{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZH6ACGH6M3D3KQGHAG2SXVS6VA","short_pith_number":"pith:ZH6ACGH6","canonical_record":{"source":{"id":"1201.0253","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-31T12:56:24Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"a5bb1dc24af88ec0571c00f24bf791499806b9b0b67655000000dbba063c7e4b","abstract_canon_sha256":"9100265084011e007c4bb31b15e3952c8414e920060974f968cdfcca512ee138"},"schema_version":"1.0"},"canonical_sha256":"c9fc0118fe66c7b540c701b52bd65ea82769fc9e282e739e98baadf69dcba829","source":{"kind":"arxiv","id":"1201.0253","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0253","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0253v1","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0253","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZH6ACGH6M3D3","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZH6ACGH6M3D3KQGH","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZH6ACGH6","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZH6ACGH6M3D3KQGHAG2SXVS6VA","target":"record","payload":{"canonical_record":{"source":{"id":"1201.0253","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-31T12:56:24Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"a5bb1dc24af88ec0571c00f24bf791499806b9b0b67655000000dbba063c7e4b","abstract_canon_sha256":"9100265084011e007c4bb31b15e3952c8414e920060974f968cdfcca512ee138"},"schema_version":"1.0"},"canonical_sha256":"c9fc0118fe66c7b540c701b52bd65ea82769fc9e282e739e98baadf69dcba829","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:26.836749Z","signature_b64":"POi98Cod/5X0oWDn+TWqZ01Fd1y9wGv2s3FBIiP3om1Ysiqzzvj/qxDgKc2AqZDP+h3nFa9enuEbr/PGPJOTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9fc0118fe66c7b540c701b52bd65ea82769fc9e282e739e98baadf69dcba829","last_reissued_at":"2026-05-18T02:21:26.835996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:26.835996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.0253","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":"2026-05-18T02:21:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QX3VvisUbs9z9GChK11zXyjV80oKDus1xmXyXNcjeOJVXpljfdlxIJ61dLpyBC+zDpZ8SXlMPfOqSev9vCoUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T03:08:06.814705Z"},"content_sha256":"7e591ae520dfb5a36677c702be82f56f684a61024cbdf7dd7a1941876aba2dc3","schema_version":"1.0","event_id":"sha256:7e591ae520dfb5a36677c702be82f56f684a61024cbdf7dd7a1941876aba2dc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZH6ACGH6M3D3KQGHAG2SXVS6VA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Lower Bound for Estimating High Moments of a Data Stream","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Sumit Ganguly","submitted_at":"2011-12-31T12:56:24Z","abstract_excerpt":"We show an improved lower bound for the Fp estimation problem in a data stream setting for p>2. A data stream is a sequence of items from the domain [n] with possible repetitions. The frequency vector x is an n-dimensional non-negative integer vector x such that x(i) is the number of occurrences of i in the sequence. Given an accuracy parameter Omega(n^{-1/p}) < \\epsilon < 1, the problem of estimating Fp is to estimate \\norm{x}_p^p = \\sum_{i \\in [n]} \\abs{x(i)}^p correctly to within a relative accuracy of 1\\pm \\epsilon with high constant probability in an online fashion and using as little spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0253","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":"2026-05-18T02:21:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nZi2EvRZVuGtADL7PfMd6b/DeTABr8QF6Xy/mylOnBr5C+UNSSgs2scP6CRtLXF7k8J1x3VL6MPPDokWFRcTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T03:08:06.815355Z"},"content_sha256":"ee503557b37d36660f392743e04b5c5e825282510eb9eb88a738ccd2b2452ebc","schema_version":"1.0","event_id":"sha256:ee503557b37d36660f392743e04b5c5e825282510eb9eb88a738ccd2b2452ebc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZH6ACGH6M3D3KQGHAG2SXVS6VA/bundle.json","state_url":"https://pith.science/pith/ZH6ACGH6M3D3KQGHAG2SXVS6VA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZH6ACGH6M3D3KQGHAG2SXVS6VA/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":"2026-08-14T03:08:06Z","links":{"resolver":"https://pith.science/pith/ZH6ACGH6M3D3KQGHAG2SXVS6VA","bundle":"https://pith.science/pith/ZH6ACGH6M3D3KQGHAG2SXVS6VA/bundle.json","state":"https://pith.science/pith/ZH6ACGH6M3D3KQGHAG2SXVS6VA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZH6ACGH6M3D3KQGHAG2SXVS6VA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZH6ACGH6M3D3KQGHAG2SXVS6VA","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":"9100265084011e007c4bb31b15e3952c8414e920060974f968cdfcca512ee138","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-31T12:56:24Z","title_canon_sha256":"a5bb1dc24af88ec0571c00f24bf791499806b9b0b67655000000dbba063c7e4b"},"schema_version":"1.0","source":{"id":"1201.0253","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0253","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0253v1","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0253","created_at":"2026-05-18T02:21:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZH6ACGH6M3D3","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZH6ACGH6M3D3KQGH","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZH6ACGH6","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:ee503557b37d36660f392743e04b5c5e825282510eb9eb88a738ccd2b2452ebc","target":"graph","created_at":"2026-05-18T02:21:26Z","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 show an improved lower bound for the Fp estimation problem in a data stream setting for p>2. A data stream is a sequence of items from the domain [n] with possible repetitions. The frequency vector x is an n-dimensional non-negative integer vector x such that x(i) is the number of occurrences of i in the sequence. Given an accuracy parameter Omega(n^{-1/p}) < \\epsilon < 1, the problem of estimating Fp is to estimate \\norm{x}_p^p = \\sum_{i \\in [n]} \\abs{x(i)}^p correctly to within a relative accuracy of 1\\pm \\epsilon with high constant probability in an online fashion and using as little spa","authors_text":"Sumit Ganguly","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-31T12:56:24Z","title":"A Lower Bound for Estimating High Moments of a Data Stream"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0253","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":"sha256:7e591ae520dfb5a36677c702be82f56f684a61024cbdf7dd7a1941876aba2dc3","target":"record","created_at":"2026-05-18T02:21:26Z","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":"9100265084011e007c4bb31b15e3952c8414e920060974f968cdfcca512ee138","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-12-31T12:56:24Z","title_canon_sha256":"a5bb1dc24af88ec0571c00f24bf791499806b9b0b67655000000dbba063c7e4b"},"schema_version":"1.0","source":{"id":"1201.0253","kind":"arxiv","version":1}},"canonical_sha256":"c9fc0118fe66c7b540c701b52bd65ea82769fc9e282e739e98baadf69dcba829","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9fc0118fe66c7b540c701b52bd65ea82769fc9e282e739e98baadf69dcba829","first_computed_at":"2026-05-18T02:21:26.835996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:26.835996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"POi98Cod/5X0oWDn+TWqZ01Fd1y9wGv2s3FBIiP3om1Ysiqzzvj/qxDgKc2AqZDP+h3nFa9enuEbr/PGPJOTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:26.836749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0253","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e591ae520dfb5a36677c702be82f56f684a61024cbdf7dd7a1941876aba2dc3","sha256:ee503557b37d36660f392743e04b5c5e825282510eb9eb88a738ccd2b2452ebc"],"state_sha256":"9fedd05c16106be6603d7a5e1f359663aa6fac039c2117f60f732a5e73ddaeac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cJnDFVZCxTIYnPiA4c0VS73cZttUFZ9RPV5EhMWC2CxuzRd4qLSTQQtlGussrCN6DYrLESwPlR15HSrMmHllCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T03:08:06.820342Z","bundle_sha256":"a92c99c028471a1e88ed9c8ca3ba516d85993633ef4efba5a3f7f876a9fb1507"}}