{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JDPH3MUR5WJLL5PVMLQIO2LSLS","short_pith_number":"pith:JDPH3MUR","schema_version":"1.0","canonical_sha256":"48de7db291ed92b5f5f562e08769725c88dded3004444713ee0e81e8cbeafb25","source":{"kind":"arxiv","id":"1406.5147","version":1},"attestation_state":"computed","paper":{"title":"Sandpiles, spanning trees, and plane duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Caryn Werner, Darren Glass, David Perkinson, Matthew Macauley, Melody Chan, Qiaoyu Yang","submitted_at":"2014-06-19T18:47:38Z","abstract_excerpt":"Let G be a connected, loopless multigraph. The sandpile group of G is a finite abelian group associated to G whose order is equal to the number of spanning trees in G. Holroyd et al. used a dynamical process on graphs called rotor-routing to define a simply transitive action of the sandpile group of G on its set of spanning trees. Their definition depends on two pieces of auxiliary data: a choice of a ribbon graph structure on G, and a choice of a root vertex. Chan, Church, and Grochow showed that if G is a planar ribbon graph, it has a canonical rotor-routing action associated to it, i.e., th"},"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":"1406.5147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-19T18:47:38Z","cross_cats_sorted":[],"title_canon_sha256":"49f29aa7adf8f5e0b436fc8628d2606073e2b3b7ee0b87aaa224065c87322104","abstract_canon_sha256":"0a141f552c65f3472774187a4cd9ac3292aecb3b495a74bf59a6dc0bcdfe2e94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:20.843610Z","signature_b64":"N0glE7xCGhiUE0FSI0nQGxJwRyRiEpnWtkJXs8APw6AVhZBTVGLMJKnBY58XkiNA5DTDqXBOXiAYrNlaE6m2Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48de7db291ed92b5f5f562e08769725c88dded3004444713ee0e81e8cbeafb25","last_reissued_at":"2026-05-18T02:49:20.842936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:20.842936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sandpiles, spanning trees, and plane duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Caryn Werner, Darren Glass, David Perkinson, Matthew Macauley, Melody Chan, Qiaoyu Yang","submitted_at":"2014-06-19T18:47:38Z","abstract_excerpt":"Let G be a connected, loopless multigraph. The sandpile group of G is a finite abelian group associated to G whose order is equal to the number of spanning trees in G. Holroyd et al. used a dynamical process on graphs called rotor-routing to define a simply transitive action of the sandpile group of G on its set of spanning trees. Their definition depends on two pieces of auxiliary data: a choice of a ribbon graph structure on G, and a choice of a root vertex. Chan, Church, and Grochow showed that if G is a planar ribbon graph, it has a canonical rotor-routing action associated to it, i.e., th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5147","kind":"arxiv","version":1},"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":"1406.5147","created_at":"2026-05-18T02:49:20.843038+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.5147v1","created_at":"2026-05-18T02:49:20.843038+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5147","created_at":"2026-05-18T02:49:20.843038+00:00"},{"alias_kind":"pith_short_12","alias_value":"JDPH3MUR5WJL","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"JDPH3MUR5WJLL5PV","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"JDPH3MUR","created_at":"2026-05-18T12:28:33.132498+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/JDPH3MUR5WJLL5PVMLQIO2LSLS","json":"https://pith.science/pith/JDPH3MUR5WJLL5PVMLQIO2LSLS.json","graph_json":"https://pith.science/api/pith-number/JDPH3MUR5WJLL5PVMLQIO2LSLS/graph.json","events_json":"https://pith.science/api/pith-number/JDPH3MUR5WJLL5PVMLQIO2LSLS/events.json","paper":"https://pith.science/paper/JDPH3MUR"},"agent_actions":{"view_html":"https://pith.science/pith/JDPH3MUR5WJLL5PVMLQIO2LSLS","download_json":"https://pith.science/pith/JDPH3MUR5WJLL5PVMLQIO2LSLS.json","view_paper":"https://pith.science/paper/JDPH3MUR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.5147&json=true","fetch_graph":"https://pith.science/api/pith-number/JDPH3MUR5WJLL5PVMLQIO2LSLS/graph.json","fetch_events":"https://pith.science/api/pith-number/JDPH3MUR5WJLL5PVMLQIO2LSLS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JDPH3MUR5WJLL5PVMLQIO2LSLS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JDPH3MUR5WJLL5PVMLQIO2LSLS/action/storage_attestation","attest_author":"https://pith.science/pith/JDPH3MUR5WJLL5PVMLQIO2LSLS/action/author_attestation","sign_citation":"https://pith.science/pith/JDPH3MUR5WJLL5PVMLQIO2LSLS/action/citation_signature","submit_replication":"https://pith.science/pith/JDPH3MUR5WJLL5PVMLQIO2LSLS/action/replication_record"}},"created_at":"2026-05-18T02:49:20.843038+00:00","updated_at":"2026-05-18T02:49:20.843038+00:00"}