{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QSYOBRUTWUWI4EJP6R6WTMSFWH","short_pith_number":"pith:QSYOBRUT","canonical_record":{"source":{"id":"2407.16980","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-24T03:53:23Z","cross_cats_sorted":[],"title_canon_sha256":"994b8858460a0ba77132790f09b227522c064e8cd79707c38d4f1fba0aac9d6d","abstract_canon_sha256":"ec1c6afdb74270e041cb44524aea09719784ee81cbb95cd24d09736f985b5ddb"},"schema_version":"1.0"},"canonical_sha256":"84b0e0c693b52c8e112ff47d69b245b1cb289b89faf1cbbb1c1bfdba6c241b75","source":{"kind":"arxiv","id":"2407.16980","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.16980","created_at":"2026-07-05T08:48:00Z"},{"alias_kind":"arxiv_version","alias_value":"2407.16980v1","created_at":"2026-07-05T08:48:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.16980","created_at":"2026-07-05T08:48:00Z"},{"alias_kind":"pith_short_12","alias_value":"QSYOBRUTWUWI","created_at":"2026-07-05T08:48:00Z"},{"alias_kind":"pith_short_16","alias_value":"QSYOBRUTWUWI4EJP","created_at":"2026-07-05T08:48:00Z"},{"alias_kind":"pith_short_8","alias_value":"QSYOBRUT","created_at":"2026-07-05T08:48:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QSYOBRUTWUWI4EJP6R6WTMSFWH","target":"record","payload":{"canonical_record":{"source":{"id":"2407.16980","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-24T03:53:23Z","cross_cats_sorted":[],"title_canon_sha256":"994b8858460a0ba77132790f09b227522c064e8cd79707c38d4f1fba0aac9d6d","abstract_canon_sha256":"ec1c6afdb74270e041cb44524aea09719784ee81cbb95cd24d09736f985b5ddb"},"schema_version":"1.0"},"canonical_sha256":"84b0e0c693b52c8e112ff47d69b245b1cb289b89faf1cbbb1c1bfdba6c241b75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:48:00.436253Z","signature_b64":"Ev5eKd4nEFBNETaigFoh7ngl6OF9RpVMRj9pSQNvkgtui5Sj0yOTElQvi1bCR6hxH4pcvGWYWBFBimAmf1uaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84b0e0c693b52c8e112ff47d69b245b1cb289b89faf1cbbb1c1bfdba6c241b75","last_reissued_at":"2026-07-05T08:48:00.435864Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:48:00.435864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.16980","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":"2026-07-05T08:48:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SNCtO1dERe0yuomt2A0p3zEQmZGxOq0LVrl678Xr+JD3SB7xDilnoCnuunyZJHN+dBsPs+pQVRabX+mskb26Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-25T11:24:36.012546Z"},"content_sha256":"b0eb252187a46c36455cccbec9d2f9985c7428617edd58f287b9f498a177bcda","schema_version":"1.0","event_id":"sha256:b0eb252187a46c36455cccbec9d2f9985c7428617edd58f287b9f498a177bcda"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QSYOBRUTWUWI4EJP6R6WTMSFWH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the rate of convergence of the martingale central limit theorem in Wasserstein distances","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xiaoqin Guo","submitted_at":"2024-07-24T03:53:23Z","abstract_excerpt":"For martingales with a wide range of integrability, we will quantify the rate of convergence of the central limit theorem via Wasserstein distances of order $r$, $1\\le r\\le 3$. Our bounds are in terms of Lyapunov's coefficients and the $\\mathscr L^{r/2}$ fluctuation of the total conditional variances. We will show that our Wasserstein-1 bound is optimal up to a multiplicative constant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16980","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/2407.16980/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":"2026-07-05T08:48:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VGB+qoj5dpOtZslWtIrD1B5Z31w5XXuc3iI+1B47zx+HP7l0J9BudQr9QyiyROYduy6tyDGamYhzF471bF5PDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-25T11:24:36.013209Z"},"content_sha256":"04b1b90c35514ee11d174881a75a33e7362236db6ac700758c76d90688daaa6e","schema_version":"1.0","event_id":"sha256:04b1b90c35514ee11d174881a75a33e7362236db6ac700758c76d90688daaa6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QSYOBRUTWUWI4EJP6R6WTMSFWH/bundle.json","state_url":"https://pith.science/pith/QSYOBRUTWUWI4EJP6R6WTMSFWH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QSYOBRUTWUWI4EJP6R6WTMSFWH/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":"2026-07-25T11:24:36Z","links":{"resolver":"https://pith.science/pith/QSYOBRUTWUWI4EJP6R6WTMSFWH","bundle":"https://pith.science/pith/QSYOBRUTWUWI4EJP6R6WTMSFWH/bundle.json","state":"https://pith.science/pith/QSYOBRUTWUWI4EJP6R6WTMSFWH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QSYOBRUTWUWI4EJP6R6WTMSFWH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QSYOBRUTWUWI4EJP6R6WTMSFWH","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":"ec1c6afdb74270e041cb44524aea09719784ee81cbb95cd24d09736f985b5ddb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-24T03:53:23Z","title_canon_sha256":"994b8858460a0ba77132790f09b227522c064e8cd79707c38d4f1fba0aac9d6d"},"schema_version":"1.0","source":{"id":"2407.16980","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.16980","created_at":"2026-07-05T08:48:00Z"},{"alias_kind":"arxiv_version","alias_value":"2407.16980v1","created_at":"2026-07-05T08:48:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.16980","created_at":"2026-07-05T08:48:00Z"},{"alias_kind":"pith_short_12","alias_value":"QSYOBRUTWUWI","created_at":"2026-07-05T08:48:00Z"},{"alias_kind":"pith_short_16","alias_value":"QSYOBRUTWUWI4EJP","created_at":"2026-07-05T08:48:00Z"},{"alias_kind":"pith_short_8","alias_value":"QSYOBRUT","created_at":"2026-07-05T08:48:00Z"}],"graph_snapshots":[{"event_id":"sha256:04b1b90c35514ee11d174881a75a33e7362236db6ac700758c76d90688daaa6e","target":"graph","created_at":"2026-07-05T08:48:00Z","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/2407.16980/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For martingales with a wide range of integrability, we will quantify the rate of convergence of the central limit theorem via Wasserstein distances of order $r$, $1\\le r\\le 3$. Our bounds are in terms of Lyapunov's coefficients and the $\\mathscr L^{r/2}$ fluctuation of the total conditional variances. We will show that our Wasserstein-1 bound is optimal up to a multiplicative constant.","authors_text":"Xiaoqin Guo","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-24T03:53:23Z","title":"On the rate of convergence of the martingale central limit theorem in Wasserstein distances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16980","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:b0eb252187a46c36455cccbec9d2f9985c7428617edd58f287b9f498a177bcda","target":"record","created_at":"2026-07-05T08:48:00Z","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":"ec1c6afdb74270e041cb44524aea09719784ee81cbb95cd24d09736f985b5ddb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-07-24T03:53:23Z","title_canon_sha256":"994b8858460a0ba77132790f09b227522c064e8cd79707c38d4f1fba0aac9d6d"},"schema_version":"1.0","source":{"id":"2407.16980","kind":"arxiv","version":1}},"canonical_sha256":"84b0e0c693b52c8e112ff47d69b245b1cb289b89faf1cbbb1c1bfdba6c241b75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84b0e0c693b52c8e112ff47d69b245b1cb289b89faf1cbbb1c1bfdba6c241b75","first_computed_at":"2026-07-05T08:48:00.435864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:48:00.435864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ev5eKd4nEFBNETaigFoh7ngl6OF9RpVMRj9pSQNvkgtui5Sj0yOTElQvi1bCR6hxH4pcvGWYWBFBimAmf1uaCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:48:00.436253Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.16980","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0eb252187a46c36455cccbec9d2f9985c7428617edd58f287b9f498a177bcda","sha256:04b1b90c35514ee11d174881a75a33e7362236db6ac700758c76d90688daaa6e"],"state_sha256":"1bf3294684dac988281c8c1f105785a2756a31eb090554a84da58d0f15afe1a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yq9ThkPtmnjceAnpZ9upMFtKxOroLf5ynLQSAwZ3+9eQQxZVa/Dsi7fcn/i//oOFuuI+/APDFjuLxa3JDbeeCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-25T11:24:36.016234Z","bundle_sha256":"ba41793daf36c1acc22c05bc279c80bfab4242064881df607906d4c966d87a4c"}}