{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:27VNC2INDOCLZM2LGWWRYMCN6Y","short_pith_number":"pith:27VNC2IN","canonical_record":{"source":{"id":"1101.3804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-01-20T00:36:00Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"73708e7eaa83c741113a56bb468133e7b497c854cb66bc9706e52239f9574248","abstract_canon_sha256":"7259f3e76b3febdb5977acf62f8334b0e6b324d27830e2007d7cf31db9463c04"},"schema_version":"1.0"},"canonical_sha256":"d7ead1690d1b84bcb34b35ad1c304df6334899c520402a0525c21ffe8b46df09","source":{"kind":"arxiv","id":"1101.3804","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3804","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3804v1","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3804","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"pith_short_12","alias_value":"27VNC2INDOCL","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"27VNC2INDOCLZM2L","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"27VNC2IN","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:27VNC2INDOCLZM2LGWWRYMCN6Y","target":"record","payload":{"canonical_record":{"source":{"id":"1101.3804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-01-20T00:36:00Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"73708e7eaa83c741113a56bb468133e7b497c854cb66bc9706e52239f9574248","abstract_canon_sha256":"7259f3e76b3febdb5977acf62f8334b0e6b324d27830e2007d7cf31db9463c04"},"schema_version":"1.0"},"canonical_sha256":"d7ead1690d1b84bcb34b35ad1c304df6334899c520402a0525c21ffe8b46df09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:21.320340Z","signature_b64":"qPqsZh5KiwzucmnyXZtSiSuqJXwIk2H2sFRXmwhKLpwigyhPii1m9DKwkzcTrXr+SWaMCqtusJZ3oP+supUXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7ead1690d1b84bcb34b35ad1c304df6334899c520402a0525c21ffe8b46df09","last_reissued_at":"2026-05-18T04:31:21.319756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:21.319756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.3804","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":"2026-05-18T04:31:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bokoIPP6xGNnXgW3UeLW5waG6LH/16LSesRw+P8+1IOu6pfj27HcOrpMDj5LIISjV0it9Q/0g9GjFRTcZwtNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:40:30.293925Z"},"content_sha256":"f4c448ee7f5bda300f46dc324b533d9607cb624d77f5cba77ea745d948ba1bbb","schema_version":"1.0","event_id":"sha256:f4c448ee7f5bda300f46dc324b533d9607cb624d77f5cba77ea745d948ba1bbb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:27VNC2INDOCLZM2LGWWRYMCN6Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimating the Average of a Lipschitz-Continuous Function from One Sample","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Abhimanyu Das, David Kempe","submitted_at":"2011-01-20T00:36:00Z","abstract_excerpt":"We study the problem of estimating the average of a Lipschitz continuous function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal is to find a distribution minimizing the expected estimation error against an adversarially chosen Lipschitz continuous function. Our work falls into the broad class of estimating aggregate statistics of a function from a small number of carefully chosen samples. The general problem has a wide range of practical applications in areas as diverse as sensor ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3804","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":"2026-05-18T04:31:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F5Wd8hcMhmWYFwWcWMP7GOmtn2u7xFoRdgerbJDF68FDS/KxbtR4Z/zTEv62wRAup9+T2WE+YL6lXBZvR44XCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:40:30.294934Z"},"content_sha256":"8c13604f3ff1fe82c41a59770d01738e41bae98be9f628e9684f190f915f40dd","schema_version":"1.0","event_id":"sha256:8c13604f3ff1fe82c41a59770d01738e41bae98be9f628e9684f190f915f40dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/27VNC2INDOCLZM2LGWWRYMCN6Y/bundle.json","state_url":"https://pith.science/pith/27VNC2INDOCLZM2LGWWRYMCN6Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/27VNC2INDOCLZM2LGWWRYMCN6Y/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":"2026-06-05T19:40:30Z","links":{"resolver":"https://pith.science/pith/27VNC2INDOCLZM2LGWWRYMCN6Y","bundle":"https://pith.science/pith/27VNC2INDOCLZM2LGWWRYMCN6Y/bundle.json","state":"https://pith.science/pith/27VNC2INDOCLZM2LGWWRYMCN6Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/27VNC2INDOCLZM2LGWWRYMCN6Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:27VNC2INDOCLZM2LGWWRYMCN6Y","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":"7259f3e76b3febdb5977acf62f8334b0e6b324d27830e2007d7cf31db9463c04","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-01-20T00:36:00Z","title_canon_sha256":"73708e7eaa83c741113a56bb468133e7b497c854cb66bc9706e52239f9574248"},"schema_version":"1.0","source":{"id":"1101.3804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3804","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3804v1","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3804","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"pith_short_12","alias_value":"27VNC2INDOCL","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"27VNC2INDOCLZM2L","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"27VNC2IN","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:8c13604f3ff1fe82c41a59770d01738e41bae98be9f628e9684f190f915f40dd","target":"graph","created_at":"2026-05-18T04:31:21Z","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 study the problem of estimating the average of a Lipschitz continuous function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal is to find a distribution minimizing the expected estimation error against an adversarially chosen Lipschitz continuous function. Our work falls into the broad class of estimating aggregate statistics of a function from a small number of carefully chosen samples. The general problem has a wide range of practical applications in areas as diverse as sensor ne","authors_text":"Abhimanyu Das, David Kempe","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-01-20T00:36:00Z","title":"Estimating the Average of a Lipschitz-Continuous Function from One Sample"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3804","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:f4c448ee7f5bda300f46dc324b533d9607cb624d77f5cba77ea745d948ba1bbb","target":"record","created_at":"2026-05-18T04:31:21Z","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":"7259f3e76b3febdb5977acf62f8334b0e6b324d27830e2007d7cf31db9463c04","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-01-20T00:36:00Z","title_canon_sha256":"73708e7eaa83c741113a56bb468133e7b497c854cb66bc9706e52239f9574248"},"schema_version":"1.0","source":{"id":"1101.3804","kind":"arxiv","version":1}},"canonical_sha256":"d7ead1690d1b84bcb34b35ad1c304df6334899c520402a0525c21ffe8b46df09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7ead1690d1b84bcb34b35ad1c304df6334899c520402a0525c21ffe8b46df09","first_computed_at":"2026-05-18T04:31:21.319756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:21.319756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qPqsZh5KiwzucmnyXZtSiSuqJXwIk2H2sFRXmwhKLpwigyhPii1m9DKwkzcTrXr+SWaMCqtusJZ3oP+supUXBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:21.320340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4c448ee7f5bda300f46dc324b533d9607cb624d77f5cba77ea745d948ba1bbb","sha256:8c13604f3ff1fe82c41a59770d01738e41bae98be9f628e9684f190f915f40dd"],"state_sha256":"a7f9ecd2485d8aa229d30f84c13c59f3a4b9a11cb1597e3f0256416dfb9d9980"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k1FTpoEofWzBknlNkTDYIymSHpHTom6hSgaHEJvBZek3fbAztx02LL0vnzuw2wsrXOCrmhlWQ4nZkRKKhRWfAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:40:30.298565Z","bundle_sha256":"6a4abc2fb11f287c6310e4f1387069e4642c0a3b2526854f5b974a090fe0e38d"}}