{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4WR3ZXZPYDWFFTDZBHVFUIFJEI","short_pith_number":"pith:4WR3ZXZP","canonical_record":{"source":{"id":"1708.06141","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T10:21:25Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"8a78d5825ad761045734c903a47aaaf2854cf2ccba925bc41ca701b292a7fb48","abstract_canon_sha256":"7786303370714c687c123bd30b741aae886dddde87e511417c2660fee2a57501"},"schema_version":"1.0"},"canonical_sha256":"e5a3bcdf2fc0ec52cc7909ea5a20a92221a9d851e6894d777175f25239e0cb25","source":{"kind":"arxiv","id":"1708.06141","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06141","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06141v4","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06141","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"pith_short_12","alias_value":"4WR3ZXZPYDWF","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4WR3ZXZPYDWFFTDZ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4WR3ZXZP","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4WR3ZXZPYDWFFTDZBHVFUIFJEI","target":"record","payload":{"canonical_record":{"source":{"id":"1708.06141","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T10:21:25Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"8a78d5825ad761045734c903a47aaaf2854cf2ccba925bc41ca701b292a7fb48","abstract_canon_sha256":"7786303370714c687c123bd30b741aae886dddde87e511417c2660fee2a57501"},"schema_version":"1.0"},"canonical_sha256":"e5a3bcdf2fc0ec52cc7909ea5a20a92221a9d851e6894d777175f25239e0cb25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:01.442105Z","signature_b64":"55UZsE5nCWNWo3h6B+4dap9DdUaYlu6MQ0oZePtLjoKNS8qMMAlYxs5a0r6ykkQjsloK89fiDQoayk7qg+AhCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5a3bcdf2fc0ec52cc7909ea5a20a92221a9d851e6894d777175f25239e0cb25","last_reissued_at":"2026-05-17T23:53:01.441429Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:01.441429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.06141","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nYG2mVOwhVc3m7UdCXdA0py2OLG0PljR5wzJWDv/QkfD9Fe1uRAhr87DU/1zSS75gFLTPsxoOIfD+QiWcUvdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:38:34.468480Z"},"content_sha256":"4411a0ebeb972e23615978bb850bf2a6f95171ec303afe373c156f40c788972e","schema_version":"1.0","event_id":"sha256:4411a0ebeb972e23615978bb850bf2a6f95171ec303afe373c156f40c788972e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4WR3ZXZPYDWFFTDZBHVFUIFJEI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-posedness and Optimal Regularity of Stochastic Evolution Equations with Multiplicative Noises","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Jialin Hong, Zhihui Liu","submitted_at":"2017-08-21T10:21:25Z","abstract_excerpt":"In this paper, we establish the well-posedness and optimal trajectory regularity for the solution of stochastic evolution equations with generalized Lipschitz-type coefficients driven by general multiplicative noises. To ensure the well-posedness of the problem, the linear operator of the equations is only need to be a generator of a $\\CC_0$-semigroup and the proposed noises are quite general, which include space-time white noise and rougher noises. When the linear operator generates an analytic $\\CC_0$-semigroup, we derive the optimal trajectory regularity of the solution through a generalize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06141","kind":"arxiv","version":4},"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":"2026-05-17T23:53:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1G36j9o9D+h5IqszByLX0HibUxBsgglgYsd8wfi/8sSSFIWz0Uzss0T2HWl8B5nJe9MwPL2Q3Djxr/NgYs2bBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:38:34.469308Z"},"content_sha256":"c0ffb0281f12ce0c4ae64ba42db23d6877034890986ef689d3c74591c42ce0d3","schema_version":"1.0","event_id":"sha256:c0ffb0281f12ce0c4ae64ba42db23d6877034890986ef689d3c74591c42ce0d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WR3ZXZPYDWFFTDZBHVFUIFJEI/bundle.json","state_url":"https://pith.science/pith/4WR3ZXZPYDWFFTDZBHVFUIFJEI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WR3ZXZPYDWFFTDZBHVFUIFJEI/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":"2026-05-30T07:38:34Z","links":{"resolver":"https://pith.science/pith/4WR3ZXZPYDWFFTDZBHVFUIFJEI","bundle":"https://pith.science/pith/4WR3ZXZPYDWFFTDZBHVFUIFJEI/bundle.json","state":"https://pith.science/pith/4WR3ZXZPYDWFFTDZBHVFUIFJEI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WR3ZXZPYDWFFTDZBHVFUIFJEI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4WR3ZXZPYDWFFTDZBHVFUIFJEI","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":"7786303370714c687c123bd30b741aae886dddde87e511417c2660fee2a57501","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T10:21:25Z","title_canon_sha256":"8a78d5825ad761045734c903a47aaaf2854cf2ccba925bc41ca701b292a7fb48"},"schema_version":"1.0","source":{"id":"1708.06141","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06141","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06141v4","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06141","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"pith_short_12","alias_value":"4WR3ZXZPYDWF","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4WR3ZXZPYDWFFTDZ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4WR3ZXZP","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:c0ffb0281f12ce0c4ae64ba42db23d6877034890986ef689d3c74591c42ce0d3","target":"graph","created_at":"2026-05-17T23:53:01Z","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 well-posedness and optimal trajectory regularity for the solution of stochastic evolution equations with generalized Lipschitz-type coefficients driven by general multiplicative noises. To ensure the well-posedness of the problem, the linear operator of the equations is only need to be a generator of a $\\CC_0$-semigroup and the proposed noises are quite general, which include space-time white noise and rougher noises. When the linear operator generates an analytic $\\CC_0$-semigroup, we derive the optimal trajectory regularity of the solution through a generalize","authors_text":"Jialin Hong, Zhihui Liu","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T10:21:25Z","title":"Well-posedness and Optimal Regularity of Stochastic Evolution Equations with Multiplicative Noises"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06141","kind":"arxiv","version":4},"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":"sha256:4411a0ebeb972e23615978bb850bf2a6f95171ec303afe373c156f40c788972e","target":"record","created_at":"2026-05-17T23:53:01Z","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":"7786303370714c687c123bd30b741aae886dddde87e511417c2660fee2a57501","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T10:21:25Z","title_canon_sha256":"8a78d5825ad761045734c903a47aaaf2854cf2ccba925bc41ca701b292a7fb48"},"schema_version":"1.0","source":{"id":"1708.06141","kind":"arxiv","version":4}},"canonical_sha256":"e5a3bcdf2fc0ec52cc7909ea5a20a92221a9d851e6894d777175f25239e0cb25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5a3bcdf2fc0ec52cc7909ea5a20a92221a9d851e6894d777175f25239e0cb25","first_computed_at":"2026-05-17T23:53:01.441429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:01.441429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"55UZsE5nCWNWo3h6B+4dap9DdUaYlu6MQ0oZePtLjoKNS8qMMAlYxs5a0r6ykkQjsloK89fiDQoayk7qg+AhCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:01.442105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06141","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4411a0ebeb972e23615978bb850bf2a6f95171ec303afe373c156f40c788972e","sha256:c0ffb0281f12ce0c4ae64ba42db23d6877034890986ef689d3c74591c42ce0d3"],"state_sha256":"8ac356551d641ee4e7437c97de13d71e7e0ae483d8a4b3e5530822f2d1421de2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wbgiBdtm4I7NOVHRzDrwWiL1+1rR2Ng1Cr9oIKaGf+SXk1Ic6eV0DX/mdutRYSwTQf0eU5BxKh9wOgW2zFDUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:38:34.474076Z","bundle_sha256":"9d2894e444915f4e1ace05f07767a62fee137db2b6a1b22002a36f0317dbe668"}}