{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:HT5DVXC6FD2US3DJ4APPNETBDI","short_pith_number":"pith:HT5DVXC6","canonical_record":{"source":{"id":"2107.14384","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-30T01:18:58Z","cross_cats_sorted":[],"title_canon_sha256":"1ac9019ad229a6e01949f625801cf5c8bfe5c49081be257052b20d8bcfa135ce","abstract_canon_sha256":"a1c0520c4ae1978f2307e9b71b10432d9113295a94a95e81931114a43a3228f2"},"schema_version":"1.0"},"canonical_sha256":"3cfa3adc5e28f5496c69e01ef692611a276d98539cbd505bcade5eb802dba198","source":{"kind":"arxiv","id":"2107.14384","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.14384","created_at":"2026-07-05T03:01:59Z"},{"alias_kind":"arxiv_version","alias_value":"2107.14384v1","created_at":"2026-07-05T03:01:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.14384","created_at":"2026-07-05T03:01:59Z"},{"alias_kind":"pith_short_12","alias_value":"HT5DVXC6FD2U","created_at":"2026-07-05T03:01:59Z"},{"alias_kind":"pith_short_16","alias_value":"HT5DVXC6FD2US3DJ","created_at":"2026-07-05T03:01:59Z"},{"alias_kind":"pith_short_8","alias_value":"HT5DVXC6","created_at":"2026-07-05T03:01:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:HT5DVXC6FD2US3DJ4APPNETBDI","target":"record","payload":{"canonical_record":{"source":{"id":"2107.14384","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-30T01:18:58Z","cross_cats_sorted":[],"title_canon_sha256":"1ac9019ad229a6e01949f625801cf5c8bfe5c49081be257052b20d8bcfa135ce","abstract_canon_sha256":"a1c0520c4ae1978f2307e9b71b10432d9113295a94a95e81931114a43a3228f2"},"schema_version":"1.0"},"canonical_sha256":"3cfa3adc5e28f5496c69e01ef692611a276d98539cbd505bcade5eb802dba198","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:01:59.783649Z","signature_b64":"u14qhOUgX+j8BgnBsL/IDDYzgMvCOWwqxO+xAeyK52sO/KT5cEONZY/JIIeBsgmOaxfX4M1svY3L8BKqGXoaAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cfa3adc5e28f5496c69e01ef692611a276d98539cbd505bcade5eb802dba198","last_reissued_at":"2026-07-05T03:01:59.783291Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:01:59.783291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.14384","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":"2026-07-05T03:01:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6jQlyE3ra4KaJOsWw1qIwtkyvlK5wG3dJMrMsTErHP6TvnKTq9WIFXs+JUllKd0JjbK3ubnrf/tdweSMEV2sCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:16:58.660555Z"},"content_sha256":"df61541355cdee15c151756e8d5b00a41a9a5081eaf01394cc1d25b63947c74b","schema_version":"1.0","event_id":"sha256:df61541355cdee15c151756e8d5b00a41a9a5081eaf01394cc1d25b63947c74b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:HT5DVXC6FD2US3DJ4APPNETBDI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of strong solutions for It\\^o's stochastic equations via approximations. Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"I. Gy\\\"ongy, N.V. Krylov","submitted_at":"2021-07-30T01:18:58Z","abstract_excerpt":"Given strong uniqueness for an It\\^o's stochastic equation, we prove that its solution can beconstructed on \"any\" probability space by using, for example, Euler's polygonal approximations. Stochastic equations in $\\mathbb{R}^{d}$ and in domains in $\\mathbb{R}^{d}$ are considered. This is almost a copy of an old article in which we correct errors in the original proof of Lemma 4.1 found by Martin Dieckmann in 2013. We present also a new result on the convergence of \"tamed Euler approximations\" for SDEs with locally unbounded drifts, which we achieve by proving an estimate for appropriate expone"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.14384","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/2107.14384/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":"2026-07-05T03:01:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6VDwWIRBROyd3TkS6XkHTPPCHvebfui19SE0Y/nRQxDPRZVA8yyEGw2De9RnG+bLodcX+UCPOAcJyCjpwtPeDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:16:58.661083Z"},"content_sha256":"0ae4e23c3a600aace5f485e72f5811bbb75d13fe78501759268aaef981e3874c","schema_version":"1.0","event_id":"sha256:0ae4e23c3a600aace5f485e72f5811bbb75d13fe78501759268aaef981e3874c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HT5DVXC6FD2US3DJ4APPNETBDI/bundle.json","state_url":"https://pith.science/pith/HT5DVXC6FD2US3DJ4APPNETBDI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HT5DVXC6FD2US3DJ4APPNETBDI/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":"2026-08-07T23:16:58Z","links":{"resolver":"https://pith.science/pith/HT5DVXC6FD2US3DJ4APPNETBDI","bundle":"https://pith.science/pith/HT5DVXC6FD2US3DJ4APPNETBDI/bundle.json","state":"https://pith.science/pith/HT5DVXC6FD2US3DJ4APPNETBDI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HT5DVXC6FD2US3DJ4APPNETBDI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:HT5DVXC6FD2US3DJ4APPNETBDI","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":"a1c0520c4ae1978f2307e9b71b10432d9113295a94a95e81931114a43a3228f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-30T01:18:58Z","title_canon_sha256":"1ac9019ad229a6e01949f625801cf5c8bfe5c49081be257052b20d8bcfa135ce"},"schema_version":"1.0","source":{"id":"2107.14384","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.14384","created_at":"2026-07-05T03:01:59Z"},{"alias_kind":"arxiv_version","alias_value":"2107.14384v1","created_at":"2026-07-05T03:01:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.14384","created_at":"2026-07-05T03:01:59Z"},{"alias_kind":"pith_short_12","alias_value":"HT5DVXC6FD2U","created_at":"2026-07-05T03:01:59Z"},{"alias_kind":"pith_short_16","alias_value":"HT5DVXC6FD2US3DJ","created_at":"2026-07-05T03:01:59Z"},{"alias_kind":"pith_short_8","alias_value":"HT5DVXC6","created_at":"2026-07-05T03:01:59Z"}],"graph_snapshots":[{"event_id":"sha256:0ae4e23c3a600aace5f485e72f5811bbb75d13fe78501759268aaef981e3874c","target":"graph","created_at":"2026-07-05T03:01:59Z","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/2107.14384/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given strong uniqueness for an It\\^o's stochastic equation, we prove that its solution can beconstructed on \"any\" probability space by using, for example, Euler's polygonal approximations. Stochastic equations in $\\mathbb{R}^{d}$ and in domains in $\\mathbb{R}^{d}$ are considered. This is almost a copy of an old article in which we correct errors in the original proof of Lemma 4.1 found by Martin Dieckmann in 2013. We present also a new result on the convergence of \"tamed Euler approximations\" for SDEs with locally unbounded drifts, which we achieve by proving an estimate for appropriate expone","authors_text":"I. Gy\\\"ongy, N.V. Krylov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-30T01:18:58Z","title":"Existence of strong solutions for It\\^o's stochastic equations via approximations. Revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.14384","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:df61541355cdee15c151756e8d5b00a41a9a5081eaf01394cc1d25b63947c74b","target":"record","created_at":"2026-07-05T03:01:59Z","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":"a1c0520c4ae1978f2307e9b71b10432d9113295a94a95e81931114a43a3228f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-07-30T01:18:58Z","title_canon_sha256":"1ac9019ad229a6e01949f625801cf5c8bfe5c49081be257052b20d8bcfa135ce"},"schema_version":"1.0","source":{"id":"2107.14384","kind":"arxiv","version":1}},"canonical_sha256":"3cfa3adc5e28f5496c69e01ef692611a276d98539cbd505bcade5eb802dba198","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cfa3adc5e28f5496c69e01ef692611a276d98539cbd505bcade5eb802dba198","first_computed_at":"2026-07-05T03:01:59.783291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:01:59.783291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u14qhOUgX+j8BgnBsL/IDDYzgMvCOWwqxO+xAeyK52sO/KT5cEONZY/JIIeBsgmOaxfX4M1svY3L8BKqGXoaAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:01:59.783649Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.14384","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df61541355cdee15c151756e8d5b00a41a9a5081eaf01394cc1d25b63947c74b","sha256:0ae4e23c3a600aace5f485e72f5811bbb75d13fe78501759268aaef981e3874c"],"state_sha256":"5b5cb6450bfbac719988a9caeb73192f2fc8f03e4a01d554529326226048a800"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QvV57xNxZH0CavdOnfqbKa17EnxTV/WQKKxhe6U3cjQLeAGUriIP5kul+YchZpLywx2HX2ZDi7kQn+A+FBR1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T23:16:58.665445Z","bundle_sha256":"f4f445d6dc3cc1ba81f37403a0f0d21633bd7ee0c81c5075d3857a4fb7fc073f"}}