{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PZP7LPCKF2R2DA3FTXKNKIFYRS","short_pith_number":"pith:PZP7LPCK","canonical_record":{"source":{"id":"1808.05497","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-16T14:00:44Z","cross_cats_sorted":[],"title_canon_sha256":"4116d2b193ea762f37bbeca22d3383cee546f7937737d93efdc78ce17cf40a97","abstract_canon_sha256":"a52076d842add85cde300d28738db105cc31d9c8ad3c37c777e7f87f89df803c"},"schema_version":"1.0"},"canonical_sha256":"7e5ff5bc4a2ea3a183659dd4d520b88cac3532da978ab625b66b54e4480f8297","source":{"kind":"arxiv","id":"1808.05497","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.05497","created_at":"2026-07-05T00:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1808.05497v3","created_at":"2026-07-05T00:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05497","created_at":"2026-07-05T00:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"PZP7LPCKF2R2","created_at":"2026-07-05T00:18:04Z"},{"alias_kind":"pith_short_16","alias_value":"PZP7LPCKF2R2DA3F","created_at":"2026-07-05T00:18:04Z"},{"alias_kind":"pith_short_8","alias_value":"PZP7LPCK","created_at":"2026-07-05T00:18:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PZP7LPCKF2R2DA3FTXKNKIFYRS","target":"record","payload":{"canonical_record":{"source":{"id":"1808.05497","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-16T14:00:44Z","cross_cats_sorted":[],"title_canon_sha256":"4116d2b193ea762f37bbeca22d3383cee546f7937737d93efdc78ce17cf40a97","abstract_canon_sha256":"a52076d842add85cde300d28738db105cc31d9c8ad3c37c777e7f87f89df803c"},"schema_version":"1.0"},"canonical_sha256":"7e5ff5bc4a2ea3a183659dd4d520b88cac3532da978ab625b66b54e4480f8297","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:18:04.856926Z","signature_b64":"2xUvnIxrlzGk7GWIceac74yVi8ITgvCxogxebk92Q4jzQ1pHWngRd3we8NnuG/xlqEvV10cJIFolpqVk6ALNBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e5ff5bc4a2ea3a183659dd4d520b88cac3532da978ab625b66b54e4480f8297","last_reissued_at":"2026-07-05T00:18:04.856542Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:18:04.856542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.05497","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":"2026-07-05T00:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1vrAoPiLxxw699a6//r6b3CXoRnfrKJVS4m+hqcZrjoM3G1sWspuA1t8o3MzDmEqjik1QhEKh8Mn1p3mWyY5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T14:20:07.429865Z"},"content_sha256":"47fa9c288f007a8b5ba324ce0f6ca6be5d28a5c1ff953a11e32f89c4fb8c8f2d","schema_version":"1.0","event_id":"sha256:47fa9c288f007a8b5ba324ce0f6ca6be5d28a5c1ff953a11e32f89c4fb8c8f2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PZP7LPCKF2R2DA3FTXKNKIFYRS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perfect $L_p$ Sampling in a Data Stream","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Rajesh Jayaram","submitted_at":"2018-08-16T14:00:44Z","abstract_excerpt":"In this paper, we resolve the one-pass space complexity of $L_p$ sampling for $p \\in (0,2)$. Given a stream of updates (insertions and deletions) to the coordinates of an underlying vector $f \\in \\mathbb{R}^n$, a perfect $L_p$ sampler must output an index $i$ with probability $|f_i|^p/\\|f\\|_p^p$, and is allowed to fail with some probability $\\delta$. So far, for $p > 0$ no algorithm has been shown to solve the problem exactly using $\\text{poly}( \\log n)$-bits of space. In 2010, Monemizadeh and Woodruff introduced an approximate $L_p$ sampler, which outputs $i$ with probability $(1 \\pm \\nu)|f_i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05497","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1808.05497/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:18:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1EU7PYzNrZ5P4hCO8F3frVMoLGgCrU6P4aZOdrdFY560oU1YB6sgCh2Z2CHZhdcGYUkq6fuEU0lRJ7/QAnUKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T14:20:07.430745Z"},"content_sha256":"66a2940c6dd2510bb96cb5dc23a31ae1d117ec34dad73d0525b353163b480332","schema_version":"1.0","event_id":"sha256:66a2940c6dd2510bb96cb5dc23a31ae1d117ec34dad73d0525b353163b480332"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZP7LPCKF2R2DA3FTXKNKIFYRS/bundle.json","state_url":"https://pith.science/pith/PZP7LPCKF2R2DA3FTXKNKIFYRS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZP7LPCKF2R2DA3FTXKNKIFYRS/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":"2026-08-11T14:20:07Z","links":{"resolver":"https://pith.science/pith/PZP7LPCKF2R2DA3FTXKNKIFYRS","bundle":"https://pith.science/pith/PZP7LPCKF2R2DA3FTXKNKIFYRS/bundle.json","state":"https://pith.science/pith/PZP7LPCKF2R2DA3FTXKNKIFYRS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZP7LPCKF2R2DA3FTXKNKIFYRS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PZP7LPCKF2R2DA3FTXKNKIFYRS","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":"a52076d842add85cde300d28738db105cc31d9c8ad3c37c777e7f87f89df803c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-16T14:00:44Z","title_canon_sha256":"4116d2b193ea762f37bbeca22d3383cee546f7937737d93efdc78ce17cf40a97"},"schema_version":"1.0","source":{"id":"1808.05497","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.05497","created_at":"2026-07-05T00:18:04Z"},{"alias_kind":"arxiv_version","alias_value":"1808.05497v3","created_at":"2026-07-05T00:18:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05497","created_at":"2026-07-05T00:18:04Z"},{"alias_kind":"pith_short_12","alias_value":"PZP7LPCKF2R2","created_at":"2026-07-05T00:18:04Z"},{"alias_kind":"pith_short_16","alias_value":"PZP7LPCKF2R2DA3F","created_at":"2026-07-05T00:18:04Z"},{"alias_kind":"pith_short_8","alias_value":"PZP7LPCK","created_at":"2026-07-05T00:18:04Z"}],"graph_snapshots":[{"event_id":"sha256:66a2940c6dd2510bb96cb5dc23a31ae1d117ec34dad73d0525b353163b480332","target":"graph","created_at":"2026-07-05T00:18:04Z","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/1808.05497/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we resolve the one-pass space complexity of $L_p$ sampling for $p \\in (0,2)$. Given a stream of updates (insertions and deletions) to the coordinates of an underlying vector $f \\in \\mathbb{R}^n$, a perfect $L_p$ sampler must output an index $i$ with probability $|f_i|^p/\\|f\\|_p^p$, and is allowed to fail with some probability $\\delta$. So far, for $p > 0$ no algorithm has been shown to solve the problem exactly using $\\text{poly}( \\log n)$-bits of space. In 2010, Monemizadeh and Woodruff introduced an approximate $L_p$ sampler, which outputs $i$ with probability $(1 \\pm \\nu)|f_i","authors_text":"David P. Woodruff, Rajesh Jayaram","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-16T14:00:44Z","title":"Perfect $L_p$ Sampling in a Data Stream"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05497","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":"sha256:47fa9c288f007a8b5ba324ce0f6ca6be5d28a5c1ff953a11e32f89c4fb8c8f2d","target":"record","created_at":"2026-07-05T00:18:04Z","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":"a52076d842add85cde300d28738db105cc31d9c8ad3c37c777e7f87f89df803c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-16T14:00:44Z","title_canon_sha256":"4116d2b193ea762f37bbeca22d3383cee546f7937737d93efdc78ce17cf40a97"},"schema_version":"1.0","source":{"id":"1808.05497","kind":"arxiv","version":3}},"canonical_sha256":"7e5ff5bc4a2ea3a183659dd4d520b88cac3532da978ab625b66b54e4480f8297","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e5ff5bc4a2ea3a183659dd4d520b88cac3532da978ab625b66b54e4480f8297","first_computed_at":"2026-07-05T00:18:04.856542Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:18:04.856542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2xUvnIxrlzGk7GWIceac74yVi8ITgvCxogxebk92Q4jzQ1pHWngRd3we8NnuG/xlqEvV10cJIFolpqVk6ALNBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:18:04.856926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.05497","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47fa9c288f007a8b5ba324ce0f6ca6be5d28a5c1ff953a11e32f89c4fb8c8f2d","sha256:66a2940c6dd2510bb96cb5dc23a31ae1d117ec34dad73d0525b353163b480332"],"state_sha256":"20d0e7a73f907c58dab59704d3ebd12fdf04c6db378f742d492f806985365336"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FysBWuELBvqVq82grET5EQwZ2m6pGxxFQMoRsqBI5UfXDhUlSxB0ITQm517nv6lBjTSjps0O5Ihv6pUi5vhoCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T14:20:07.451429Z","bundle_sha256":"a8f3df3ac8f2c0d4f07d8f2f6061f580fb2e98ee43cbd5c53502e38d3a14276d"}}