{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:AGRN5CZBRWXMQBE2HLKJQVQK5X","short_pith_number":"pith:AGRN5CZB","canonical_record":{"source":{"id":"1111.2368","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-09T23:43:54Z","cross_cats_sorted":["stat.OT"],"title_canon_sha256":"5243a8bbd8a5d75097abd3ac2e7fd062ccf4819c9a854c178d9c988970c1514e","abstract_canon_sha256":"0c8b23e5e1f2ec1b2357b5176b84bb6aaffd01a26fbe5674ae8df378ed745a0f"},"schema_version":"1.0"},"canonical_sha256":"01a2de8b218daec8049a3ad498560aedd3ea62cd7865e2546c683ef121c40e48","source":{"kind":"arxiv","id":"1111.2368","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2368","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2368v1","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2368","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"pith_short_12","alias_value":"AGRN5CZBRWXM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AGRN5CZBRWXMQBE2","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AGRN5CZB","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:AGRN5CZBRWXMQBE2HLKJQVQK5X","target":"record","payload":{"canonical_record":{"source":{"id":"1111.2368","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-09T23:43:54Z","cross_cats_sorted":["stat.OT"],"title_canon_sha256":"5243a8bbd8a5d75097abd3ac2e7fd062ccf4819c9a854c178d9c988970c1514e","abstract_canon_sha256":"0c8b23e5e1f2ec1b2357b5176b84bb6aaffd01a26fbe5674ae8df378ed745a0f"},"schema_version":"1.0"},"canonical_sha256":"01a2de8b218daec8049a3ad498560aedd3ea62cd7865e2546c683ef121c40e48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:34.343494Z","signature_b64":"WXETF15jCdwcRxl8FU4gEXhszxw/tvuYar1HKcCCIGKw9sS/5csL/GGnKNw/S/25OkIufxsIYzccKFtHgIUZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01a2de8b218daec8049a3ad498560aedd3ea62cd7865e2546c683ef121c40e48","last_reissued_at":"2026-05-18T04:08:34.343031Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:34.343031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.2368","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":"2026-05-18T04:08:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XS5ooUtKCWDGeDNkeG+jsVqvpVdg4BKJskQ/Ewa3p3b4T32hpFVGQLgKtR0x0sfdKqvKQTIsjko2g+8fvopbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:16:40.928856Z"},"content_sha256":"d5ef0948c20e3c86918a4fa6f24cae1e4e9a1f647669c929f0ddf76d62c7649c","schema_version":"1.0","event_id":"sha256:d5ef0948c20e3c86918a4fa6f24cae1e4e9a1f647669c929f0ddf76d62c7649c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:AGRN5CZBRWXMQBE2HLKJQVQK5X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a connection between Stein characterizations and Fisher information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.OT"],"primary_cat":"math.PR","authors_text":"Christophe Ley, Yvik Swan","submitted_at":"2011-11-09T23:43:54Z","abstract_excerpt":"We generalize the so-called density approach to Stein characterizations of probability distributions. We prove an elementary factorization property of the resulting Stein operator in terms of a generalized (standardized) score function. We use this result to connect Stein characterizations with information distances such as the generalized (standardized) Fisher information."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2368","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":"2026-05-18T04:08:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oEqDf3yicjEoTa5Sq4jF0Lxip//iyHi26xVcz7lyrNswwzY4lscIFAqSyfkfbBsw7ak2FlEDgFOVW6et0jKrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:16:40.929534Z"},"content_sha256":"745903016a26201b2f336b7b5e797b9cf1eb27e9cb1f7d0d5bd9a9f76efe0a03","schema_version":"1.0","event_id":"sha256:745903016a26201b2f336b7b5e797b9cf1eb27e9cb1f7d0d5bd9a9f76efe0a03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AGRN5CZBRWXMQBE2HLKJQVQK5X/bundle.json","state_url":"https://pith.science/pith/AGRN5CZBRWXMQBE2HLKJQVQK5X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AGRN5CZBRWXMQBE2HLKJQVQK5X/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":"2026-06-07T23:16:40Z","links":{"resolver":"https://pith.science/pith/AGRN5CZBRWXMQBE2HLKJQVQK5X","bundle":"https://pith.science/pith/AGRN5CZBRWXMQBE2HLKJQVQK5X/bundle.json","state":"https://pith.science/pith/AGRN5CZBRWXMQBE2HLKJQVQK5X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AGRN5CZBRWXMQBE2HLKJQVQK5X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AGRN5CZBRWXMQBE2HLKJQVQK5X","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":"0c8b23e5e1f2ec1b2357b5176b84bb6aaffd01a26fbe5674ae8df378ed745a0f","cross_cats_sorted":["stat.OT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-09T23:43:54Z","title_canon_sha256":"5243a8bbd8a5d75097abd3ac2e7fd062ccf4819c9a854c178d9c988970c1514e"},"schema_version":"1.0","source":{"id":"1111.2368","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2368","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2368v1","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2368","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"pith_short_12","alias_value":"AGRN5CZBRWXM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AGRN5CZBRWXMQBE2","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AGRN5CZB","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:745903016a26201b2f336b7b5e797b9cf1eb27e9cb1f7d0d5bd9a9f76efe0a03","target":"graph","created_at":"2026-05-18T04:08:34Z","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 generalize the so-called density approach to Stein characterizations of probability distributions. We prove an elementary factorization property of the resulting Stein operator in terms of a generalized (standardized) score function. We use this result to connect Stein characterizations with information distances such as the generalized (standardized) Fisher information.","authors_text":"Christophe Ley, Yvik Swan","cross_cats":["stat.OT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-09T23:43:54Z","title":"On a connection between Stein characterizations and Fisher information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2368","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:d5ef0948c20e3c86918a4fa6f24cae1e4e9a1f647669c929f0ddf76d62c7649c","target":"record","created_at":"2026-05-18T04:08:34Z","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":"0c8b23e5e1f2ec1b2357b5176b84bb6aaffd01a26fbe5674ae8df378ed745a0f","cross_cats_sorted":["stat.OT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-09T23:43:54Z","title_canon_sha256":"5243a8bbd8a5d75097abd3ac2e7fd062ccf4819c9a854c178d9c988970c1514e"},"schema_version":"1.0","source":{"id":"1111.2368","kind":"arxiv","version":1}},"canonical_sha256":"01a2de8b218daec8049a3ad498560aedd3ea62cd7865e2546c683ef121c40e48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01a2de8b218daec8049a3ad498560aedd3ea62cd7865e2546c683ef121c40e48","first_computed_at":"2026-05-18T04:08:34.343031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:34.343031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WXETF15jCdwcRxl8FU4gEXhszxw/tvuYar1HKcCCIGKw9sS/5csL/GGnKNw/S/25OkIufxsIYzccKFtHgIUZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:34.343494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2368","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5ef0948c20e3c86918a4fa6f24cae1e4e9a1f647669c929f0ddf76d62c7649c","sha256:745903016a26201b2f336b7b5e797b9cf1eb27e9cb1f7d0d5bd9a9f76efe0a03"],"state_sha256":"2deffceccbf61cbc80a76c07503a561d23540e7fbd35b180fa8c69510ec5627f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7oVogL6n5LmjzHIXSPHZH1n0eB4ZrF11u4BfHqbSXhJ8yAoGAK17Pd8GU97AvSjal8ukgQZTj3MSNy7zw//BCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:16:40.933172Z","bundle_sha256":"b8a6e5d8b82fdbe6d9854c09f22f49e6098f4ce4b3090c8f048b6e47370cc9e2"}}