{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:IOGISJS3YKY4PNC5UEB6PMZHX4","short_pith_number":"pith:IOGISJS3","schema_version":"1.0","canonical_sha256":"438c89265bc2b1c7b45da103e7b327bf0e9b6835fa90178fdfe6f85b67d6c47a","source":{"kind":"arxiv","id":"0912.0287","version":3},"attestation_state":"computed","paper":{"title":"Tight Thresholds for Cuckoo Hashing via XORSAT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andrea Montanari, Andreas Goerdt, Martin Dietzfelbinger, Michael Mitzenmacher, Michael Rink, Rasmus Pagh","submitted_at":"2009-12-01T22:23:48Z","abstract_excerpt":"We settle the question of tight thresholds for offline cuckoo hashing. The problem can be stated as follows: we have n keys to be hashed into m buckets each capable of holding a single key. Each key has k >= 3 (distinct) associated buckets chosen uniformly at random and independently of the choices of other keys. A hash table can be constructed successfully if each key can be placed into one of its buckets. We seek thresholds alpha_k such that, as n goes to infinity, if n/m <= alpha for some alpha < alpha_k then a hash table can be constructed successfully with high probability, and if n/m >= "},"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":"0912.0287","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-12-01T22:23:48Z","cross_cats_sorted":[],"title_canon_sha256":"230aac83c47864bc97a34d242f766943b8fc757770da212530eb14b5e0ab2473","abstract_canon_sha256":"fa679d767e9200d089a79fcefdac967e20b43d6f244ceba197a48c10c229506f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:54.575383Z","signature_b64":"XU3rqFFgsuISnksNYSVwnCy60aLRJUAySxvd5GQncb44+bC15Lg+/5y6cFSWFZrtYL0VEVpTovBdd6VlJCSRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"438c89265bc2b1c7b45da103e7b327bf0e9b6835fa90178fdfe6f85b67d6c47a","last_reissued_at":"2026-05-18T04:32:54.574735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:54.574735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tight Thresholds for Cuckoo Hashing via XORSAT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andrea Montanari, Andreas Goerdt, Martin Dietzfelbinger, Michael Mitzenmacher, Michael Rink, Rasmus Pagh","submitted_at":"2009-12-01T22:23:48Z","abstract_excerpt":"We settle the question of tight thresholds for offline cuckoo hashing. The problem can be stated as follows: we have n keys to be hashed into m buckets each capable of holding a single key. Each key has k >= 3 (distinct) associated buckets chosen uniformly at random and independently of the choices of other keys. A hash table can be constructed successfully if each key can be placed into one of its buckets. We seek thresholds alpha_k such that, as n goes to infinity, if n/m <= alpha for some alpha < alpha_k then a hash table can be constructed successfully with high probability, and if n/m >= "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0287","kind":"arxiv","version":3},"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":"0912.0287","created_at":"2026-05-18T04:32:54.574844+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.0287v3","created_at":"2026-05-18T04:32:54.574844+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0287","created_at":"2026-05-18T04:32:54.574844+00:00"},{"alias_kind":"pith_short_12","alias_value":"IOGISJS3YKY4","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"IOGISJS3YKY4PNC5","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"IOGISJS3","created_at":"2026-05-18T12:26:00.592388+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/IOGISJS3YKY4PNC5UEB6PMZHX4","json":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4.json","graph_json":"https://pith.science/api/pith-number/IOGISJS3YKY4PNC5UEB6PMZHX4/graph.json","events_json":"https://pith.science/api/pith-number/IOGISJS3YKY4PNC5UEB6PMZHX4/events.json","paper":"https://pith.science/paper/IOGISJS3"},"agent_actions":{"view_html":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4","download_json":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4.json","view_paper":"https://pith.science/paper/IOGISJS3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.0287&json=true","fetch_graph":"https://pith.science/api/pith-number/IOGISJS3YKY4PNC5UEB6PMZHX4/graph.json","fetch_events":"https://pith.science/api/pith-number/IOGISJS3YKY4PNC5UEB6PMZHX4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4/action/storage_attestation","attest_author":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4/action/author_attestation","sign_citation":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4/action/citation_signature","submit_replication":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4/action/replication_record"}},"created_at":"2026-05-18T04:32:54.574844+00:00","updated_at":"2026-05-18T04:32:54.574844+00:00"}