{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TO64Y6TJGNRZOOKBS3L3GROW7Z","short_pith_number":"pith:TO64Y6TJ","canonical_record":{"source":{"id":"1503.01156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-03T22:58:55Z","cross_cats_sorted":[],"title_canon_sha256":"0977274442ca1f9a764a59e54e7ca7d9928847960b5d510a088a5e46114548a2","abstract_canon_sha256":"7c30e1ee47ec844d5984e74a6b7bfb88ce1c4b4fa87c60506360e8b697157328"},"schema_version":"1.0"},"canonical_sha256":"9bbdcc7a69336397394196d7b345d6fe67a508d616c62bf1b24580f8267ba102","source":{"kind":"arxiv","id":"1503.01156","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01156","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01156v1","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01156","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"TO64Y6TJGNRZ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TO64Y6TJGNRZOOKB","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TO64Y6TJ","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TO64Y6TJGNRZOOKBS3L3GROW7Z","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01156","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-03T22:58:55Z","cross_cats_sorted":[],"title_canon_sha256":"0977274442ca1f9a764a59e54e7ca7d9928847960b5d510a088a5e46114548a2","abstract_canon_sha256":"7c30e1ee47ec844d5984e74a6b7bfb88ce1c4b4fa87c60506360e8b697157328"},"schema_version":"1.0"},"canonical_sha256":"9bbdcc7a69336397394196d7b345d6fe67a508d616c62bf1b24580f8267ba102","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:39.757889Z","signature_b64":"1II5xcESJ9uQmhf37gw8SHaDEoGxZeLDTcJE25jBHdNNBnIJnZX8mWLn1yKYBcgJfFOcnCvujnlV5Cm3LCoBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bbdcc7a69336397394196d7b345d6fe67a508d616c62bf1b24580f8267ba102","last_reissued_at":"2026-05-18T02:25:39.757035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:39.757035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01156","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f1C1c3SoBmfORPfpG+weA7ySWsXxJZJP/lONM8+hR64HuJp9j1ywhI1+7pyqvZe07A+Hvk5bwDL4AroNdxc1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:27:44.044343Z"},"content_sha256":"c514a44fc0621020827d52e4ce6177ad35e3bf36be69291c4637753cf701f0e2","schema_version":"1.0","event_id":"sha256:c514a44fc0621020827d52e4ce6177ad35e3bf36be69291c4637753cf701f0e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TO64Y6TJGNRZOOKBS3L3GROW7Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A randomized online quantile summary in $O(\\frac{1}{\\varepsilon} \\log \\frac{1}{\\varepsilon})$ words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David Felber, Rafail Ostrovsky","submitted_at":"2015-03-03T22:58:55Z","abstract_excerpt":"A quantile summary is a data structure that approximates to $\\varepsilon$-relative error the order statistics of a much larger underlying dataset.\n  In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses $O(\\frac{1}{\\varepsilon} \\log \\frac{1}{\\varepsilon})$ words of memory. This improves upon the previous best upper bound of $O(\\frac{1}{\\varepsilon} \\log^{3/2} \\frac{1}{\\varepsilon})$ by Agarwal et. al. (PODS 2012). Further, by a lower bound of Hung and Ting (FAW 2010) no deterministic summary for the compa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01156","kind":"arxiv","version":1},"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":"2026-05-18T02:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dYYY3lKPD33623sEhDFiuv2IdNlLfDQe9yhZmSDEeOnspThasFfQury5nWsoDNQSJ9C0O3kccs5Fedo/rTqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:27:44.045104Z"},"content_sha256":"25a7d238facb2aeacee63062ea26840c531e7592de6c841dba77f7773be7ef06","schema_version":"1.0","event_id":"sha256:25a7d238facb2aeacee63062ea26840c531e7592de6c841dba77f7773be7ef06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TO64Y6TJGNRZOOKBS3L3GROW7Z/bundle.json","state_url":"https://pith.science/pith/TO64Y6TJGNRZOOKBS3L3GROW7Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TO64Y6TJGNRZOOKBS3L3GROW7Z/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":"2026-06-08T19:27:44Z","links":{"resolver":"https://pith.science/pith/TO64Y6TJGNRZOOKBS3L3GROW7Z","bundle":"https://pith.science/pith/TO64Y6TJGNRZOOKBS3L3GROW7Z/bundle.json","state":"https://pith.science/pith/TO64Y6TJGNRZOOKBS3L3GROW7Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TO64Y6TJGNRZOOKBS3L3GROW7Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TO64Y6TJGNRZOOKBS3L3GROW7Z","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":"7c30e1ee47ec844d5984e74a6b7bfb88ce1c4b4fa87c60506360e8b697157328","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-03T22:58:55Z","title_canon_sha256":"0977274442ca1f9a764a59e54e7ca7d9928847960b5d510a088a5e46114548a2"},"schema_version":"1.0","source":{"id":"1503.01156","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01156","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01156v1","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01156","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"TO64Y6TJGNRZ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TO64Y6TJGNRZOOKB","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TO64Y6TJ","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:25a7d238facb2aeacee63062ea26840c531e7592de6c841dba77f7773be7ef06","target":"graph","created_at":"2026-05-18T02:25:39Z","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 quantile summary is a data structure that approximates to $\\varepsilon$-relative error the order statistics of a much larger underlying dataset.\n  In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses $O(\\frac{1}{\\varepsilon} \\log \\frac{1}{\\varepsilon})$ words of memory. This improves upon the previous best upper bound of $O(\\frac{1}{\\varepsilon} \\log^{3/2} \\frac{1}{\\varepsilon})$ by Agarwal et. al. (PODS 2012). Further, by a lower bound of Hung and Ting (FAW 2010) no deterministic summary for the compa","authors_text":"David Felber, Rafail Ostrovsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-03T22:58:55Z","title":"A randomized online quantile summary in $O(\\frac{1}{\\varepsilon} \\log \\frac{1}{\\varepsilon})$ words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01156","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:c514a44fc0621020827d52e4ce6177ad35e3bf36be69291c4637753cf701f0e2","target":"record","created_at":"2026-05-18T02:25:39Z","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":"7c30e1ee47ec844d5984e74a6b7bfb88ce1c4b4fa87c60506360e8b697157328","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-03-03T22:58:55Z","title_canon_sha256":"0977274442ca1f9a764a59e54e7ca7d9928847960b5d510a088a5e46114548a2"},"schema_version":"1.0","source":{"id":"1503.01156","kind":"arxiv","version":1}},"canonical_sha256":"9bbdcc7a69336397394196d7b345d6fe67a508d616c62bf1b24580f8267ba102","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bbdcc7a69336397394196d7b345d6fe67a508d616c62bf1b24580f8267ba102","first_computed_at":"2026-05-18T02:25:39.757035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:39.757035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1II5xcESJ9uQmhf37gw8SHaDEoGxZeLDTcJE25jBHdNNBnIJnZX8mWLn1yKYBcgJfFOcnCvujnlV5Cm3LCoBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:39.757889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01156","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c514a44fc0621020827d52e4ce6177ad35e3bf36be69291c4637753cf701f0e2","sha256:25a7d238facb2aeacee63062ea26840c531e7592de6c841dba77f7773be7ef06"],"state_sha256":"65562d7911a4bff17946a42501a4ddd0ead72b8702569eb5c900765bb8f018d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N58ofHZ4Ro7ReKUG8RclpnpbN3ZFw0bTz075B1YdF/HQCkJAIswVMac3M03tYZX91zCytp9gpTha6b3KPY18BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:27:44.048856Z","bundle_sha256":"cc092d5ea78618e7912b9c9e9dcc568b7c81063bf837ec28e18d55e350ecf0d8"}}