{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:4GZPH7NIS66ZT3DAVHCTZETLRJ","short_pith_number":"pith:4GZPH7NI","canonical_record":{"source":{"id":"2412.17997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-12-23T21:40:01Z","cross_cats_sorted":["cs.DS","cs.LG","cs.NA","math.NA","stat.ML","stat.TH"],"title_canon_sha256":"6dfba7e3beb37d3a201a1e28fb50dd149fedc8b696513e0a5bf562e169c678d4","abstract_canon_sha256":"d22ecc919b72ccddbda0bdc6a08537c44b92b2906521a1e911e72fa518340322"},"schema_version":"1.0"},"canonical_sha256":"e1b2f3fda897bd99ec60a9c53c926b8a7949cd8d993d9bac92d12798fa4defb9","source":{"kind":"arxiv","id":"2412.17997","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.17997","created_at":"2026-07-05T09:53:32Z"},{"alias_kind":"arxiv_version","alias_value":"2412.17997v1","created_at":"2026-07-05T09:53:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.17997","created_at":"2026-07-05T09:53:32Z"},{"alias_kind":"pith_short_12","alias_value":"4GZPH7NIS66Z","created_at":"2026-07-05T09:53:32Z"},{"alias_kind":"pith_short_16","alias_value":"4GZPH7NIS66ZT3DA","created_at":"2026-07-05T09:53:32Z"},{"alias_kind":"pith_short_8","alias_value":"4GZPH7NI","created_at":"2026-07-05T09:53:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:4GZPH7NIS66ZT3DAVHCTZETLRJ","target":"record","payload":{"canonical_record":{"source":{"id":"2412.17997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-12-23T21:40:01Z","cross_cats_sorted":["cs.DS","cs.LG","cs.NA","math.NA","stat.ML","stat.TH"],"title_canon_sha256":"6dfba7e3beb37d3a201a1e28fb50dd149fedc8b696513e0a5bf562e169c678d4","abstract_canon_sha256":"d22ecc919b72ccddbda0bdc6a08537c44b92b2906521a1e911e72fa518340322"},"schema_version":"1.0"},"canonical_sha256":"e1b2f3fda897bd99ec60a9c53c926b8a7949cd8d993d9bac92d12798fa4defb9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:53:32.138023Z","signature_b64":"GZUPxwFVYXQfg4QxuJ9rhUzFTlirZ/zmEkv6CiGV2WgkTN7wr9ZKYZMfEaIsbl/uvny3YOBcHAo95EtrxugSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1b2f3fda897bd99ec60a9c53c926b8a7949cd8d993d9bac92d12798fa4defb9","last_reissued_at":"2026-07-05T09:53:32.137589Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:53:32.137589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.17997","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":"2026-07-05T09:53:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uu2iYlyG4xHd7fq1LxulPk9W2eRl6YurAi9bL4H4FPn1tklWIiIq5pLBayQCCPtOMtxFs/xfjhLjnDZsgfePBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:43:57.224283Z"},"content_sha256":"bc0c4aa2c2cec286f1b60898223d2e08c3968662c09c8143dcc95a48952738c1","schema_version":"1.0","event_id":"sha256:bc0c4aa2c2cec286f1b60898223d2e08c3968662c09c8143dcc95a48952738c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:4GZPH7NIS66ZT3DAVHCTZETLRJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shifted Composition III: Local Error Framework for KL Divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG","cs.NA","math.NA","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Jason M. Altschuler, Sinho Chewi","submitted_at":"2024-12-23T21:40:01Z","abstract_excerpt":"Coupling arguments are a central tool for bounding the deviation between two stochastic processes, but traditionally have been limited to Wasserstein metrics. In this paper, we apply the shifted composition rule--an information-theoretic principle introduced in our earlier work--in order to adapt coupling arguments to the Kullback-Leibler (KL) divergence. Our framework combine the strengths of two previously disparate approaches: local error analysis and Girsanov's theorem. Akin to the former, it yields tight bounds by incorporating the so-called weak error, and is user-friendly in that it onl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.17997","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.17997/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":"2026-07-05T09:53:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mY1ZBWUFX6/bmIyFN7CyJG/tp7yNLN9e0RdSNMzsdJ018Y8vbSeXPkmknVP7s7TYfCCsyzoZAcaf5EjwGvzVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:43:57.224800Z"},"content_sha256":"30869da64452ce981ef3021e323c1b7488b595b10d87532cfb459cfd4eab5ee6","schema_version":"1.0","event_id":"sha256:30869da64452ce981ef3021e323c1b7488b595b10d87532cfb459cfd4eab5ee6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4GZPH7NIS66ZT3DAVHCTZETLRJ/bundle.json","state_url":"https://pith.science/pith/4GZPH7NIS66ZT3DAVHCTZETLRJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4GZPH7NIS66ZT3DAVHCTZETLRJ/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":"2026-08-09T12:43:57Z","links":{"resolver":"https://pith.science/pith/4GZPH7NIS66ZT3DAVHCTZETLRJ","bundle":"https://pith.science/pith/4GZPH7NIS66ZT3DAVHCTZETLRJ/bundle.json","state":"https://pith.science/pith/4GZPH7NIS66ZT3DAVHCTZETLRJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4GZPH7NIS66ZT3DAVHCTZETLRJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4GZPH7NIS66ZT3DAVHCTZETLRJ","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":"d22ecc919b72ccddbda0bdc6a08537c44b92b2906521a1e911e72fa518340322","cross_cats_sorted":["cs.DS","cs.LG","cs.NA","math.NA","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-12-23T21:40:01Z","title_canon_sha256":"6dfba7e3beb37d3a201a1e28fb50dd149fedc8b696513e0a5bf562e169c678d4"},"schema_version":"1.0","source":{"id":"2412.17997","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.17997","created_at":"2026-07-05T09:53:32Z"},{"alias_kind":"arxiv_version","alias_value":"2412.17997v1","created_at":"2026-07-05T09:53:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.17997","created_at":"2026-07-05T09:53:32Z"},{"alias_kind":"pith_short_12","alias_value":"4GZPH7NIS66Z","created_at":"2026-07-05T09:53:32Z"},{"alias_kind":"pith_short_16","alias_value":"4GZPH7NIS66ZT3DA","created_at":"2026-07-05T09:53:32Z"},{"alias_kind":"pith_short_8","alias_value":"4GZPH7NI","created_at":"2026-07-05T09:53:32Z"}],"graph_snapshots":[{"event_id":"sha256:30869da64452ce981ef3021e323c1b7488b595b10d87532cfb459cfd4eab5ee6","target":"graph","created_at":"2026-07-05T09:53:32Z","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/2412.17997/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Coupling arguments are a central tool for bounding the deviation between two stochastic processes, but traditionally have been limited to Wasserstein metrics. In this paper, we apply the shifted composition rule--an information-theoretic principle introduced in our earlier work--in order to adapt coupling arguments to the Kullback-Leibler (KL) divergence. Our framework combine the strengths of two previously disparate approaches: local error analysis and Girsanov's theorem. Akin to the former, it yields tight bounds by incorporating the so-called weak error, and is user-friendly in that it onl","authors_text":"Jason M. Altschuler, Sinho Chewi","cross_cats":["cs.DS","cs.LG","cs.NA","math.NA","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-12-23T21:40:01Z","title":"Shifted Composition III: Local Error Framework for KL Divergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.17997","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:bc0c4aa2c2cec286f1b60898223d2e08c3968662c09c8143dcc95a48952738c1","target":"record","created_at":"2026-07-05T09:53:32Z","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":"d22ecc919b72ccddbda0bdc6a08537c44b92b2906521a1e911e72fa518340322","cross_cats_sorted":["cs.DS","cs.LG","cs.NA","math.NA","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-12-23T21:40:01Z","title_canon_sha256":"6dfba7e3beb37d3a201a1e28fb50dd149fedc8b696513e0a5bf562e169c678d4"},"schema_version":"1.0","source":{"id":"2412.17997","kind":"arxiv","version":1}},"canonical_sha256":"e1b2f3fda897bd99ec60a9c53c926b8a7949cd8d993d9bac92d12798fa4defb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1b2f3fda897bd99ec60a9c53c926b8a7949cd8d993d9bac92d12798fa4defb9","first_computed_at":"2026-07-05T09:53:32.137589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:53:32.137589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GZUPxwFVYXQfg4QxuJ9rhUzFTlirZ/zmEkv6CiGV2WgkTN7wr9ZKYZMfEaIsbl/uvny3YOBcHAo95EtrxugSDA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:53:32.138023Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.17997","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc0c4aa2c2cec286f1b60898223d2e08c3968662c09c8143dcc95a48952738c1","sha256:30869da64452ce981ef3021e323c1b7488b595b10d87532cfb459cfd4eab5ee6"],"state_sha256":"ccb3b8f22fcb46f1782c895609e9d450e0cb4fad01f86cc8dd02c9dc250dae4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RIL2k8tCDcDF1MtIiQdpojsR9ms9QVeHGGwqPVc12FqbCC6yHJm9GR+CHPeRqdL3F3mZFgGw4odRCryj/Jv2AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T12:43:57.229532Z","bundle_sha256":"61102fcffa5b719730680939e8f8c8378a154cc92dfc0afe6d03a1b4bd0e9df3"}}