{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4667WKH7W2FWXCI3VVTHVBODDG","short_pith_number":"pith:4667WKH7","schema_version":"1.0","canonical_sha256":"e7bdfb28ffb68b6b891bad667a85c3198bbb0fd1288d8ab871105df0fa55e8cd","source":{"kind":"arxiv","id":"1504.00614","version":1},"attestation_state":"computed","paper":{"title":"Scaling hypothesis for the Euclidean bipartite matching problem II. Correlation functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.dis-nn","authors_text":"Gabriele Sicuro, Sergio Caracciolo","submitted_at":"2015-04-02T16:53:26Z","abstract_excerpt":"We analyze the random Euclidean bipartite matching problem on the hypertorus in $d$ dimensions with quadratic cost and we derive the two--point correlation function for the optimal matching, using a proper ansatz introduced by Caracciolo et al. to evaluate the average optimal matching cost. We consider both the grid--Poisson matching problem and the Poisson--Poisson matching problem. We also show that the correlation function is strictly related to the Green's function of the Laplace operator on the hypertorus."},"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":"1504.00614","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-04-02T16:53:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fc23b14ca3bf9b7af640c0aa5f8906a283a21837596120709acce47fcb67baba","abstract_canon_sha256":"57242957382c8850c35740e90ab2b95a684d365f3f01a3d704138074994bcebe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:41:46.072805Z","signature_b64":"wfM+esI4ImEWY2PGgvHFMIj5Fop2slRVAlRQWMbVcYpo4yXCyZn0FKfGoF8gCxWuSf1Vr2A5L0oJnKQ3LzyUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7bdfb28ffb68b6b891bad667a85c3198bbb0fd1288d8ab871105df0fa55e8cd","last_reissued_at":"2026-05-18T01:41:46.072402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:41:46.072402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scaling hypothesis for the Euclidean bipartite matching problem II. Correlation functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.dis-nn","authors_text":"Gabriele Sicuro, Sergio Caracciolo","submitted_at":"2015-04-02T16:53:26Z","abstract_excerpt":"We analyze the random Euclidean bipartite matching problem on the hypertorus in $d$ dimensions with quadratic cost and we derive the two--point correlation function for the optimal matching, using a proper ansatz introduced by Caracciolo et al. to evaluate the average optimal matching cost. We consider both the grid--Poisson matching problem and the Poisson--Poisson matching problem. We also show that the correlation function is strictly related to the Green's function of the Laplace operator on the hypertorus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00614","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":"1504.00614","created_at":"2026-05-18T01:41:46.072459+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.00614v1","created_at":"2026-05-18T01:41:46.072459+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00614","created_at":"2026-05-18T01:41:46.072459+00:00"},{"alias_kind":"pith_short_12","alias_value":"4667WKH7W2FW","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4667WKH7W2FWXCI3","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4667WKH7","created_at":"2026-05-18T12:29:05.191682+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/4667WKH7W2FWXCI3VVTHVBODDG","json":"https://pith.science/pith/4667WKH7W2FWXCI3VVTHVBODDG.json","graph_json":"https://pith.science/api/pith-number/4667WKH7W2FWXCI3VVTHVBODDG/graph.json","events_json":"https://pith.science/api/pith-number/4667WKH7W2FWXCI3VVTHVBODDG/events.json","paper":"https://pith.science/paper/4667WKH7"},"agent_actions":{"view_html":"https://pith.science/pith/4667WKH7W2FWXCI3VVTHVBODDG","download_json":"https://pith.science/pith/4667WKH7W2FWXCI3VVTHVBODDG.json","view_paper":"https://pith.science/paper/4667WKH7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.00614&json=true","fetch_graph":"https://pith.science/api/pith-number/4667WKH7W2FWXCI3VVTHVBODDG/graph.json","fetch_events":"https://pith.science/api/pith-number/4667WKH7W2FWXCI3VVTHVBODDG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4667WKH7W2FWXCI3VVTHVBODDG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4667WKH7W2FWXCI3VVTHVBODDG/action/storage_attestation","attest_author":"https://pith.science/pith/4667WKH7W2FWXCI3VVTHVBODDG/action/author_attestation","sign_citation":"https://pith.science/pith/4667WKH7W2FWXCI3VVTHVBODDG/action/citation_signature","submit_replication":"https://pith.science/pith/4667WKH7W2FWXCI3VVTHVBODDG/action/replication_record"}},"created_at":"2026-05-18T01:41:46.072459+00:00","updated_at":"2026-05-18T01:41:46.072459+00:00"}