{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:EMSZCJDTBWMEWJ2IHT6BOQIFJG","short_pith_number":"pith:EMSZCJDT","canonical_record":{"source":{"id":"1904.02940","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-05T08:56:42Z","cross_cats_sorted":[],"title_canon_sha256":"d5234a16240fb723eafd67ade4352ea332cf791c8bab0ca35e3f5cb4bb769bee","abstract_canon_sha256":"578a5a8b8fc0a37c1768f0c01432e2a248862197270e767797438207296ffd9d"},"schema_version":"1.0"},"canonical_sha256":"23259124730d984b27483cfc17410549bc0c6c846e57eefb6d2f782e9a81f54b","source":{"kind":"arxiv","id":"1904.02940","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02940","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02940v1","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02940","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"pith_short_12","alias_value":"EMSZCJDTBWME","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EMSZCJDTBWMEWJ2I","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EMSZCJDT","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:EMSZCJDTBWMEWJ2IHT6BOQIFJG","target":"record","payload":{"canonical_record":{"source":{"id":"1904.02940","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-05T08:56:42Z","cross_cats_sorted":[],"title_canon_sha256":"d5234a16240fb723eafd67ade4352ea332cf791c8bab0ca35e3f5cb4bb769bee","abstract_canon_sha256":"578a5a8b8fc0a37c1768f0c01432e2a248862197270e767797438207296ffd9d"},"schema_version":"1.0"},"canonical_sha256":"23259124730d984b27483cfc17410549bc0c6c846e57eefb6d2f782e9a81f54b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:19.148124Z","signature_b64":"oNFESr0HkxvJ3KA4zIiy3rI3dxgtleptGtSUIaXp/dDRQ3yCSNYjpRMyzNpg2SPRCrm60fcMMSsZrNaL2I9oDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23259124730d984b27483cfc17410549bc0c6c846e57eefb6d2f782e9a81f54b","last_reissued_at":"2026-05-17T23:49:19.147480Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:19.147480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.02940","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":"2026-05-17T23:49:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3C7SpPnZ5emDBtAkljfRD+gkvZgbfIte6yyJCtrJBPk6K47xK642lDrSlnUr3OrBjlLLE2CNd/8ooLnG9D8GDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T19:05:32.121413Z"},"content_sha256":"ba4434b39b6a4a5fd1568d92bc7216c28286feac4149153761e4580462d1543d","schema_version":"1.0","event_id":"sha256:ba4434b39b6a4a5fd1568d92bc7216c28286feac4149153761e4580462d1543d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:EMSZCJDTBWMEWJ2IHT6BOQIFJG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit Theorems for Additive Functionals of Path-Dependent SDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chenggui Yuan, Feng-Yu Wang, Jianhai Bao","submitted_at":"2019-04-05T08:56:42Z","abstract_excerpt":"By using limit theorems of uniform mixing Markov processes and martingale difference sequences, the strong law of large numbers, central limit theorem, and the law of iterated logarithm are established for additive functionals of path-dependent stochastic differential equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02940","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":"2026-05-17T23:49:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fUDipA1l1MrA13Lop1ZreNBzKw65nzp/ww186briEN8AXTQfRKXuHTrE9fzf6DK7/QwVR+ZTS3KdsDsAA99WDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T19:05:32.122064Z"},"content_sha256":"f3905c86c5e6bf852af315ee62e2fda5581b1973e00cf8b058fe2444e3153493","schema_version":"1.0","event_id":"sha256:f3905c86c5e6bf852af315ee62e2fda5581b1973e00cf8b058fe2444e3153493"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EMSZCJDTBWMEWJ2IHT6BOQIFJG/bundle.json","state_url":"https://pith.science/pith/EMSZCJDTBWMEWJ2IHT6BOQIFJG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EMSZCJDTBWMEWJ2IHT6BOQIFJG/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":"2026-05-23T19:05:32Z","links":{"resolver":"https://pith.science/pith/EMSZCJDTBWMEWJ2IHT6BOQIFJG","bundle":"https://pith.science/pith/EMSZCJDTBWMEWJ2IHT6BOQIFJG/bundle.json","state":"https://pith.science/pith/EMSZCJDTBWMEWJ2IHT6BOQIFJG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EMSZCJDTBWMEWJ2IHT6BOQIFJG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:EMSZCJDTBWMEWJ2IHT6BOQIFJG","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":"578a5a8b8fc0a37c1768f0c01432e2a248862197270e767797438207296ffd9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-05T08:56:42Z","title_canon_sha256":"d5234a16240fb723eafd67ade4352ea332cf791c8bab0ca35e3f5cb4bb769bee"},"schema_version":"1.0","source":{"id":"1904.02940","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02940","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02940v1","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02940","created_at":"2026-05-17T23:49:19Z"},{"alias_kind":"pith_short_12","alias_value":"EMSZCJDTBWME","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EMSZCJDTBWMEWJ2I","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EMSZCJDT","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:f3905c86c5e6bf852af315ee62e2fda5581b1973e00cf8b058fe2444e3153493","target":"graph","created_at":"2026-05-17T23:49:19Z","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":"By using limit theorems of uniform mixing Markov processes and martingale difference sequences, the strong law of large numbers, central limit theorem, and the law of iterated logarithm are established for additive functionals of path-dependent stochastic differential equations.","authors_text":"Chenggui Yuan, Feng-Yu Wang, Jianhai Bao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-05T08:56:42Z","title":"Limit Theorems for Additive Functionals of Path-Dependent SDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02940","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:ba4434b39b6a4a5fd1568d92bc7216c28286feac4149153761e4580462d1543d","target":"record","created_at":"2026-05-17T23:49:19Z","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":"578a5a8b8fc0a37c1768f0c01432e2a248862197270e767797438207296ffd9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-05T08:56:42Z","title_canon_sha256":"d5234a16240fb723eafd67ade4352ea332cf791c8bab0ca35e3f5cb4bb769bee"},"schema_version":"1.0","source":{"id":"1904.02940","kind":"arxiv","version":1}},"canonical_sha256":"23259124730d984b27483cfc17410549bc0c6c846e57eefb6d2f782e9a81f54b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23259124730d984b27483cfc17410549bc0c6c846e57eefb6d2f782e9a81f54b","first_computed_at":"2026-05-17T23:49:19.147480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:19.147480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oNFESr0HkxvJ3KA4zIiy3rI3dxgtleptGtSUIaXp/dDRQ3yCSNYjpRMyzNpg2SPRCrm60fcMMSsZrNaL2I9oDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:19.148124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02940","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba4434b39b6a4a5fd1568d92bc7216c28286feac4149153761e4580462d1543d","sha256:f3905c86c5e6bf852af315ee62e2fda5581b1973e00cf8b058fe2444e3153493"],"state_sha256":"eccf5180a32a33ffc82d139d1e2713b83082abf3c6f57abe7b6ccaac2f1f13ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bz2WjjLciuXad+B43k6Ic1eUNocpzZbejOU1vtE/Zb9GWpH79VQtoCWLFo7uP1H/PqYuZCJyS+rFX3io609EDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T19:05:32.125635Z","bundle_sha256":"b9bad4d64fba66606c16bce13df5b86a2578ed75708e3fd3f1cbe8ec72946e14"}}