{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:IOGISJS3YKY4PNC5UEB6PMZHX4","short_pith_number":"pith:IOGISJS3","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"},"canonical_sha256":"438c89265bc2b1c7b45da103e7b327bf0e9b6835fa90178fdfe6f85b67d6c47a","source":{"kind":"arxiv","id":"0912.0287","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0287","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0287v3","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0287","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"IOGISJS3YKY4","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"IOGISJS3YKY4PNC5","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"IOGISJS3","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:IOGISJS3YKY4PNC5UEB6PMZHX4","target":"record","payload":{"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"},"canonical_sha256":"438c89265bc2b1c7b45da103e7b327bf0e9b6835fa90178fdfe6f85b67d6c47a","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"},"source_kind":"arxiv","source_id":"0912.0287","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yFNjSphYrC+BF1JVuT+aDJAgjw3+Ww++2RkZEsJLMg49yaOTTXV8GGLE/3yoUIOfQJ3RDMGucAx9xn4rolZrAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:30:41.411533Z"},"content_sha256":"945549f833bfadc22d4990f5a39e8c510720f4000fc195d666559c9a52da297b","schema_version":"1.0","event_id":"sha256:945549f833bfadc22d4990f5a39e8c510720f4000fc195d666559c9a52da297b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:IOGISJS3YKY4PNC5UEB6PMZHX4","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LSLr2Hb6xLhASb6Uv76mHZ4mFHs3IVjY5jTL193N2LyeSblpvP5uUVSFn57nDd8oEYeidx+j2KSIf5yQVwK1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:30:41.411872Z"},"content_sha256":"96dcd932b84b75e2c5c297523c1568b9314f2a5105130d522d803a89245fea53","schema_version":"1.0","event_id":"sha256:96dcd932b84b75e2c5c297523c1568b9314f2a5105130d522d803a89245fea53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4/bundle.json","state_url":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOGISJS3YKY4PNC5UEB6PMZHX4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T22:30:41Z","links":{"resolver":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4","bundle":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4/bundle.json","state":"https://pith.science/pith/IOGISJS3YKY4PNC5UEB6PMZHX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOGISJS3YKY4PNC5UEB6PMZHX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:IOGISJS3YKY4PNC5UEB6PMZHX4","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":"fa679d767e9200d089a79fcefdac967e20b43d6f244ceba197a48c10c229506f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-12-01T22:23:48Z","title_canon_sha256":"230aac83c47864bc97a34d242f766943b8fc757770da212530eb14b5e0ab2473"},"schema_version":"1.0","source":{"id":"0912.0287","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0287","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0287v3","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0287","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"IOGISJS3YKY4","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"IOGISJS3YKY4PNC5","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"IOGISJS3","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:96dcd932b84b75e2c5c297523c1568b9314f2a5105130d522d803a89245fea53","target":"graph","created_at":"2026-05-18T04:32:54Z","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":"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 >= ","authors_text":"Andrea Montanari, Andreas Goerdt, Martin Dietzfelbinger, Michael Mitzenmacher, Michael Rink, Rasmus Pagh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-12-01T22:23:48Z","title":"Tight Thresholds for Cuckoo Hashing via XORSAT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0287","kind":"arxiv","version":3},"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":"sha256:945549f833bfadc22d4990f5a39e8c510720f4000fc195d666559c9a52da297b","target":"record","created_at":"2026-05-18T04:32:54Z","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":"fa679d767e9200d089a79fcefdac967e20b43d6f244ceba197a48c10c229506f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-12-01T22:23:48Z","title_canon_sha256":"230aac83c47864bc97a34d242f766943b8fc757770da212530eb14b5e0ab2473"},"schema_version":"1.0","source":{"id":"0912.0287","kind":"arxiv","version":3}},"canonical_sha256":"438c89265bc2b1c7b45da103e7b327bf0e9b6835fa90178fdfe6f85b67d6c47a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"438c89265bc2b1c7b45da103e7b327bf0e9b6835fa90178fdfe6f85b67d6c47a","first_computed_at":"2026-05-18T04:32:54.574735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:54.574735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XU3rqFFgsuISnksNYSVwnCy60aLRJUAySxvd5GQncb44+bC15Lg+/5y6cFSWFZrtYL0VEVpTovBdd6VlJCSRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:54.575383Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0287","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:945549f833bfadc22d4990f5a39e8c510720f4000fc195d666559c9a52da297b","sha256:96dcd932b84b75e2c5c297523c1568b9314f2a5105130d522d803a89245fea53"],"state_sha256":"839326145fcdeaf9e52110908ebdca5066e6afb6fbc01903046563a76752b27d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tSfsyw3dpL626ViZN+Rg6GNc6h6iYKuKVrHr2OjpxCydpZlsM/ulzaXavPsIQpGUAI/aHKJ+IlLKR/ppyBDPAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:30:41.413807Z","bundle_sha256":"0d912822432ae84c7224a3d194e237b638c0c51e252ce755de1fc95decb8cbb7"}}