{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BCAOOVTN7QHSZH33XIM7FGIBDZ","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":"4f3ba4e0e8441afd8a425d2a2af76d40712fe2cb6caeee04f3900643659b660f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-25T17:23:48Z","title_canon_sha256":"951e4fce2092958226ec3d6c1e1e20356acb23a8cafd4434654b8c59fd68b83b"},"schema_version":"1.0","source":{"id":"1804.09684","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09684","created_at":"2026-05-18T00:17:31Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09684v1","created_at":"2026-05-18T00:17:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09684","created_at":"2026-05-18T00:17:31Z"},{"alias_kind":"pith_short_12","alias_value":"BCAOOVTN7QHS","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"BCAOOVTN7QHSZH33","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"BCAOOVTN","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:0bd4d93e32621d05d625c16aca8e0161a0ba062d690f4d12939631286b831e5f","target":"graph","created_at":"2026-05-18T00:17:31Z","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 that we are to place $m$ balls into $n$ bins sequentially using the $d$-choice paradigm: For each ball we are given a choice of $d$ bins, according to $d$ hash functions $h_1,\\dots,h_d$ and we place the ball in the least loaded of these bins breaking ties arbitrarily. Our interest is in the number of balls in the fullest bin after all $m$ balls have been placed.\n  Azar et al. [STOC'94] proved that when $m=O(n)$ and when the hash functions are fully random the maximum load is at most $\\frac{\\lg \\lg n }{\\lg d}+O(1)$ whp (i.e. with probability $1-O(n^{-\\gamma})$ for any choice of $\\gamma$","authors_text":"Anders Aamand, Mathias B{\\ae}k Tejs Knudsen, Mikkel Thorup","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-25T17:23:48Z","title":"Power of $d$ Choices with Simple Tabulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09684","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:dfdace272e380a78b48401f75b7bc062b3827508a9ed80443510406abecddddd","target":"record","created_at":"2026-05-18T00:17:31Z","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":"4f3ba4e0e8441afd8a425d2a2af76d40712fe2cb6caeee04f3900643659b660f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-04-25T17:23:48Z","title_canon_sha256":"951e4fce2092958226ec3d6c1e1e20356acb23a8cafd4434654b8c59fd68b83b"},"schema_version":"1.0","source":{"id":"1804.09684","kind":"arxiv","version":1}},"canonical_sha256":"0880e7566dfc0f2c9f7bba19f299011e46c6c08b3be212a3f2fab7643ccc6144","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0880e7566dfc0f2c9f7bba19f299011e46c6c08b3be212a3f2fab7643ccc6144","first_computed_at":"2026-05-18T00:17:31.077456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:31.077456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v5jbPR5c8wFwbJt71CWiHrLqDljUV6TfNESathrXB8GCQ/VZUR7oY0AIEhTxSBPp8axd+AxSgTM16Ah7p9ZIBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:31.078169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09684","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfdace272e380a78b48401f75b7bc062b3827508a9ed80443510406abecddddd","sha256:0bd4d93e32621d05d625c16aca8e0161a0ba062d690f4d12939631286b831e5f"],"state_sha256":"de7820f00dd9eebcf6d9251652df13e83b977c8e9e224a1db7a7162ee9a47486"}