{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3HBFD3GX6PZGVP3LC2QZ2BHZNO","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":"9b8ef1bcb6bd6759eeeac56270fe7e0d60d63bda9c481668f3dfdc41c4ff3d28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-09-24T17:12:11Z","title_canon_sha256":"f2e23b27b0e77fc5621a8ebabf08dc0bf9a9cef7825f7362205e781eb1b151b0"},"schema_version":"1.0","source":{"id":"1809.09063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09063","created_at":"2026-05-18T00:05:01Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09063v1","created_at":"2026-05-18T00:05:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09063","created_at":"2026-05-18T00:05:01Z"},{"alias_kind":"pith_short_12","alias_value":"3HBFD3GX6PZG","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3HBFD3GX6PZGVP3L","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3HBFD3GX","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:cedac878f336150d85adaaff126ea7d360d187b0a3f79b014c596a0e8d9df55c","target":"graph","created_at":"2026-05-18T00:05:01Z","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":"We study the relation between streaming algorithms and linear sketching algorithms, in the context of binary updates. We show that for inputs in $n$ dimensions, the existence of efficient streaming algorithms which can process $\\Omega(n^2)$ updates implies efficient linear sketching algorithms with comparable cost. This improves upon the previous work of Li, Nguyen and Woodruff [LNW14] and Ai, Hu, Li and Woodruff [AHLW16] which required a triple-exponential number of updates to achieve a similar result for updates over integers. We extend our results to updates modulo $p$ for integers $p \\ge 2","authors_text":"Grigory Yaroslavtsev, Kaave Hosseini, Shachar Lovett","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-09-24T17:12:11Z","title":"Optimality of Linear Sketching under Modular Updates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09063","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:cb0aedf46e0be2c07f7ce65b2182382b13caaada96027b53a5736d6cc84c5269","target":"record","created_at":"2026-05-18T00:05:01Z","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":"9b8ef1bcb6bd6759eeeac56270fe7e0d60d63bda9c481668f3dfdc41c4ff3d28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-09-24T17:12:11Z","title_canon_sha256":"f2e23b27b0e77fc5621a8ebabf08dc0bf9a9cef7825f7362205e781eb1b151b0"},"schema_version":"1.0","source":{"id":"1809.09063","kind":"arxiv","version":1}},"canonical_sha256":"d9c251ecd7f3f26abf6b16a19d04f96b9c2e9182b3ad90b543df129a7caec55a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9c251ecd7f3f26abf6b16a19d04f96b9c2e9182b3ad90b543df129a7caec55a","first_computed_at":"2026-05-18T00:05:01.211091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:01.211091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qef2OV/YXVSN90sqRRdc1qrfomAsKeGxvaEQdBuQ//7R8AYw8+gHXiUh2Jl+gD5N0BzuWNoSWAarktEKFB6gCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:01.211716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb0aedf46e0be2c07f7ce65b2182382b13caaada96027b53a5736d6cc84c5269","sha256:cedac878f336150d85adaaff126ea7d360d187b0a3f79b014c596a0e8d9df55c"],"state_sha256":"bbdddae761b3a9adaa831db89843d8ad3e1aba6b4f7f4865ddfd94df0cc398cf"}