{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5EIZNGGRRNKZBWZ6SQYJ2JOVMT","short_pith_number":"pith:5EIZNGGR","canonical_record":{"source":{"id":"1703.08821","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-26T14:43:22Z","cross_cats_sorted":[],"title_canon_sha256":"e85ddf171e58e0ee8098f36a10a58331d5f3b302d2dddd9a15b769618723dac7","abstract_canon_sha256":"b48fd1c23f344a7aaf1f2e5d022a5358360ff579391428cb36cc1369aa513f95"},"schema_version":"1.0"},"canonical_sha256":"e9119698d18b5590db3e94309d25d564e50d3cc58040bac29890705b67b01a5e","source":{"kind":"arxiv","id":"1703.08821","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08821","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08821v2","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08821","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"5EIZNGGRRNKZ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5EIZNGGRRNKZBWZ6","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5EIZNGGR","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5EIZNGGRRNKZBWZ6SQYJ2JOVMT","target":"record","payload":{"canonical_record":{"source":{"id":"1703.08821","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-26T14:43:22Z","cross_cats_sorted":[],"title_canon_sha256":"e85ddf171e58e0ee8098f36a10a58331d5f3b302d2dddd9a15b769618723dac7","abstract_canon_sha256":"b48fd1c23f344a7aaf1f2e5d022a5358360ff579391428cb36cc1369aa513f95"},"schema_version":"1.0"},"canonical_sha256":"e9119698d18b5590db3e94309d25d564e50d3cc58040bac29890705b67b01a5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:31.913754Z","signature_b64":"K/pPdKPr1tgfO9Vw20QTfVUSLeRBE8FtNsW7eolCKkvTyqhhTUvZOex1xJRCbo8qHnaE5+YVvLAQvMWDmSHTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9119698d18b5590db3e94309d25d564e50d3cc58040bac29890705b67b01a5e","last_reissued_at":"2026-05-18T00:18:31.913399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:31.913399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.08821","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Z0ZhHmSveH+Lvtpz8F1m58Y89wF70gDczOUrlvj8/F4Mn6//30fODilhaUdQAhxyuk8iTvKWhvtbiEJRSuzDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:19:22.488939Z"},"content_sha256":"ee36ec84df482ecda4722ac5c90dff6c65158f01356c6e704ab320536f4e83cd","schema_version":"1.0","event_id":"sha256:ee36ec84df482ecda4722ac5c90dff6c65158f01356c6e704ab320536f4e83cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5EIZNGGRRNKZBWZ6SQYJ2JOVMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random dynamics of two-dimensional stochastic second grade fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Shijie Shang","submitted_at":"2017-03-26T14:43:22Z","abstract_excerpt":"In this paper, we consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\\mathbb{R}^2$ with multiplicative noise. We first show that the solutions to the stochastic equations of second grade fluids generate a continuous random dynamical system. Second, we investigate the Fr\\'{e}chet differentiability of the random dynamical system. Finally, we establish the asymptotic compactness of the random dynamical system, and the existence of random attractors for the random dynamical system, we also obtain the upper semi-continuity of the perturbed ran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08821","kind":"arxiv","version":2},"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":"2026-05-18T00:18:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eZ0S3IG/wycJyxRH8VZfE28/h6RDthZkyn6iHqBan1sFYirC87aFEqd1+mws93fIZTHh4DjCdSQBBA+5j6B0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:19:22.489326Z"},"content_sha256":"48a7e07f104d4d58bf323ddfe74ad1d1de77cd58970c8dab38937d5232eb5ad2","schema_version":"1.0","event_id":"sha256:48a7e07f104d4d58bf323ddfe74ad1d1de77cd58970c8dab38937d5232eb5ad2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5EIZNGGRRNKZBWZ6SQYJ2JOVMT/bundle.json","state_url":"https://pith.science/pith/5EIZNGGRRNKZBWZ6SQYJ2JOVMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5EIZNGGRRNKZBWZ6SQYJ2JOVMT/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":"2026-06-26T14:19:22Z","links":{"resolver":"https://pith.science/pith/5EIZNGGRRNKZBWZ6SQYJ2JOVMT","bundle":"https://pith.science/pith/5EIZNGGRRNKZBWZ6SQYJ2JOVMT/bundle.json","state":"https://pith.science/pith/5EIZNGGRRNKZBWZ6SQYJ2JOVMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5EIZNGGRRNKZBWZ6SQYJ2JOVMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5EIZNGGRRNKZBWZ6SQYJ2JOVMT","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":"b48fd1c23f344a7aaf1f2e5d022a5358360ff579391428cb36cc1369aa513f95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-26T14:43:22Z","title_canon_sha256":"e85ddf171e58e0ee8098f36a10a58331d5f3b302d2dddd9a15b769618723dac7"},"schema_version":"1.0","source":{"id":"1703.08821","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08821","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08821v2","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08821","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"5EIZNGGRRNKZ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5EIZNGGRRNKZBWZ6","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5EIZNGGR","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:48a7e07f104d4d58bf323ddfe74ad1d1de77cd58970c8dab38937d5232eb5ad2","target":"graph","created_at":"2026-05-18T00:18:31Z","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 consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\\mathbb{R}^2$ with multiplicative noise. We first show that the solutions to the stochastic equations of second grade fluids generate a continuous random dynamical system. Second, we investigate the Fr\\'{e}chet differentiability of the random dynamical system. Finally, we establish the asymptotic compactness of the random dynamical system, and the existence of random attractors for the random dynamical system, we also obtain the upper semi-continuity of the perturbed ran","authors_text":"Shijie Shang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-26T14:43:22Z","title":"Random dynamics of two-dimensional stochastic second grade fluids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08821","kind":"arxiv","version":2},"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:ee36ec84df482ecda4722ac5c90dff6c65158f01356c6e704ab320536f4e83cd","target":"record","created_at":"2026-05-18T00:18:31Z","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":"b48fd1c23f344a7aaf1f2e5d022a5358360ff579391428cb36cc1369aa513f95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-26T14:43:22Z","title_canon_sha256":"e85ddf171e58e0ee8098f36a10a58331d5f3b302d2dddd9a15b769618723dac7"},"schema_version":"1.0","source":{"id":"1703.08821","kind":"arxiv","version":2}},"canonical_sha256":"e9119698d18b5590db3e94309d25d564e50d3cc58040bac29890705b67b01a5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9119698d18b5590db3e94309d25d564e50d3cc58040bac29890705b67b01a5e","first_computed_at":"2026-05-18T00:18:31.913399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:31.913399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K/pPdKPr1tgfO9Vw20QTfVUSLeRBE8FtNsW7eolCKkvTyqhhTUvZOex1xJRCbo8qHnaE5+YVvLAQvMWDmSHTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:31.913754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08821","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee36ec84df482ecda4722ac5c90dff6c65158f01356c6e704ab320536f4e83cd","sha256:48a7e07f104d4d58bf323ddfe74ad1d1de77cd58970c8dab38937d5232eb5ad2"],"state_sha256":"fcd5d782bd5e62466afb972eae8a7ef6c1762ab55df9534f094fef91f77e0d2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WWVlSxMnMJyAuGi0VqSSl1+1PBEhPOBSUuu8Drd46yvrFXtXdwsyBzyRgu2nS09b+pxelrwqHAOCSCiRnXltCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:19:22.491344Z","bundle_sha256":"3017f64c63d330ee140182bab028897938d56645af350bd0f25d7613258ca3bc"}}