{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TMCDYL2OX6E3NBSSPA535T5OAA","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":"ff5655ff5a5425387f8adb38a698f08609005db25c1e3bbf7c6c3b6232500992","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-15T20:43:38Z","title_canon_sha256":"90c150a334a87f00c588f0da0b270e7e91045858adb8ad4f31ee314a66064717"},"schema_version":"1.0","source":{"id":"1301.3482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3482","created_at":"2026-05-18T03:36:25Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3482v1","created_at":"2026-05-18T03:36:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3482","created_at":"2026-05-18T03:36:25Z"},{"alias_kind":"pith_short_12","alias_value":"TMCDYL2OX6E3","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TMCDYL2OX6E3NBSS","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TMCDYL2O","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:ab0ca10f72e8add7bcb1c623160ee975243914f5d47bcf30dae7ce8db6bf8f1e","target":"graph","created_at":"2026-05-18T03:36:25Z","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 A and B be two finite sets of points with total cardinality n, the many to many point matching with demands and capacities matches each point ai in A to at least alpha'i and at most alphai points in B, and each point bj in B to at least betaj and at most beta'j points in A for all 1 <= i <= s and 1 <= j <= t. In this paper, we present an upper bound for this problem using our new polynomial time algorithm.","authors_text":"Alireza Bagheri, Fatemeh Rajabi-Alni","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-15T20:43:38Z","title":"Many to Many Matching with Demands and Capacities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3482","kind":"arxiv","version":1},"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":"sha256:30ea56629663a735d07cd730b3395cdc84ee261719e1aa9633894ac7bd1be6ce","target":"record","created_at":"2026-05-18T03:36:25Z","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":"ff5655ff5a5425387f8adb38a698f08609005db25c1e3bbf7c6c3b6232500992","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-15T20:43:38Z","title_canon_sha256":"90c150a334a87f00c588f0da0b270e7e91045858adb8ad4f31ee314a66064717"},"schema_version":"1.0","source":{"id":"1301.3482","kind":"arxiv","version":1}},"canonical_sha256":"9b043c2f4ebf89b68652783bbecfae000facdc77cc6479aa011911d534cc4b64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b043c2f4ebf89b68652783bbecfae000facdc77cc6479aa011911d534cc4b64","first_computed_at":"2026-05-18T03:36:25.534855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:25.534855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MGA5MGRB/+x3u+iX75wb9/XgwaBHquDn4296nSOoy5qPy/6llp+/30BcNaj0oW3ngx47PH5LNvI2juElj2E4Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:25.535283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30ea56629663a735d07cd730b3395cdc84ee261719e1aa9633894ac7bd1be6ce","sha256:ab0ca10f72e8add7bcb1c623160ee975243914f5d47bcf30dae7ce8db6bf8f1e"],"state_sha256":"c7075cbf0cd370c7cca06d87ea441de6505ce096df23d1ac94816027958b2b44"}