{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ISHXKSQNSR75PBJYX7QB43AZ6P","short_pith_number":"pith:ISHXKSQN","canonical_record":{"source":{"id":"1808.01393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-04T00:15:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"fba8a78e3eae33cc6a7dbd05674bb2e4ac8e0d131a67f79f548fcd27c7bcee68","abstract_canon_sha256":"f5c31303bc4d98b7242f39c61bcf6e227dbd1d802d482fd8cdd6d9b9cfe97743"},"schema_version":"1.0"},"canonical_sha256":"448f754a0d947fd78538bfe01e6c19f3efa7eb11e0ecd4a99800a3a2236ffcc5","source":{"kind":"arxiv","id":"1808.01393","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01393","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01393v2","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01393","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"pith_short_12","alias_value":"ISHXKSQNSR75","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"ISHXKSQNSR75PBJY","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"ISHXKSQN","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ISHXKSQNSR75PBJYX7QB43AZ6P","target":"record","payload":{"canonical_record":{"source":{"id":"1808.01393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-04T00:15:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"fba8a78e3eae33cc6a7dbd05674bb2e4ac8e0d131a67f79f548fcd27c7bcee68","abstract_canon_sha256":"f5c31303bc4d98b7242f39c61bcf6e227dbd1d802d482fd8cdd6d9b9cfe97743"},"schema_version":"1.0"},"canonical_sha256":"448f754a0d947fd78538bfe01e6c19f3efa7eb11e0ecd4a99800a3a2236ffcc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:02.578599Z","signature_b64":"L+ap/kMpgo5GUHdnVxdVmw7kHK1RI8Ulx6ReOM/ZIbIZlnqFaMX25ET1SreJ+H8u8Q64PIKBkRD450r58i3JCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"448f754a0d947fd78538bfe01e6c19f3efa7eb11e0ecd4a99800a3a2236ffcc5","last_reissued_at":"2026-05-18T00:08:02.577934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:02.577934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.01393","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/rabTX4WA0e3qvUcmatnyXbP4tnfAV70mxuNFkbHgjk/2G88ozGnr+yJCXBP2Khgvn4EPUn1yXiJexhe+nE4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:34:16.684800Z"},"content_sha256":"00c51314329abfd51f315419bf17b975e9bb6c6397b029e5478f415624232bd2","schema_version":"1.0","event_id":"sha256:00c51314329abfd51f315419bf17b975e9bb6c6397b029e5478f415624232bd2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ISHXKSQNSR75PBJYX7QB43AZ6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounded Statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Konstantina Trivisa, Pranava Chaitanya Jayanti","submitted_at":"2018-08-04T00:15:34Z","abstract_excerpt":"If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below is an algorithm to quantitatively estimate this \"similarity\" between the given PDFs, depending on how many moments one has information about. This method involves the concept of functions behaving \"similarly\" at certain \"length scales\", which is also precisely defined. This technique could find use in data analysis, to compare a data set with a PDF or anoth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01393","kind":"arxiv","version":2},"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":"2026-05-18T00:08:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rVZrtFsTffGSdjAxJY5b8GjaknL5oIt7UEj9gXaKljfO3IsFC+vbCd14bh6vwKhB7MwBIuImeSrx1ID5JfPWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:34:16.685532Z"},"content_sha256":"9944f12676245e1a5ca043b3a00e8d1cfb86a8b5e50d3476ef17c509f9a3fe90","schema_version":"1.0","event_id":"sha256:9944f12676245e1a5ca043b3a00e8d1cfb86a8b5e50d3476ef17c509f9a3fe90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ISHXKSQNSR75PBJYX7QB43AZ6P/bundle.json","state_url":"https://pith.science/pith/ISHXKSQNSR75PBJYX7QB43AZ6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ISHXKSQNSR75PBJYX7QB43AZ6P/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":"2026-06-07T18:34:16Z","links":{"resolver":"https://pith.science/pith/ISHXKSQNSR75PBJYX7QB43AZ6P","bundle":"https://pith.science/pith/ISHXKSQNSR75PBJYX7QB43AZ6P/bundle.json","state":"https://pith.science/pith/ISHXKSQNSR75PBJYX7QB43AZ6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ISHXKSQNSR75PBJYX7QB43AZ6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ISHXKSQNSR75PBJYX7QB43AZ6P","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":"f5c31303bc4d98b7242f39c61bcf6e227dbd1d802d482fd8cdd6d9b9cfe97743","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-04T00:15:34Z","title_canon_sha256":"fba8a78e3eae33cc6a7dbd05674bb2e4ac8e0d131a67f79f548fcd27c7bcee68"},"schema_version":"1.0","source":{"id":"1808.01393","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01393","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01393v2","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01393","created_at":"2026-05-18T00:08:02Z"},{"alias_kind":"pith_short_12","alias_value":"ISHXKSQNSR75","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"ISHXKSQNSR75PBJY","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"ISHXKSQN","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:9944f12676245e1a5ca043b3a00e8d1cfb86a8b5e50d3476ef17c509f9a3fe90","target":"graph","created_at":"2026-05-18T00:08:02Z","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":"If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below is an algorithm to quantitatively estimate this \"similarity\" between the given PDFs, depending on how many moments one has information about. This method involves the concept of functions behaving \"similarly\" at certain \"length scales\", which is also precisely defined. This technique could find use in data analysis, to compare a data set with a PDF or anoth","authors_text":"Konstantina Trivisa, Pranava Chaitanya Jayanti","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-04T00:15:34Z","title":"Bounded Statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01393","kind":"arxiv","version":2},"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":"sha256:00c51314329abfd51f315419bf17b975e9bb6c6397b029e5478f415624232bd2","target":"record","created_at":"2026-05-18T00:08:02Z","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":"f5c31303bc4d98b7242f39c61bcf6e227dbd1d802d482fd8cdd6d9b9cfe97743","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-04T00:15:34Z","title_canon_sha256":"fba8a78e3eae33cc6a7dbd05674bb2e4ac8e0d131a67f79f548fcd27c7bcee68"},"schema_version":"1.0","source":{"id":"1808.01393","kind":"arxiv","version":2}},"canonical_sha256":"448f754a0d947fd78538bfe01e6c19f3efa7eb11e0ecd4a99800a3a2236ffcc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"448f754a0d947fd78538bfe01e6c19f3efa7eb11e0ecd4a99800a3a2236ffcc5","first_computed_at":"2026-05-18T00:08:02.577934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:02.577934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L+ap/kMpgo5GUHdnVxdVmw7kHK1RI8Ulx6ReOM/ZIbIZlnqFaMX25ET1SreJ+H8u8Q64PIKBkRD450r58i3JCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:02.578599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01393","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00c51314329abfd51f315419bf17b975e9bb6c6397b029e5478f415624232bd2","sha256:9944f12676245e1a5ca043b3a00e8d1cfb86a8b5e50d3476ef17c509f9a3fe90"],"state_sha256":"a9753fc3faba7354462007f0b17b10a68a188ffb94815e51e65489b171774a91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZagV8KI+KkIaxY9PwSHiQpijhUgPXpe7IKJzn1T0yyQxRE8hYfPjt2GHdI/+/J9DYUGUwU9095zqeyvpZTuXCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:34:16.689244Z","bundle_sha256":"35d55a27eeb81441ef69794c346e043e7e00a675d54ae1a2ebe6458bebc2796b"}}