{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XWRALHKAM3LS5BK4YOPEBP3VVP","short_pith_number":"pith:XWRALHKA","canonical_record":{"source":{"id":"1012.3130","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-12-14T18:52:58Z","cross_cats_sorted":[],"title_canon_sha256":"c9e33d83ae566b42cd44c65dab2b1397ef7156310b0c42396f34799a4f7da57f","abstract_canon_sha256":"350f66f419caf59f079cfd647d4091087fed04430d8b705e6991c89d900ac1f0"},"schema_version":"1.0"},"canonical_sha256":"bda2059d4066d72e855cc39e40bf75abc45897de8247d1eb55230ff79b224461","source":{"kind":"arxiv","id":"1012.3130","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3130","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3130v3","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3130","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"XWRALHKAM3LS","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XWRALHKAM3LS5BK4","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XWRALHKA","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XWRALHKAM3LS5BK4YOPEBP3VVP","target":"record","payload":{"canonical_record":{"source":{"id":"1012.3130","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-12-14T18:52:58Z","cross_cats_sorted":[],"title_canon_sha256":"c9e33d83ae566b42cd44c65dab2b1397ef7156310b0c42396f34799a4f7da57f","abstract_canon_sha256":"350f66f419caf59f079cfd647d4091087fed04430d8b705e6991c89d900ac1f0"},"schema_version":"1.0"},"canonical_sha256":"bda2059d4066d72e855cc39e40bf75abc45897de8247d1eb55230ff79b224461","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:31.743826Z","signature_b64":"SLBgE14YI4sAMEfz5pq99CqqPBRpT0kLgx9+zcEYK6vfOGsilKZxvCOUNgWJ8UZele8mBd58B+vtgnhSAs3+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bda2059d4066d72e855cc39e40bf75abc45897de8247d1eb55230ff79b224461","last_reissued_at":"2026-05-18T02:46:31.743451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:31.743451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.3130","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o4SGbiuJhGGNNZLKmgSDevhrQcCvuLkPLFasRuAem1HVbIID/In3IQx4d/DUsik1/xdNxhygoTt2Chry60RFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:33:16.850953Z"},"content_sha256":"3912a315daa00b0d66a65d23c05dea77e71e19cc0bd057570e4ffab7851b9e2b","schema_version":"1.0","event_id":"sha256:3912a315daa00b0d66a65d23c05dea77e71e19cc0bd057570e4ffab7851b9e2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XWRALHKAM3LS5BK4YOPEBP3VVP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How to Catch L_2-Heavy-Hitters on Sliding Windows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Rafail Ostrovsky, Ran Gelles, Vladimir Braverman","submitted_at":"2010-12-14T18:52:58Z","abstract_excerpt":"Finding heavy-elements (heavy-hitters) in streaming data is one of the central, and well-understood tasks. Despite the importance of this problem, when considering the sliding windows model of streaming (where elements eventually expire) the problem of finding L_2-heavy elements has remained completely open despite multiple papers and considerable success in finding L_1-heavy elements.\n  In this paper, we develop the first poly-logarithmic-memory algorithm for finding L_2-heavy elements in sliding window model. Since L_2 heavy elements play a central role for many fundamental streaming problem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3130","kind":"arxiv","version":3},"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":"2026-05-18T02:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"neRhXDCVwkXcOc817S/gJnVtDWl5mk8BxPXe3SlM0wo+fqUlJfQ4+vQM20tXM/R557iaDHxPg6f0eigdPoNlAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:33:16.851620Z"},"content_sha256":"3363ff97e2f2779fe8ec13222d13f7a0a3a950e9d5add91c043e89a21a1ad9b6","schema_version":"1.0","event_id":"sha256:3363ff97e2f2779fe8ec13222d13f7a0a3a950e9d5add91c043e89a21a1ad9b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XWRALHKAM3LS5BK4YOPEBP3VVP/bundle.json","state_url":"https://pith.science/pith/XWRALHKAM3LS5BK4YOPEBP3VVP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XWRALHKAM3LS5BK4YOPEBP3VVP/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":"2026-05-26T18:33:16Z","links":{"resolver":"https://pith.science/pith/XWRALHKAM3LS5BK4YOPEBP3VVP","bundle":"https://pith.science/pith/XWRALHKAM3LS5BK4YOPEBP3VVP/bundle.json","state":"https://pith.science/pith/XWRALHKAM3LS5BK4YOPEBP3VVP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XWRALHKAM3LS5BK4YOPEBP3VVP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XWRALHKAM3LS5BK4YOPEBP3VVP","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":"350f66f419caf59f079cfd647d4091087fed04430d8b705e6991c89d900ac1f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-12-14T18:52:58Z","title_canon_sha256":"c9e33d83ae566b42cd44c65dab2b1397ef7156310b0c42396f34799a4f7da57f"},"schema_version":"1.0","source":{"id":"1012.3130","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3130","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3130v3","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3130","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"XWRALHKAM3LS","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XWRALHKAM3LS5BK4","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XWRALHKA","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:3363ff97e2f2779fe8ec13222d13f7a0a3a950e9d5add91c043e89a21a1ad9b6","target":"graph","created_at":"2026-05-18T02:46:31Z","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":"Finding heavy-elements (heavy-hitters) in streaming data is one of the central, and well-understood tasks. Despite the importance of this problem, when considering the sliding windows model of streaming (where elements eventually expire) the problem of finding L_2-heavy elements has remained completely open despite multiple papers and considerable success in finding L_1-heavy elements.\n  In this paper, we develop the first poly-logarithmic-memory algorithm for finding L_2-heavy elements in sliding window model. Since L_2 heavy elements play a central role for many fundamental streaming problem","authors_text":"Rafail Ostrovsky, Ran Gelles, Vladimir Braverman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-12-14T18:52:58Z","title":"How to Catch L_2-Heavy-Hitters on Sliding Windows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3130","kind":"arxiv","version":3},"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":"sha256:3912a315daa00b0d66a65d23c05dea77e71e19cc0bd057570e4ffab7851b9e2b","target":"record","created_at":"2026-05-18T02:46:31Z","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":"350f66f419caf59f079cfd647d4091087fed04430d8b705e6991c89d900ac1f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-12-14T18:52:58Z","title_canon_sha256":"c9e33d83ae566b42cd44c65dab2b1397ef7156310b0c42396f34799a4f7da57f"},"schema_version":"1.0","source":{"id":"1012.3130","kind":"arxiv","version":3}},"canonical_sha256":"bda2059d4066d72e855cc39e40bf75abc45897de8247d1eb55230ff79b224461","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bda2059d4066d72e855cc39e40bf75abc45897de8247d1eb55230ff79b224461","first_computed_at":"2026-05-18T02:46:31.743451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:31.743451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SLBgE14YI4sAMEfz5pq99CqqPBRpT0kLgx9+zcEYK6vfOGsilKZxvCOUNgWJ8UZele8mBd58B+vtgnhSAs3+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:31.743826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3130","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3912a315daa00b0d66a65d23c05dea77e71e19cc0bd057570e4ffab7851b9e2b","sha256:3363ff97e2f2779fe8ec13222d13f7a0a3a950e9d5add91c043e89a21a1ad9b6"],"state_sha256":"4a2829ba84c95dbed05f82351509a45f669b8c2c543a4e64c2a5f8c113c875ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jh0TNWw/iic5Q0TKFALl8/ZAGJOPLLM7rbd0y57c/gSSKp7zFhN6Ff8mTibAEAa2lAKKtI8KkZ+sb/LLtV2XDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:33:16.854669Z","bundle_sha256":"a17866e9e33c11c70f9a51240d9768787fa30acf29d2fede9580a74531e36cd2"}}