDRDD3NHE2KH3FFLLGRE4G5N.json","view_paper":"https://pith.science/paper/32GDRDD3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.10925&json=true","fetch_graph":"https://pith.science/api/pith-number/32GDRDD3NHE2KH3FFLLGRE4G5N/graph.json","fetch_events":"https://pith.science/api/pith-number/32GDRDD3NHE2KH3FFLLGRE4G5N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/32GDRDD3NHE2KH3FFLLGRE4G5N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/32GDRDD3NHE2KH3FFLLGRE4G5N/action/storage_attestation","attest_author":"https://pith.science/pith/32GDRDD3NHE2KH3FFLLGRE4G5N/action/author_attestation","sign_citation":"https://pith.science/pith/32GDRDD3NHE2KH3FFLLGRE4G5N/action/citation_signature","submit_replication":"https://pith.science/pith/32GDRDD3NHE2KH3FFLLGRE4G5N/action/replication_record"}},"created_at":"2026-05-18T00:20:17.159167+00:00","updated_at":"2026-05-18T00:20:17.159167+00:00"}