{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DMQXPONRF4TWH3ULOL626XRE4M","short_pith_number":"pith:DMQXPONR","schema_version":"1.0","canonical_sha256":"1b2177b9b12f2763ee8b72fdaf5e24e30033a8d7583cbd6474d4dce8e66aff99","source":{"kind":"arxiv","id":"1407.1983","version":6},"attestation_state":"computed","paper":{"title":"From G-parking functions to B-parking functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fengming Dong","submitted_at":"2014-07-08T08:04:08Z","abstract_excerpt":"A matching $M$ in a multigraph $G=(V,E)$ is said to be uniquely restricted if $M$ is the only perfect matching in the subgraph of $G$ induced by $V(M)$ (i.e., the set of vertices saturated by $M$). For any fixed vertex $x_0$ in $G$, there is a bijection from the set of spanning trees of $G$ to the set of uniquely restricted matchings of size $|V|-1$ in $S(G)-x_0$, where $S(G)$ is the bipartite graph obtained from $G$ by subdividing each edge in $G$. Thus the notion \"uniquely restricted matchings of a bipartite graph $H$ saturating all vertices in a partite set $X$\" can be viewed as an extensio"},"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":"1407.1983","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-08T08:04:08Z","cross_cats_sorted":[],"title_canon_sha256":"d47adcfc680de6da366d0bc65099a6ac6f027a9b52d38c02e69d025cf1c50d61","abstract_canon_sha256":"f2bc4f1cd1180d790351d3bec66bf763181d30d716a1843cd7e9f3370f69b83a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:06.022835Z","signature_b64":"1tseCCCTZcd3YzFfdp1fGle7inss1QsLBuHUw4sT4dDSJvSsYvN767ENc0Yp3cL5igr7lQn4TFdQeNwA4zuhBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b2177b9b12f2763ee8b72fdaf5e24e30033a8d7583cbd6474d4dce8e66aff99","last_reissued_at":"2026-05-18T00:09:06.022276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:06.022276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From G-parking functions to B-parking functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fengming Dong","submitted_at":"2014-07-08T08:04:08Z","abstract_excerpt":"A matching $M$ in a multigraph $G=(V,E)$ is said to be uniquely restricted if $M$ is the only perfect matching in the subgraph of $G$ induced by $V(M)$ (i.e., the set of vertices saturated by $M$). For any fixed vertex $x_0$ in $G$, there is a bijection from the set of spanning trees of $G$ to the set of uniquely restricted matchings of size $|V|-1$ in $S(G)-x_0$, where $S(G)$ is the bipartite graph obtained from $G$ by subdividing each edge in $G$. Thus the notion \"uniquely restricted matchings of a bipartite graph $H$ saturating all vertices in a partite set $X$\" can be viewed as an extensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1983","kind":"arxiv","version":6},"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":"1407.1983","created_at":"2026-05-18T00:09:06.022383+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.1983v6","created_at":"2026-05-18T00:09:06.022383+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1983","created_at":"2026-05-18T00:09:06.022383+00:00"},{"alias_kind":"pith_short_12","alias_value":"DMQXPONRF4TW","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DMQXPONRF4TWH3UL","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DMQXPONR","created_at":"2026-05-18T12:28:25.294606+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/DMQXPONRF4TWH3ULOL626XRE4M","json":"https://pith.science/pith/DMQXPONRF4TWH3ULOL626XRE4M.json","graph_json":"https://pith.science/api/pith-number/DMQXPONRF4TWH3ULOL626XRE4M/graph.json","events_json":"https://pith.science/api/pith-number/DMQXPONRF4TWH3ULOL626XRE4M/events.json","paper":"https://pith.science/paper/DMQXPONR"},"agent_actions":{"view_html":"https://pith.science/pith/DMQXPONRF4TWH3ULOL626XRE4M","download_json":"https://pith.science/pith/DMQXPONRF4TWH3ULOL626XRE4M.json","view_paper":"https://pith.science/paper/DMQXPONR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.1983&json=true","fetch_graph":"https://pith.science/api/pith-number/DMQXPONRF4TWH3ULOL626XRE4M/graph.json","fetch_events":"https://pith.science/api/pith-number/DMQXPONRF4TWH3ULOL626XRE4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DMQXPONRF4TWH3ULOL626XRE4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DMQXPONRF4TWH3ULOL626XRE4M/action/storage_attestation","attest_author":"https://pith.science/pith/DMQXPONRF4TWH3ULOL626XRE4M/action/author_attestation","sign_citation":"https://pith.science/pith/DMQXPONRF4TWH3ULOL626XRE4M/action/citation_signature","submit_replication":"https://pith.science/pith/DMQXPONRF4TWH3ULOL626XRE4M/action/replication_record"}},"created_at":"2026-05-18T00:09:06.022383+00:00","updated_at":"2026-05-18T00:09:06.022383+00:00"}