{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:T6XSQKSCCDMHSABQBFH27C65FB","short_pith_number":"pith:T6XSQKSC","canonical_record":{"source":{"id":"0901.1155","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-01-09T00:23:33Z","cross_cats_sorted":["cs.DM","math.PR"],"title_canon_sha256":"c86abb126cc8852b208f61f88ed47935fbc2fd172ea8be3161526918623496fb","abstract_canon_sha256":"bf1496e08972dd6cfa0375664642c7db12688a73e1b68aee46d2dbe2407e06bf"},"schema_version":"1.0"},"canonical_sha256":"9faf282a4210d8790030094faf8bdd285a172cdb5e19c4a20118e0b30f2e1ad2","source":{"kind":"arxiv","id":"0901.1155","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1155","created_at":"2026-05-18T03:45:51Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1155v2","created_at":"2026-05-18T03:45:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1155","created_at":"2026-05-18T03:45:51Z"},{"alias_kind":"pith_short_12","alias_value":"T6XSQKSCCDMH","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"T6XSQKSCCDMHSABQ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"T6XSQKSC","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:T6XSQKSCCDMHSABQBFH27C65FB","target":"record","payload":{"canonical_record":{"source":{"id":"0901.1155","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-01-09T00:23:33Z","cross_cats_sorted":["cs.DM","math.PR"],"title_canon_sha256":"c86abb126cc8852b208f61f88ed47935fbc2fd172ea8be3161526918623496fb","abstract_canon_sha256":"bf1496e08972dd6cfa0375664642c7db12688a73e1b68aee46d2dbe2407e06bf"},"schema_version":"1.0"},"canonical_sha256":"9faf282a4210d8790030094faf8bdd285a172cdb5e19c4a20118e0b30f2e1ad2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:51.936697Z","signature_b64":"+SOrEMYWeJCoJ+bHBe3waT2p29LBtuNHyMr+AMRT6ap6L4DzSaYoQyCF6AqwQAosrX6djhptCwF5hSJtGsTgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9faf282a4210d8790030094faf8bdd285a172cdb5e19c4a20118e0b30f2e1ad2","last_reissued_at":"2026-05-18T03:45:51.935613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:51.935613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.1155","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V0e6FMGrqPcNDBmU3qytxB2qrs7PxgEZdutPDmk8FiNJLMilpxI5/+KlTCb+2TJbhnFNhgo7RnFOE7Xrc0UuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:32:49.636962Z"},"content_sha256":"140ec8d236ff9557201a69d6b6d064d20727fa40016d6f4299a28ede3fa8f70a","schema_version":"1.0","event_id":"sha256:140ec8d236ff9557201a69d6b6d064d20727fa40016d6f4299a28ede3fa8f70a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:T6XSQKSCCDMHSABQBFH27C65FB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Balanced allocation: Memory performance tradeoffs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"cs.DS","authors_text":"Itai Benjamini, Yury Makarychev","submitted_at":"2009-01-09T00:23:33Z","abstract_excerpt":"Suppose we sequentially put $n$ balls into $n$ bins. If we put each ball into a random bin then the heaviest bin will contain ${\\sim}\\log n/\\log\\log n$ balls with high probability. However, Azar, Broder, Karlin and Upfal [SIAM J. Comput. 29 (1999) 180--200] showed that if each time we choose two bins at random and put the ball in the least loaded bin among the two, then the heaviest bin will contain only ${\\sim}\\log\\log n$ balls with high probability. How much memory do we need to implement this scheme? We need roughly $\\log\\log\\log n$ bits per bin, and $n\\log\\log\\log n$ bits in total. Let us "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1155","kind":"arxiv","version":2},"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":"2026-05-18T03:45:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dz2mfveNWP4k5BmbZBiSCBl0GBRqDF5A6G2xGXPmfv2ydHcsATSn4X4PmA/h6F1cbjWv+hoMReJcs5tmkIv3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:32:49.637702Z"},"content_sha256":"fe174e59e5406aede0d68c5791b54fbdc25f3aa2f5ada6933f851673771ef70a","schema_version":"1.0","event_id":"sha256:fe174e59e5406aede0d68c5791b54fbdc25f3aa2f5ada6933f851673771ef70a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T6XSQKSCCDMHSABQBFH27C65FB/bundle.json","state_url":"https://pith.science/pith/T6XSQKSCCDMHSABQBFH27C65FB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T6XSQKSCCDMHSABQBFH27C65FB/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":"2026-05-26T00:32:49Z","links":{"resolver":"https://pith.science/pith/T6XSQKSCCDMHSABQBFH27C65FB","bundle":"https://pith.science/pith/T6XSQKSCCDMHSABQBFH27C65FB/bundle.json","state":"https://pith.science/pith/T6XSQKSCCDMHSABQBFH27C65FB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T6XSQKSCCDMHSABQBFH27C65FB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:T6XSQKSCCDMHSABQBFH27C65FB","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":"bf1496e08972dd6cfa0375664642c7db12688a73e1b68aee46d2dbe2407e06bf","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-01-09T00:23:33Z","title_canon_sha256":"c86abb126cc8852b208f61f88ed47935fbc2fd172ea8be3161526918623496fb"},"schema_version":"1.0","source":{"id":"0901.1155","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1155","created_at":"2026-05-18T03:45:51Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1155v2","created_at":"2026-05-18T03:45:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1155","created_at":"2026-05-18T03:45:51Z"},{"alias_kind":"pith_short_12","alias_value":"T6XSQKSCCDMH","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"T6XSQKSCCDMHSABQ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"T6XSQKSC","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:fe174e59e5406aede0d68c5791b54fbdc25f3aa2f5ada6933f851673771ef70a","target":"graph","created_at":"2026-05-18T03:45:51Z","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":"Suppose we sequentially put $n$ balls into $n$ bins. If we put each ball into a random bin then the heaviest bin will contain ${\\sim}\\log n/\\log\\log n$ balls with high probability. However, Azar, Broder, Karlin and Upfal [SIAM J. Comput. 29 (1999) 180--200] showed that if each time we choose two bins at random and put the ball in the least loaded bin among the two, then the heaviest bin will contain only ${\\sim}\\log\\log n$ balls with high probability. How much memory do we need to implement this scheme? We need roughly $\\log\\log\\log n$ bits per bin, and $n\\log\\log\\log n$ bits in total. Let us ","authors_text":"Itai Benjamini, Yury Makarychev","cross_cats":["cs.DM","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-01-09T00:23:33Z","title":"Balanced allocation: Memory performance tradeoffs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1155","kind":"arxiv","version":2},"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":"sha256:140ec8d236ff9557201a69d6b6d064d20727fa40016d6f4299a28ede3fa8f70a","target":"record","created_at":"2026-05-18T03:45:51Z","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":"bf1496e08972dd6cfa0375664642c7db12688a73e1b68aee46d2dbe2407e06bf","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2009-01-09T00:23:33Z","title_canon_sha256":"c86abb126cc8852b208f61f88ed47935fbc2fd172ea8be3161526918623496fb"},"schema_version":"1.0","source":{"id":"0901.1155","kind":"arxiv","version":2}},"canonical_sha256":"9faf282a4210d8790030094faf8bdd285a172cdb5e19c4a20118e0b30f2e1ad2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9faf282a4210d8790030094faf8bdd285a172cdb5e19c4a20118e0b30f2e1ad2","first_computed_at":"2026-05-18T03:45:51.935613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:51.935613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+SOrEMYWeJCoJ+bHBe3waT2p29LBtuNHyMr+AMRT6ap6L4DzSaYoQyCF6AqwQAosrX6djhptCwF5hSJtGsTgCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:51.936697Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.1155","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:140ec8d236ff9557201a69d6b6d064d20727fa40016d6f4299a28ede3fa8f70a","sha256:fe174e59e5406aede0d68c5791b54fbdc25f3aa2f5ada6933f851673771ef70a"],"state_sha256":"f70d6fa07ed7b01441e9323698ce645a0b0d37c6b21c4d576bba7be0a586648d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"92ZNDy0RvaIUf4EIIFHgFcSGJ/IqCNrBkox4h3PKdMvsgMSCW7y1KF/DxmcwCNtHEz5hsP3NMBNtdUZdy8YQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:32:49.641450Z","bundle_sha256":"2a92b8a699ad165975ee021421b5bd5ca2aa57ce3597635e7007debbad61f80c"}}