{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:32GDRDD3NHE2KH3FFLLGRE4G5N","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":"01602df9849e2ca6a66cf3da5934b97065092c5d55282028cdb7763684e3c325","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-31T02:48:01Z","title_canon_sha256":"005cb54f5405d8cd497fc6d557de0e58309ca9e030c468ee8195f2c4ae991008"},"schema_version":"1.0","source":{"id":"1705.10925","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10925","created_at":"2026-05-18T00:20:17Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10925v2","created_at":"2026-05-18T00:20:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10925","created_at":"2026-05-18T00:20:17Z"},{"alias_kind":"pith_short_12","alias_value":"32GDRDD3NHE2","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"32GDRDD3NHE2KH3F","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"32GDRDD3","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:26f711675052ec873b01996c6a3488a34babc672c15937962e001091339f15ca","target":"graph","created_at":"2026-05-18T00:20:17Z","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":"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","authors_text":"Sinho Chewi, Venkat Anantharam","cross_cats":["cs.DM","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-31T02:48:01Z","title":"A combinatorial proof of a formula of Biane and Chapuy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10925","kind":"arxiv","version":2},"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:af036f74191b274621332f70eea1927ef970decf8e3a00c978733f176968fba0","target":"record","created_at":"2026-05-18T00:20:17Z","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":"01602df9849e2ca6a66cf3da5934b97065092c5d55282028cdb7763684e3c325","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-31T02:48:01Z","title_canon_sha256":"005cb54f5405d8cd497fc6d557de0e58309ca9e030c468ee8195f2c4ae991008"},"schema_version":"1.0","source":{"id":"1705.10925","kind":"arxiv","version":2}},"canonical_sha256":"de8c388c7b69c9a51f652ad6689386eb47dd76d234df91aac93d2e0daee86fdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de8c388c7b69c9a51f652ad6689386eb47dd76d234df91aac93d2e0daee86fdb","first_computed_at":"2026-05-18T00:20:17.159064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:17.159064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4pV286axMyBlqS7VtH6u4bexho9ZvIlSYQwvJSPrLoOOVG/+5uc16xgroiCU/fHGLUqrIGAExUgVUw4zgyzFBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:17.159622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10925","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af036f74191b274621332f70eea1927ef970decf8e3a00c978733f176968fba0","sha256:26f711675052ec873b01996c6a3488a34babc672c15937962e001091339f15ca"],"state_sha256":"758c712d4b3f9845f52e95a1ac8a3f973ca2cb500cf0d652934080044168a5b1"}