{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TZMGVZRT3MLROIQ7F2Z6UGZFW5","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":"bc89924d650e891fba184ae577171f2b0d1c766a590b9910fa79359e2d5bfb82","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-07T14:15:22Z","title_canon_sha256":"bf15f131dd82c777a5630730ee089b14cded0bef45535dd2dace0b174d242aaf"},"schema_version":"1.0","source":{"id":"2607.06312","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06312","created_at":"2026-07-08T01:19:20Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06312v1","created_at":"2026-07-08T01:19:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06312","created_at":"2026-07-08T01:19:20Z"},{"alias_kind":"pith_short_12","alias_value":"TZMGVZRT3MLR","created_at":"2026-07-08T01:19:20Z"},{"alias_kind":"pith_short_16","alias_value":"TZMGVZRT3MLROIQ7","created_at":"2026-07-08T01:19:20Z"},{"alias_kind":"pith_short_8","alias_value":"TZMGVZRT","created_at":"2026-07-08T01:19:20Z"}],"graph_snapshots":[{"event_id":"sha256:e5df30e229d90a888b50ef28b5fe5af437dc19a2674a2b88158687f5900f5804","target":"graph","created_at":"2026-07-08T01:19:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.06312/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study adversarially robust algorithms for insertion-deletion (turnstile) streams, where future updates may depend on past algorithm outputs. While recent work achieved a robust $(1+\\epsilon)$-approximation for the second moment $F_2$ in polylogarithmic space, achieving high accuracy for other frequency moments remained a major open question; for $p\\in[0,2)$, including the fundamental distinct elements problem ($F_0$), only constant-factor approximations were known in sublinear space. We close this gap, showing that $(1+\\epsilon)$-approximate robustness can be achieved in polylogarithmic spa","authors_text":"David P. Woodruff, Elena Gribelyuk, Honghao Lin, Huacheng Yu, Samson Zhou","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-07T14:15:22Z","title":"Adversarial Robustness for Small Frequency Moments and a Weak Equivalence Theorem for Turnstile Streams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06312","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":"sha256:98c5e09ccf140a7848f38cfb4c6804916d8d343facf6ffa88d4cc730dc9c9ce2","target":"record","created_at":"2026-07-08T01:19:20Z","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":"bc89924d650e891fba184ae577171f2b0d1c766a590b9910fa79359e2d5bfb82","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-07T14:15:22Z","title_canon_sha256":"bf15f131dd82c777a5630730ee089b14cded0bef45535dd2dace0b174d242aaf"},"schema_version":"1.0","source":{"id":"2607.06312","kind":"arxiv","version":1}},"canonical_sha256":"9e586ae633db1717221f2eb3ea1b25b77fb00ab5fa9f60d51ce6565f3958af30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e586ae633db1717221f2eb3ea1b25b77fb00ab5fa9f60d51ce6565f3958af30","first_computed_at":"2026-07-08T01:19:20.808399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-08T01:19:20.808399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MyFr2yBWbLq+mfZtweYQd7a5OgT0RUj0eYOMsb/NgRo++nstsuw3Y9Vs04dJa1W8OnQs0kAIPEVUGyvIDc4LAA==","signature_status":"signed_v1","signed_at":"2026-07-08T01:19:20.808834Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98c5e09ccf140a7848f38cfb4c6804916d8d343facf6ffa88d4cc730dc9c9ce2","sha256:e5df30e229d90a888b50ef28b5fe5af437dc19a2674a2b88158687f5900f5804"],"state_sha256":"c165800edb8460ddcdc6cc03ba4bfba1fed8a10cfc96f70f0045bd4537bb40d1"}