{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JQ4O2XL7SGTLEGLJ7BF3M7EWR3","short_pith_number":"pith:JQ4O2XL7","schema_version":"1.0","canonical_sha256":"4c38ed5d7f91a6b21969f84bb67c968efc4736339a6126174ab46272ce33eb23","source":{"kind":"arxiv","id":"1408.5096","version":2},"attestation_state":"computed","paper":{"title":"Universal sketches for the frequency negative moments and other decreasing streaming sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Stephen R. Chestnut, Vladimir Braverman","submitted_at":"2014-08-21T18:24:10Z","abstract_excerpt":"Given a stream with frequencies $f_d$, for $d\\in[n]$, we characterize the space necessary for approximating the frequency negative moments $F_p=\\sum |f_d|^p$, where $p<0$ and the sum is taken over all items $d\\in[n]$ with nonzero frequency, in terms of $n$, $\\epsilon$, and $m=\\sum |f_d|$. To accomplish this, we actually prove a much more general result. Given any nonnegative and nonincreasing function $g$, we characterize the space necessary for any streaming algorithm that outputs a $(1\\pm\\epsilon)$-approximation to $\\sum g(|f_d|)$, where again the sum is over items with nonzero frequency. Th"},"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":"1408.5096","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-08-21T18:24:10Z","cross_cats_sorted":[],"title_canon_sha256":"c86c4bbd5dc0f23e860dec0a533789bc1848065e95b9b1cd8892146e2a28a970","abstract_canon_sha256":"ca557471753fd1615f51479d6ba1554f4723d22b52aa27a6cc48a2f7311ea113"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:05.298429Z","signature_b64":"BZOiAA6qm8B2guq+HYQ7GIbpE8HrJbwhpp/nhgsdgHOXmuMs8KCfV+16NVbYMDh1fdKFNMck38Pg2rTreuPICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c38ed5d7f91a6b21969f84bb67c968efc4736339a6126174ab46272ce33eb23","last_reissued_at":"2026-05-18T02:27:05.298063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:05.298063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal sketches for the frequency negative moments and other decreasing streaming sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Stephen R. Chestnut, Vladimir Braverman","submitted_at":"2014-08-21T18:24:10Z","abstract_excerpt":"Given a stream with frequencies $f_d$, for $d\\in[n]$, we characterize the space necessary for approximating the frequency negative moments $F_p=\\sum |f_d|^p$, where $p<0$ and the sum is taken over all items $d\\in[n]$ with nonzero frequency, in terms of $n$, $\\epsilon$, and $m=\\sum |f_d|$. To accomplish this, we actually prove a much more general result. Given any nonnegative and nonincreasing function $g$, we characterize the space necessary for any streaming algorithm that outputs a $(1\\pm\\epsilon)$-approximation to $\\sum g(|f_d|)$, where again the sum is over items with nonzero frequency. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5096","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.5096","created_at":"2026-05-18T02:27:05.298124+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.5096v2","created_at":"2026-05-18T02:27:05.298124+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5096","created_at":"2026-05-18T02:27:05.298124+00:00"},{"alias_kind":"pith_short_12","alias_value":"JQ4O2XL7SGTL","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"JQ4O2XL7SGTLEGLJ","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"JQ4O2XL7","created_at":"2026-05-18T12:28:35.611951+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/JQ4O2XL7SGTLEGLJ7BF3M7EWR3","json":"https://pith.science/pith/JQ4O2XL7SGTLEGLJ7BF3M7EWR3.json","graph_json":"https://pith.science/api/pith-number/JQ4O2XL7SGTLEGLJ7BF3M7EWR3/graph.json","events_json":"https://pith.science/api/pith-number/JQ4O2XL7SGTLEGLJ7BF3M7EWR3/events.json","paper":"https://pith.science/paper/JQ4O2XL7"},"agent_actions":{"view_html":"https://pith.science/pith/JQ4O2XL7SGTLEGLJ7BF3M7EWR3","download_json":"https://pith.science/pith/JQ4O2XL7SGTLEGLJ7BF3M7EWR3.json","view_paper":"https://pith.science/paper/JQ4O2XL7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.5096&json=true","fetch_graph":"https://pith.science/api/pith-number/JQ4O2XL7SGTLEGLJ7BF3M7EWR3/graph.json","fetch_events":"https://pith.science/api/pith-number/JQ4O2XL7SGTLEGLJ7BF3M7EWR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JQ4O2XL7SGTLEGLJ7BF3M7EWR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JQ4O2XL7SGTLEGLJ7BF3M7EWR3/action/storage_attestation","attest_author":"https://pith.science/pith/JQ4O2XL7SGTLEGLJ7BF3M7EWR3/action/author_attestation","sign_citation":"https://pith.science/pith/JQ4O2XL7SGTLEGLJ7BF3M7EWR3/action/citation_signature","submit_replication":"https://pith.science/pith/JQ4O2XL7SGTLEGLJ7BF3M7EWR3/action/replication_record"}},"created_at":"2026-05-18T02:27:05.298124+00:00","updated_at":"2026-05-18T02:27:05.298124+00:00"}