{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HFFJPFLFJE5Z7DNYLE7WFOHDML","short_pith_number":"pith:HFFJPFLF","canonical_record":{"source":{"id":"1404.6724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-27T07:59:38Z","cross_cats_sorted":[],"title_canon_sha256":"42f30edd1018e6e442c0a8100584823164e18b22a476012983a95df49315b8ce","abstract_canon_sha256":"0e039d0a4c4a307aebe2fb83f365ff23ee4a6d3857c7dec7bd8ca94ad11c049a"},"schema_version":"1.0"},"canonical_sha256":"394a979565493b9f8db8593f62b8e362e3efc5a1b068b4396a31280958223e5c","source":{"kind":"arxiv","id":"1404.6724","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6724","created_at":"2026-05-18T02:52:49Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6724v2","created_at":"2026-05-18T02:52:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6724","created_at":"2026-05-18T02:52:49Z"},{"alias_kind":"pith_short_12","alias_value":"HFFJPFLFJE5Z","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HFFJPFLFJE5Z7DNY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HFFJPFLF","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HFFJPFLFJE5Z7DNYLE7WFOHDML","target":"record","payload":{"canonical_record":{"source":{"id":"1404.6724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-27T07:59:38Z","cross_cats_sorted":[],"title_canon_sha256":"42f30edd1018e6e442c0a8100584823164e18b22a476012983a95df49315b8ce","abstract_canon_sha256":"0e039d0a4c4a307aebe2fb83f365ff23ee4a6d3857c7dec7bd8ca94ad11c049a"},"schema_version":"1.0"},"canonical_sha256":"394a979565493b9f8db8593f62b8e362e3efc5a1b068b4396a31280958223e5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:49.191539Z","signature_b64":"lDKnDhz1vEWM6DiRI3pKFbF/6FPxtgqjh7PK7ye5qqrAVNefiDoS9rnwh9iLuSEbh4B7PMc11fWI97afSsxIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"394a979565493b9f8db8593f62b8e362e3efc5a1b068b4396a31280958223e5c","last_reissued_at":"2026-05-18T02:52:49.191141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:49.191141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.6724","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":"2026-05-18T02:52:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/v2xHGLFvs1m66J7mUCPtDv/QvW7kBcLHzOOzAnp8KaiYfwlwgoFmPF1E3RNBh7/Xrz8T0mnjDrEduJ2uXJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:54:10.385825Z"},"content_sha256":"e4e31ea8d47d606d21a7154f1d0ae63e03b46c20e28905dcfc06fc2bf3b7e062","schema_version":"1.0","event_id":"sha256:e4e31ea8d47d606d21a7154f1d0ae63e03b46c20e28905dcfc06fc2bf3b7e062"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HFFJPFLFJE5Z7DNYLE7WFOHDML","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximately Minwise Independence with Twisted Tabulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mikkel Thorup, S{\\o}ren Dahlgaard","submitted_at":"2014-04-27T07:59:38Z","abstract_excerpt":"A random hash function $h$ is $\\varepsilon$-minwise if for any set $S$, $|S|=n$, and element $x\\in S$, $\\Pr[h(x)=\\min h(S)]=(1\\pm\\varepsilon)/n$. Minwise hash functions with low bias $\\varepsilon$ have widespread applications within similarity estimation.\n  Hashing from a universe $[u]$, the twisted tabulation hashing of P\\v{a}tra\\c{s}cu and Thorup [SODA'13] makes $c=O(1)$ lookups in tables of size $u^{1/c}$. Twisted tabulation was invented to get good concentration for hashing based sampling. Here we show that twisted tabulation yields $\\tilde O(1/u^{1/c})$-minwise hashing.\n  In the classic i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6724","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":"2026-05-18T02:52:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ua+zXh+pbPLkAXjyc7CRvjnxqgDylLJywUVtbqiRwXC5wFuH/1Liethyz2UGjQ2c/amgaikf3K5xaPZbftOCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:54:10.386214Z"},"content_sha256":"14319386312c692f78f0edfe7e81c880649d40abec324ed14ae1d8df8e91b787","schema_version":"1.0","event_id":"sha256:14319386312c692f78f0edfe7e81c880649d40abec324ed14ae1d8df8e91b787"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HFFJPFLFJE5Z7DNYLE7WFOHDML/bundle.json","state_url":"https://pith.science/pith/HFFJPFLFJE5Z7DNYLE7WFOHDML/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HFFJPFLFJE5Z7DNYLE7WFOHDML/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":"2026-05-30T06:54:10Z","links":{"resolver":"https://pith.science/pith/HFFJPFLFJE5Z7DNYLE7WFOHDML","bundle":"https://pith.science/pith/HFFJPFLFJE5Z7DNYLE7WFOHDML/bundle.json","state":"https://pith.science/pith/HFFJPFLFJE5Z7DNYLE7WFOHDML/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HFFJPFLFJE5Z7DNYLE7WFOHDML/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HFFJPFLFJE5Z7DNYLE7WFOHDML","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":"0e039d0a4c4a307aebe2fb83f365ff23ee4a6d3857c7dec7bd8ca94ad11c049a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-27T07:59:38Z","title_canon_sha256":"42f30edd1018e6e442c0a8100584823164e18b22a476012983a95df49315b8ce"},"schema_version":"1.0","source":{"id":"1404.6724","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6724","created_at":"2026-05-18T02:52:49Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6724v2","created_at":"2026-05-18T02:52:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6724","created_at":"2026-05-18T02:52:49Z"},{"alias_kind":"pith_short_12","alias_value":"HFFJPFLFJE5Z","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HFFJPFLFJE5Z7DNY","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HFFJPFLF","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:14319386312c692f78f0edfe7e81c880649d40abec324ed14ae1d8df8e91b787","target":"graph","created_at":"2026-05-18T02:52:49Z","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":"A random hash function $h$ is $\\varepsilon$-minwise if for any set $S$, $|S|=n$, and element $x\\in S$, $\\Pr[h(x)=\\min h(S)]=(1\\pm\\varepsilon)/n$. Minwise hash functions with low bias $\\varepsilon$ have widespread applications within similarity estimation.\n  Hashing from a universe $[u]$, the twisted tabulation hashing of P\\v{a}tra\\c{s}cu and Thorup [SODA'13] makes $c=O(1)$ lookups in tables of size $u^{1/c}$. Twisted tabulation was invented to get good concentration for hashing based sampling. Here we show that twisted tabulation yields $\\tilde O(1/u^{1/c})$-minwise hashing.\n  In the classic i","authors_text":"Mikkel Thorup, S{\\o}ren Dahlgaard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-27T07:59:38Z","title":"Approximately Minwise Independence with Twisted Tabulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6724","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:e4e31ea8d47d606d21a7154f1d0ae63e03b46c20e28905dcfc06fc2bf3b7e062","target":"record","created_at":"2026-05-18T02:52:49Z","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":"0e039d0a4c4a307aebe2fb83f365ff23ee4a6d3857c7dec7bd8ca94ad11c049a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-27T07:59:38Z","title_canon_sha256":"42f30edd1018e6e442c0a8100584823164e18b22a476012983a95df49315b8ce"},"schema_version":"1.0","source":{"id":"1404.6724","kind":"arxiv","version":2}},"canonical_sha256":"394a979565493b9f8db8593f62b8e362e3efc5a1b068b4396a31280958223e5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"394a979565493b9f8db8593f62b8e362e3efc5a1b068b4396a31280958223e5c","first_computed_at":"2026-05-18T02:52:49.191141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:49.191141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lDKnDhz1vEWM6DiRI3pKFbF/6FPxtgqjh7PK7ye5qqrAVNefiDoS9rnwh9iLuSEbh4B7PMc11fWI97afSsxIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:49.191539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6724","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4e31ea8d47d606d21a7154f1d0ae63e03b46c20e28905dcfc06fc2bf3b7e062","sha256:14319386312c692f78f0edfe7e81c880649d40abec324ed14ae1d8df8e91b787"],"state_sha256":"af5b6be969e476445d36207c9d0a45ff88b52d04b76f03d011d5f7ad48a7a1b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HuUpsxCbrfKDNVO3Ma8DGgaR7brjq00Yx+/0aj4aq/FNPZwsrT5aaCz4fT56TnFf8JKXynoBnBsUSkB1RxKCDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:54:10.388361Z","bundle_sha256":"c19f43101b2b529143c34e72a5bcee063884b7a855a041f1d5cea84a9a022b6e"}}