{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:OPHQFCT2CSZCV3BYG36SN5X4TJ","short_pith_number":"pith:OPHQFCT2","schema_version":"1.0","canonical_sha256":"73cf028a7a14b22aec3836fd26f6fc9a5c1ba462780b08429d2e1628b1547b0b","source":{"kind":"arxiv","id":"1608.01521","version":1},"attestation_state":"computed","paper":{"title":"The sandpile model on K_{m,n} and the rank of its configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michele D'Adderio, Yvan Le Borgne","submitted_at":"2016-08-04T12:56:23Z","abstract_excerpt":"We present an algorithm to compute the rank of a configuration of the sandpile model for the complete bipartite graph K_{m,n} of complexity O(m+n). Furthermore, we provide a formula for the generating function of parking sorted configurations on complete bipartite graphs K_{m,n} according to rank, degree, and the sizes m and n.\n  The results in the present paper are similar to those found by Robert Cori and the second named author for the complete graph K_{n+1}, and they rely on the analysis of certain operators on the stable sorted configurations of K_{m,n} developed in a previous work by the"},"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":"1608.01521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-04T12:56:23Z","cross_cats_sorted":[],"title_canon_sha256":"58475645446fa3ffe0fe510a0d61c42583c6d41c1da2aafd4fc0c3fd08c80e40","abstract_canon_sha256":"498f9b7e1d97ff809f64ecc41329fcba53863c5eac4d55e81f5b1c32e6687522"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:52.243203Z","signature_b64":"nNpx3FcAzY9Tn95ITuY0kxgxI+/ED4UAhxaBwCBCY6RDh52M4LBS/Op9PNmP1hSdLRiNEzbOrBKpk8+hK6ZxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73cf028a7a14b22aec3836fd26f6fc9a5c1ba462780b08429d2e1628b1547b0b","last_reissued_at":"2026-05-18T01:09:52.242574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:52.242574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The sandpile model on K_{m,n} and the rank of its configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michele D'Adderio, Yvan Le Borgne","submitted_at":"2016-08-04T12:56:23Z","abstract_excerpt":"We present an algorithm to compute the rank of a configuration of the sandpile model for the complete bipartite graph K_{m,n} of complexity O(m+n). Furthermore, we provide a formula for the generating function of parking sorted configurations on complete bipartite graphs K_{m,n} according to rank, degree, and the sizes m and n.\n  The results in the present paper are similar to those found by Robert Cori and the second named author for the complete graph K_{n+1}, and they rely on the analysis of certain operators on the stable sorted configurations of K_{m,n} developed in a previous work by the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01521","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":"1608.01521","created_at":"2026-05-18T01:09:52.242692+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.01521v1","created_at":"2026-05-18T01:09:52.242692+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01521","created_at":"2026-05-18T01:09:52.242692+00:00"},{"alias_kind":"pith_short_12","alias_value":"OPHQFCT2CSZC","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_16","alias_value":"OPHQFCT2CSZCV3BY","created_at":"2026-05-18T12:30:36.002864+00:00"},{"alias_kind":"pith_short_8","alias_value":"OPHQFCT2","created_at":"2026-05-18T12:30:36.002864+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/OPHQFCT2CSZCV3BYG36SN5X4TJ","json":"https://pith.science/pith/OPHQFCT2CSZCV3BYG36SN5X4TJ.json","graph_json":"https://pith.science/api/pith-number/OPHQFCT2CSZCV3BYG36SN5X4TJ/graph.json","events_json":"https://pith.science/api/pith-number/OPHQFCT2CSZCV3BYG36SN5X4TJ/events.json","paper":"https://pith.science/paper/OPHQFCT2"},"agent_actions":{"view_html":"https://pith.science/pith/OPHQFCT2CSZCV3BYG36SN5X4TJ","download_json":"https://pith.science/pith/OPHQFCT2CSZCV3BYG36SN5X4TJ.json","view_paper":"https://pith.science/paper/OPHQFCT2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.01521&json=true","fetch_graph":"https://pith.science/api/pith-number/OPHQFCT2CSZCV3BYG36SN5X4TJ/graph.json","fetch_events":"https://pith.science/api/pith-number/OPHQFCT2CSZCV3BYG36SN5X4TJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OPHQFCT2CSZCV3BYG36SN5X4TJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OPHQFCT2CSZCV3BYG36SN5X4TJ/action/storage_attestation","attest_author":"https://pith.science/pith/OPHQFCT2CSZCV3BYG36SN5X4TJ/action/author_attestation","sign_citation":"https://pith.science/pith/OPHQFCT2CSZCV3BYG36SN5X4TJ/action/citation_signature","submit_replication":"https://pith.science/pith/OPHQFCT2CSZCV3BYG36SN5X4TJ/action/replication_record"}},"created_at":"2026-05-18T01:09:52.242692+00:00","updated_at":"2026-05-18T01:09:52.242692+00:00"}