{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PPGAS77CKDYDIXOIKM7UNFAGN7","short_pith_number":"pith:PPGAS77C","schema_version":"1.0","canonical_sha256":"7bcc097fe250f0345dc8533f4694066ff44a57923f590cb9dd4440c8b537d640","source":{"kind":"arxiv","id":"1706.02783","version":1},"attestation_state":"computed","paper":{"title":"Linear Hashing is Awesome","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mathias B{\\ae}k Tejs Knudsen","submitted_at":"2017-06-08T22:25:46Z","abstract_excerpt":"We consider the hash function $h(x) = ((ax+b) \\bmod p) \\bmod n$ where $a,b$ are chosen uniformly at random from $\\{0,1,\\ldots,p-1\\}$. We prove that when we use $h(x)$ in hashing with chaining to insert $n$ elements into a table of size $n$ the expected length of the longest chain is $\\tilde{O}\\!\\left(n^{1/3}\\right)$. The proof also generalises to give the same bound when we use the multiply-shift hash function by Dietzfelbinger et al. [Journal of Algorithms 1997]."},"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":"1706.02783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-06-08T22:25:46Z","cross_cats_sorted":[],"title_canon_sha256":"082d58bccbfe95d7714a5145da8f63c1e68d196bb9bdb3f7362b9d2be2a0a472","abstract_canon_sha256":"f799a88c9892229e25a8d61ba35d35b3395ef3051854e188848ec31c04900796"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:40.932078Z","signature_b64":"+grUrpThtWuFkpnIQA6hlUx2AYDqiNVpOe2znd1x1OP7GD5iMkReGnmnIRtmgdDtSIy3VeTYJDcHmxmzdmBKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bcc097fe250f0345dc8533f4694066ff44a57923f590cb9dd4440c8b537d640","last_reissued_at":"2026-05-18T00:42:40.931340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:40.931340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear Hashing is Awesome","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mathias B{\\ae}k Tejs Knudsen","submitted_at":"2017-06-08T22:25:46Z","abstract_excerpt":"We consider the hash function $h(x) = ((ax+b) \\bmod p) \\bmod n$ where $a,b$ are chosen uniformly at random from $\\{0,1,\\ldots,p-1\\}$. We prove that when we use $h(x)$ in hashing with chaining to insert $n$ elements into a table of size $n$ the expected length of the longest chain is $\\tilde{O}\\!\\left(n^{1/3}\\right)$. The proof also generalises to give the same bound when we use the multiply-shift hash function by Dietzfelbinger et al. [Journal of Algorithms 1997]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02783","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":"1706.02783","created_at":"2026-05-18T00:42:40.931463+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.02783v1","created_at":"2026-05-18T00:42:40.931463+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02783","created_at":"2026-05-18T00:42:40.931463+00:00"},{"alias_kind":"pith_short_12","alias_value":"PPGAS77CKDYD","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PPGAS77CKDYDIXOI","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PPGAS77C","created_at":"2026-05-18T12:31:37.085036+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/PPGAS77CKDYDIXOIKM7UNFAGN7","json":"https://pith.science/pith/PPGAS77CKDYDIXOIKM7UNFAGN7.json","graph_json":"https://pith.science/api/pith-number/PPGAS77CKDYDIXOIKM7UNFAGN7/graph.json","events_json":"https://pith.science/api/pith-number/PPGAS77CKDYDIXOIKM7UNFAGN7/events.json","paper":"https://pith.science/paper/PPGAS77C"},"agent_actions":{"view_html":"https://pith.science/pith/PPGAS77CKDYDIXOIKM7UNFAGN7","download_json":"https://pith.science/pith/PPGAS77CKDYDIXOIKM7UNFAGN7.json","view_paper":"https://pith.science/paper/PPGAS77C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.02783&json=true","fetch_graph":"https://pith.science/api/pith-number/PPGAS77CKDYDIXOIKM7UNFAGN7/graph.json","fetch_events":"https://pith.science/api/pith-number/PPGAS77CKDYDIXOIKM7UNFAGN7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PPGAS77CKDYDIXOIKM7UNFAGN7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PPGAS77CKDYDIXOIKM7UNFAGN7/action/storage_attestation","attest_author":"https://pith.science/pith/PPGAS77CKDYDIXOIKM7UNFAGN7/action/author_attestation","sign_citation":"https://pith.science/pith/PPGAS77CKDYDIXOIKM7UNFAGN7/action/citation_signature","submit_replication":"https://pith.science/pith/PPGAS77CKDYDIXOIKM7UNFAGN7/action/replication_record"}},"created_at":"2026-05-18T00:42:40.931463+00:00","updated_at":"2026-05-18T00:42:40.931463+00:00"}