{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YKVKY62RSEV7ZIO32W3Z3BMZXO","short_pith_number":"pith:YKVKY62R","canonical_record":{"source":{"id":"1709.05241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-15T14:49:14Z","cross_cats_sorted":[],"title_canon_sha256":"b7f318085a323d0a85b3b3772e3b328203490e3764635f2eafb981b9e149bce0","abstract_canon_sha256":"bf9d32afd1b3599190787859d039d094cb079a34599861e6d92ebfbc77dc5700"},"schema_version":"1.0"},"canonical_sha256":"c2aaac7b51912bfca1dbd5b79d8599bbbb2d304f62c2cea876abbcaf0fe44db5","source":{"kind":"arxiv","id":"1709.05241","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05241","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05241v1","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05241","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"YKVKY62RSEV7","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YKVKY62RSEV7ZIO3","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YKVKY62R","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YKVKY62RSEV7ZIO32W3Z3BMZXO","target":"record","payload":{"canonical_record":{"source":{"id":"1709.05241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-15T14:49:14Z","cross_cats_sorted":[],"title_canon_sha256":"b7f318085a323d0a85b3b3772e3b328203490e3764635f2eafb981b9e149bce0","abstract_canon_sha256":"bf9d32afd1b3599190787859d039d094cb079a34599861e6d92ebfbc77dc5700"},"schema_version":"1.0"},"canonical_sha256":"c2aaac7b51912bfca1dbd5b79d8599bbbb2d304f62c2cea876abbcaf0fe44db5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:06.260078Z","signature_b64":"XOffVRtWV8T3zWz6HY4+adC16LqYSeXMRIBMfJtobMHada88nHx7MyXhsbKYmOSLbP3Y9YaUk8j6Jvf+YpSQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2aaac7b51912bfca1dbd5b79d8599bbbb2d304f62c2cea876abbcaf0fe44db5","last_reissued_at":"2026-05-18T00:35:06.259492Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:06.259492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.05241","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":"2026-05-18T00:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mPWQwFw/4keLpzt48aLDXLUDcPLKldSplkuTj2GEECEhwjX6WtMGcyFdlISrQoo1N3ANt80J0huDs4++gyEVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T11:23:23.045709Z"},"content_sha256":"9efd952e355babe7720dcee87676a29cbded264951631988796854e3b736a182","schema_version":"1.0","event_id":"sha256:9efd952e355babe7720dcee87676a29cbded264951631988796854e3b736a182"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YKVKY62RSEV7ZIO32W3Z3BMZXO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differential equations driven by rough paths with jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Huilin Zhang, Peter K. Friz","submitted_at":"2017-09-15T14:49:14Z","abstract_excerpt":"We develop the rough path counterpart of It\\^o stochastic integration and - differential equations driven by general semimartingales. This significantly enlarges the classes of (It\\^o / forward) stochastic differential equations treatable with pathwise methods. A number of applications are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05241","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":"2026-05-18T00:35:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vnYkYwtmYeglfQFUcKrrpZy8GzavxF49ET+b8Xt0nVP4mbNK/ih5n49oye/Idse/laq51+KycOdVt9WHHEkDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T11:23:23.046042Z"},"content_sha256":"49d8d14806fdd54abca1836083fdacf9520aa1f4fa06217f6b79274a60e5ae1b","schema_version":"1.0","event_id":"sha256:49d8d14806fdd54abca1836083fdacf9520aa1f4fa06217f6b79274a60e5ae1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YKVKY62RSEV7ZIO32W3Z3BMZXO/bundle.json","state_url":"https://pith.science/pith/YKVKY62RSEV7ZIO32W3Z3BMZXO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YKVKY62RSEV7ZIO32W3Z3BMZXO/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":"2026-06-08T11:23:23Z","links":{"resolver":"https://pith.science/pith/YKVKY62RSEV7ZIO32W3Z3BMZXO","bundle":"https://pith.science/pith/YKVKY62RSEV7ZIO32W3Z3BMZXO/bundle.json","state":"https://pith.science/pith/YKVKY62RSEV7ZIO32W3Z3BMZXO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YKVKY62RSEV7ZIO32W3Z3BMZXO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YKVKY62RSEV7ZIO32W3Z3BMZXO","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":"bf9d32afd1b3599190787859d039d094cb079a34599861e6d92ebfbc77dc5700","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-15T14:49:14Z","title_canon_sha256":"b7f318085a323d0a85b3b3772e3b328203490e3764635f2eafb981b9e149bce0"},"schema_version":"1.0","source":{"id":"1709.05241","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05241","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05241v1","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05241","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"YKVKY62RSEV7","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YKVKY62RSEV7ZIO3","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YKVKY62R","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:49d8d14806fdd54abca1836083fdacf9520aa1f4fa06217f6b79274a60e5ae1b","target":"graph","created_at":"2026-05-18T00:35:06Z","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":"We develop the rough path counterpart of It\\^o stochastic integration and - differential equations driven by general semimartingales. This significantly enlarges the classes of (It\\^o / forward) stochastic differential equations treatable with pathwise methods. A number of applications are discussed.","authors_text":"Huilin Zhang, Peter K. Friz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-15T14:49:14Z","title":"Differential equations driven by rough paths with jumps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05241","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":"sha256:9efd952e355babe7720dcee87676a29cbded264951631988796854e3b736a182","target":"record","created_at":"2026-05-18T00:35:06Z","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":"bf9d32afd1b3599190787859d039d094cb079a34599861e6d92ebfbc77dc5700","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-15T14:49:14Z","title_canon_sha256":"b7f318085a323d0a85b3b3772e3b328203490e3764635f2eafb981b9e149bce0"},"schema_version":"1.0","source":{"id":"1709.05241","kind":"arxiv","version":1}},"canonical_sha256":"c2aaac7b51912bfca1dbd5b79d8599bbbb2d304f62c2cea876abbcaf0fe44db5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2aaac7b51912bfca1dbd5b79d8599bbbb2d304f62c2cea876abbcaf0fe44db5","first_computed_at":"2026-05-18T00:35:06.259492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:06.259492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XOffVRtWV8T3zWz6HY4+adC16LqYSeXMRIBMfJtobMHada88nHx7MyXhsbKYmOSLbP3Y9YaUk8j6Jvf+YpSQDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:06.260078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05241","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9efd952e355babe7720dcee87676a29cbded264951631988796854e3b736a182","sha256:49d8d14806fdd54abca1836083fdacf9520aa1f4fa06217f6b79274a60e5ae1b"],"state_sha256":"ab62afbdb17b65b79fd8bb475ee680de86ddebf20058b9da6c7882958c4779f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ZNVb6VQE+8kdmr/PS8ZBUnBVDcFHi1eiTJSh9YPlM4B92yOX4bV9NyZ7HnrhYx5TEY+2ZjVzCawU7A4bWuPBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T11:23:23.047828Z","bundle_sha256":"075788c993568e37e6dc5633b788e26780a3580ec625a0751da736f3fb3faae3"}}