{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MIMMGUVHDZW3R3MQIJDNMWW3HP","short_pith_number":"pith:MIMMGUVH","canonical_record":{"source":{"id":"1904.11526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-25T18:26:20Z","cross_cats_sorted":[],"title_canon_sha256":"1dfc5694b9735295959ce52cc4aff6e62c3899636257e6d7ab958dda977fc07c","abstract_canon_sha256":"7bc7709a7c5e38f83806e8356167ca5acfdbca93cc6eb92096a3800a5bb95b4e"},"schema_version":"1.0"},"canonical_sha256":"6218c352a71e6db8ed904246d65adb3bf7092a3819158e765129e735c85ff150","source":{"kind":"arxiv","id":"1904.11526","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11526","created_at":"2026-05-17T23:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11526v1","created_at":"2026-05-17T23:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11526","created_at":"2026-05-17T23:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"MIMMGUVHDZW3","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MIMMGUVHDZW3R3MQ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MIMMGUVH","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MIMMGUVHDZW3R3MQIJDNMWW3HP","target":"record","payload":{"canonical_record":{"source":{"id":"1904.11526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-25T18:26:20Z","cross_cats_sorted":[],"title_canon_sha256":"1dfc5694b9735295959ce52cc4aff6e62c3899636257e6d7ab958dda977fc07c","abstract_canon_sha256":"7bc7709a7c5e38f83806e8356167ca5acfdbca93cc6eb92096a3800a5bb95b4e"},"schema_version":"1.0"},"canonical_sha256":"6218c352a71e6db8ed904246d65adb3bf7092a3819158e765129e735c85ff150","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:43.482936Z","signature_b64":"ynN4SlaAOe5nXtBuWk0ABhboTPoEw12v5N0EBISXMlMJwwaNx/EihyPCi0ShpI6slY/HgQOzne66RmanLVkwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6218c352a71e6db8ed904246d65adb3bf7092a3819158e765129e735c85ff150","last_reissued_at":"2026-05-17T23:47:43.482454Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:43.482454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.11526","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":"2026-05-17T23:47:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MvLNXNn98T9Bmf68PEnpxYc1Y9cj90m3JpKhPFECBksn+fstLltiqoy6E2Q8779UWs5od/B3dRkRv4kcyNKbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:50:55.478995Z"},"content_sha256":"3fc2e81d5ad461cbae37d9ceddbdd30438b05ee245fea5df3b02cf379aa085cd","schema_version":"1.0","event_id":"sha256:3fc2e81d5ad461cbae37d9ceddbdd30438b05ee245fea5df3b02cf379aa085cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MIMMGUVHDZW3R3MQIJDNMWW3HP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On nonlinear rough paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Panqiu Xia","submitted_at":"2019-04-25T18:26:20Z","abstract_excerpt":"In this paper, we establish the theory of nonlinear rough paths. We give the definition of nonlinear rough paths, and develop the integrals. Then, we study differential equations driven by nonlinear rough paths. Afterwards, we compare the nonlinear rough paths and classic theory of linear rough paths. Finally, we apply this theory to rough partial differential equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11526","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":"2026-05-17T23:47:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FnC7AqtytFVE+s0ERKMCqZIa8PwVilvbStf7TDV1VAUHTT2/CrOr3mR94/areqlr7zQnZ8mVrXjow8DLEN6+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:50:55.479360Z"},"content_sha256":"553d5214736149a0090a2c32647df1725a511bbae1085e4f0e63360669247f85","schema_version":"1.0","event_id":"sha256:553d5214736149a0090a2c32647df1725a511bbae1085e4f0e63360669247f85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIMMGUVHDZW3R3MQIJDNMWW3HP/bundle.json","state_url":"https://pith.science/pith/MIMMGUVHDZW3R3MQIJDNMWW3HP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIMMGUVHDZW3R3MQIJDNMWW3HP/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":"2026-05-28T08:50:55Z","links":{"resolver":"https://pith.science/pith/MIMMGUVHDZW3R3MQIJDNMWW3HP","bundle":"https://pith.science/pith/MIMMGUVHDZW3R3MQIJDNMWW3HP/bundle.json","state":"https://pith.science/pith/MIMMGUVHDZW3R3MQIJDNMWW3HP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIMMGUVHDZW3R3MQIJDNMWW3HP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MIMMGUVHDZW3R3MQIJDNMWW3HP","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":"7bc7709a7c5e38f83806e8356167ca5acfdbca93cc6eb92096a3800a5bb95b4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-25T18:26:20Z","title_canon_sha256":"1dfc5694b9735295959ce52cc4aff6e62c3899636257e6d7ab958dda977fc07c"},"schema_version":"1.0","source":{"id":"1904.11526","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11526","created_at":"2026-05-17T23:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11526v1","created_at":"2026-05-17T23:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11526","created_at":"2026-05-17T23:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"MIMMGUVHDZW3","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MIMMGUVHDZW3R3MQ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MIMMGUVH","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:553d5214736149a0090a2c32647df1725a511bbae1085e4f0e63360669247f85","target":"graph","created_at":"2026-05-17T23:47:43Z","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":"In this paper, we establish the theory of nonlinear rough paths. We give the definition of nonlinear rough paths, and develop the integrals. Then, we study differential equations driven by nonlinear rough paths. Afterwards, we compare the nonlinear rough paths and classic theory of linear rough paths. Finally, we apply this theory to rough partial differential equations.","authors_text":"David Nualart, Panqiu Xia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-25T18:26:20Z","title":"On nonlinear rough paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11526","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":"sha256:3fc2e81d5ad461cbae37d9ceddbdd30438b05ee245fea5df3b02cf379aa085cd","target":"record","created_at":"2026-05-17T23:47:43Z","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":"7bc7709a7c5e38f83806e8356167ca5acfdbca93cc6eb92096a3800a5bb95b4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-25T18:26:20Z","title_canon_sha256":"1dfc5694b9735295959ce52cc4aff6e62c3899636257e6d7ab958dda977fc07c"},"schema_version":"1.0","source":{"id":"1904.11526","kind":"arxiv","version":1}},"canonical_sha256":"6218c352a71e6db8ed904246d65adb3bf7092a3819158e765129e735c85ff150","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6218c352a71e6db8ed904246d65adb3bf7092a3819158e765129e735c85ff150","first_computed_at":"2026-05-17T23:47:43.482454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:43.482454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ynN4SlaAOe5nXtBuWk0ABhboTPoEw12v5N0EBISXMlMJwwaNx/EihyPCi0ShpI6slY/HgQOzne66RmanLVkwDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:43.482936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.11526","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fc2e81d5ad461cbae37d9ceddbdd30438b05ee245fea5df3b02cf379aa085cd","sha256:553d5214736149a0090a2c32647df1725a511bbae1085e4f0e63360669247f85"],"state_sha256":"f3d62ecdf916b4b76a84b444ddae09444305de234839c1b9ee118e0e06cb7223"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lp3tHI+OVtQE6q2u/7OV2GKqe0Hy7XCDQa9yR5ffPNf1sg840zzvaGNCDTYEHuN9y8vOaHDG0mKhVHrJS2+SBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:50:55.481325Z","bundle_sha256":"9a731c307578e608c48ab5751685673de1a34e1e1e01131c0c7a07acbeb0a1e7"}}