{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:P4HYBNIFP2LKZUTSBL45XBH4SS","short_pith_number":"pith:P4HYBNIF","canonical_record":{"source":{"id":"1502.04915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-17T15:08:21Z","cross_cats_sorted":[],"title_canon_sha256":"1fb37f6dc325e1fa20ad6cffa91c4ab1932356fec54a7e8fd7ea74b53be1bdf3","abstract_canon_sha256":"dd96356323d3b02cb9406d05cd3872422fcb59d3b47807d8d2555e91361bffd4"},"schema_version":"1.0"},"canonical_sha256":"7f0f80b5057e96acd2720af9db84fc94932eda2e74beb0f25b14de74d9a36f59","source":{"kind":"arxiv","id":"1502.04915","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04915","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04915v1","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04915","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"P4HYBNIFP2LK","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P4HYBNIFP2LKZUTS","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P4HYBNIF","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:P4HYBNIFP2LKZUTSBL45XBH4SS","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-17T15:08:21Z","cross_cats_sorted":[],"title_canon_sha256":"1fb37f6dc325e1fa20ad6cffa91c4ab1932356fec54a7e8fd7ea74b53be1bdf3","abstract_canon_sha256":"dd96356323d3b02cb9406d05cd3872422fcb59d3b47807d8d2555e91361bffd4"},"schema_version":"1.0"},"canonical_sha256":"7f0f80b5057e96acd2720af9db84fc94932eda2e74beb0f25b14de74d9a36f59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:53.528967Z","signature_b64":"IVDP7F6AoqwnyTuMDkxA2E//iy5me6qbzMDcAWBQmmj2/tODDncq8iR1ONIjDSci4wfSjJRUEGNWQ1uPDz+yAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f0f80b5057e96acd2720af9db84fc94932eda2e74beb0f25b14de74d9a36f59","last_reissued_at":"2026-05-18T02:26:53.528569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:53.528569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04915","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":"2026-05-18T02:26:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fLQX6aPr0tWdH8ZDncKA8rdmypOHCCbcQSgXUHpQgCGHUZpbgydRrDoEab9wzAethz0EgMy8QYqX8GVapKGnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:06:15.427661Z"},"content_sha256":"9370e0f8e67797cc0d99e03ed9395196cb9818d7e1c2f24f10b00fbb083ff8cd","schema_version":"1.0","event_id":"sha256:9370e0f8e67797cc0d99e03ed9395196cb9818d7e1c2f24f10b00fbb083ff8cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:P4HYBNIFP2LKZUTSBL45XBH4SS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A class of stochastic differential equations with super-linear growth and non-Lipschitz coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Antoine Hakassou, Khaled Bahlali, Youssef Ouknine","submitted_at":"2015-02-17T15:08:21Z","abstract_excerpt":"The purpose of this paper is to study some properties of solutions to one dimensional as well as multidimensional stochastic differential equations (SDEs in short) with super-linear growth conditions on the coefficients. Taking inspiration from \\cite{BEHP, KBahlali, Bahlali}, we introduce a new {\\it{local condition}} which ensures the pathwise uniqueness, as well as the non-contact property. We moreover show that the solution produces a stochastic flow of continuous maps and satisfies a large deviations principle of Freidlin-Wentzell type. Our conditions on the coefficients go beyond the exist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04915","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":"2026-05-18T02:26:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l7oIZCmHPZn9k3tdlX9F5/hQ+eEhX23Gta/hFHwGl07FFhJu+TTe0Qk1DEydCCdh68na6q71a6anl6hn5FJ3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:06:15.428000Z"},"content_sha256":"63019e57cfa7540996f4e90879c3bcbcf4b94ed73c2cd8c03108257b57289e97","schema_version":"1.0","event_id":"sha256:63019e57cfa7540996f4e90879c3bcbcf4b94ed73c2cd8c03108257b57289e97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P4HYBNIFP2LKZUTSBL45XBH4SS/bundle.json","state_url":"https://pith.science/pith/P4HYBNIFP2LKZUTSBL45XBH4SS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P4HYBNIFP2LKZUTSBL45XBH4SS/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":"2026-06-02T23:06:15Z","links":{"resolver":"https://pith.science/pith/P4HYBNIFP2LKZUTSBL45XBH4SS","bundle":"https://pith.science/pith/P4HYBNIFP2LKZUTSBL45XBH4SS/bundle.json","state":"https://pith.science/pith/P4HYBNIFP2LKZUTSBL45XBH4SS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P4HYBNIFP2LKZUTSBL45XBH4SS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P4HYBNIFP2LKZUTSBL45XBH4SS","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":"dd96356323d3b02cb9406d05cd3872422fcb59d3b47807d8d2555e91361bffd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-17T15:08:21Z","title_canon_sha256":"1fb37f6dc325e1fa20ad6cffa91c4ab1932356fec54a7e8fd7ea74b53be1bdf3"},"schema_version":"1.0","source":{"id":"1502.04915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04915","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04915v1","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04915","created_at":"2026-05-18T02:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"P4HYBNIFP2LK","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P4HYBNIFP2LKZUTS","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P4HYBNIF","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:63019e57cfa7540996f4e90879c3bcbcf4b94ed73c2cd8c03108257b57289e97","target":"graph","created_at":"2026-05-18T02:26:53Z","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":"The purpose of this paper is to study some properties of solutions to one dimensional as well as multidimensional stochastic differential equations (SDEs in short) with super-linear growth conditions on the coefficients. Taking inspiration from \\cite{BEHP, KBahlali, Bahlali}, we introduce a new {\\it{local condition}} which ensures the pathwise uniqueness, as well as the non-contact property. We moreover show that the solution produces a stochastic flow of continuous maps and satisfies a large deviations principle of Freidlin-Wentzell type. Our conditions on the coefficients go beyond the exist","authors_text":"Antoine Hakassou, Khaled Bahlali, Youssef Ouknine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-17T15:08:21Z","title":"A class of stochastic differential equations with super-linear growth and non-Lipschitz coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04915","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":"sha256:9370e0f8e67797cc0d99e03ed9395196cb9818d7e1c2f24f10b00fbb083ff8cd","target":"record","created_at":"2026-05-18T02:26:53Z","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":"dd96356323d3b02cb9406d05cd3872422fcb59d3b47807d8d2555e91361bffd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-17T15:08:21Z","title_canon_sha256":"1fb37f6dc325e1fa20ad6cffa91c4ab1932356fec54a7e8fd7ea74b53be1bdf3"},"schema_version":"1.0","source":{"id":"1502.04915","kind":"arxiv","version":1}},"canonical_sha256":"7f0f80b5057e96acd2720af9db84fc94932eda2e74beb0f25b14de74d9a36f59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f0f80b5057e96acd2720af9db84fc94932eda2e74beb0f25b14de74d9a36f59","first_computed_at":"2026-05-18T02:26:53.528569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:53.528569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IVDP7F6AoqwnyTuMDkxA2E//iy5me6qbzMDcAWBQmmj2/tODDncq8iR1ONIjDSci4wfSjJRUEGNWQ1uPDz+yAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:53.528967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9370e0f8e67797cc0d99e03ed9395196cb9818d7e1c2f24f10b00fbb083ff8cd","sha256:63019e57cfa7540996f4e90879c3bcbcf4b94ed73c2cd8c03108257b57289e97"],"state_sha256":"a0f3a2c41e1065afaaae8971007d673d0a713408fd81149a5c4d1f62432107b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2cfAHmIzjivQY8y2KAUAjwkiLNS4yYo65wpiONhVEjhn6ttRwiRtB41KUh6JgxXe3/A0LHV2SzIq9pn9foH/Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:06:15.429884Z","bundle_sha256":"5351f1828dee46aca6105e021c1f107df9bb74ce9e6c3ac932ae7a21c15cb847"}}