{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AM4W4RU2J5ZVNUGR6ZA5B7S7X6","short_pith_number":"pith:AM4W4RU2","canonical_record":{"source":{"id":"1701.01242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T08:27:43Z","cross_cats_sorted":[],"title_canon_sha256":"da951949477519412c500d08fc0fa81a78fe6f36ee22eb20dae39848c0062062","abstract_canon_sha256":"398d8fcf04c2d96d41a5b38d69aa39e9704724627ce7cac730bae951402ae46b"},"schema_version":"1.0"},"canonical_sha256":"03396e469a4f7356d0d1f641d0fe5fbf9018fe05ace201070e90ba41117ff55d","source":{"kind":"arxiv","id":"1701.01242","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01242","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01242v1","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01242","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"pith_short_12","alias_value":"AM4W4RU2J5ZV","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AM4W4RU2J5ZVNUGR","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AM4W4RU2","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AM4W4RU2J5ZVNUGR6ZA5B7S7X6","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T08:27:43Z","cross_cats_sorted":[],"title_canon_sha256":"da951949477519412c500d08fc0fa81a78fe6f36ee22eb20dae39848c0062062","abstract_canon_sha256":"398d8fcf04c2d96d41a5b38d69aa39e9704724627ce7cac730bae951402ae46b"},"schema_version":"1.0"},"canonical_sha256":"03396e469a4f7356d0d1f641d0fe5fbf9018fe05ace201070e90ba41117ff55d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:20.084030Z","signature_b64":"RjrSKnZ01djdd9aRDR5GiscdJTOxnCC1uX/Mj1ygXthg5bQxjKQkBLw8IsTZwwqEoWvAPFrSu/t2mz7w53u6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03396e469a4f7356d0d1f641d0fe5fbf9018fe05ace201070e90ba41117ff55d","last_reissued_at":"2026-05-18T00:53:20.083571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:20.083571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01242","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":"2026-05-18T00:53:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+pTp+u58QCtQxi5G764wYBAozkQfnk7ItEs14128SVTeAaAl9AlkvR3LAiy+PXmrVBnEd6vJdgNZR0IFYzsHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:52:48.778855Z"},"content_sha256":"13b278475f9a55774d3ecd6247548a9ff8352ddc70d39b6909631d7a2b29fe1c","schema_version":"1.0","event_id":"sha256:13b278475f9a55774d3ecd6247548a9ff8352ddc70d39b6909631d7a2b29fe1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AM4W4RU2J5ZVNUGR6ZA5B7S7X6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of a martingale weak solution to the Equations of Non-Stationary Motion of Non-Newtonian Fluids with a stochastic perturbation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huaqiao Wang, Yucong Wang, Zhong Tan","submitted_at":"2017-01-05T08:27:43Z","abstract_excerpt":"In this paper, we consider the stochastic %equations of incompressible non-Newtonian fluids driven by a cylindrical Wiener process $W$ with shear rate dependent on viscosity in a bounded Lipschitz domain $D\\in \\mathbb{R}^n$ during the time interval $(0,T)$. For $q>\\frac{2n+2}{n+2}$ in the growth conditions (1.2), we prove the existence of a martingale weak solution with $\\nabla\\cdot u=0$ by using a pressure decomposition which is adapted to the stochastic setting, the stochastic compactness method and the $L^\\infty$-truncation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01242","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":"2026-05-18T00:53:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VFKQ/mNF42EkhPhFiVEq2rYwrsqO9nau1cJW+Gu3wdki3wFIMqPFyhDLzQ2EFMLZPC+cKFWwEF1d9mqvOqZHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:52:48.779199Z"},"content_sha256":"e1637f3d4d341846b1c8e925c4c8c8c0b551c573112f302ab5e2c61ee2bf232d","schema_version":"1.0","event_id":"sha256:e1637f3d4d341846b1c8e925c4c8c8c0b551c573112f302ab5e2c61ee2bf232d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/bundle.json","state_url":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/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":"2026-05-28T10:52:48Z","links":{"resolver":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6","bundle":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/bundle.json","state":"https://pith.science/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AM4W4RU2J5ZVNUGR6ZA5B7S7X6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AM4W4RU2J5ZVNUGR6ZA5B7S7X6","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":"398d8fcf04c2d96d41a5b38d69aa39e9704724627ce7cac730bae951402ae46b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T08:27:43Z","title_canon_sha256":"da951949477519412c500d08fc0fa81a78fe6f36ee22eb20dae39848c0062062"},"schema_version":"1.0","source":{"id":"1701.01242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01242","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01242v1","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01242","created_at":"2026-05-18T00:53:20Z"},{"alias_kind":"pith_short_12","alias_value":"AM4W4RU2J5ZV","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AM4W4RU2J5ZVNUGR","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AM4W4RU2","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:e1637f3d4d341846b1c8e925c4c8c8c0b551c573112f302ab5e2c61ee2bf232d","target":"graph","created_at":"2026-05-18T00:53:20Z","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 the stochastic %equations of incompressible non-Newtonian fluids driven by a cylindrical Wiener process $W$ with shear rate dependent on viscosity in a bounded Lipschitz domain $D\\in \\mathbb{R}^n$ during the time interval $(0,T)$. For $q>\\frac{2n+2}{n+2}$ in the growth conditions (1.2), we prove the existence of a martingale weak solution with $\\nabla\\cdot u=0$ by using a pressure decomposition which is adapted to the stochastic setting, the stochastic compactness method and the $L^\\infty$-truncation.","authors_text":"Huaqiao Wang, Yucong Wang, Zhong Tan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T08:27:43Z","title":"Existence of a martingale weak solution to the Equations of Non-Stationary Motion of Non-Newtonian Fluids with a stochastic perturbation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01242","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":"sha256:13b278475f9a55774d3ecd6247548a9ff8352ddc70d39b6909631d7a2b29fe1c","target":"record","created_at":"2026-05-18T00:53:20Z","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":"398d8fcf04c2d96d41a5b38d69aa39e9704724627ce7cac730bae951402ae46b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-05T08:27:43Z","title_canon_sha256":"da951949477519412c500d08fc0fa81a78fe6f36ee22eb20dae39848c0062062"},"schema_version":"1.0","source":{"id":"1701.01242","kind":"arxiv","version":1}},"canonical_sha256":"03396e469a4f7356d0d1f641d0fe5fbf9018fe05ace201070e90ba41117ff55d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03396e469a4f7356d0d1f641d0fe5fbf9018fe05ace201070e90ba41117ff55d","first_computed_at":"2026-05-18T00:53:20.083571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:20.083571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RjrSKnZ01djdd9aRDR5GiscdJTOxnCC1uX/Mj1ygXthg5bQxjKQkBLw8IsTZwwqEoWvAPFrSu/t2mz7w53u6DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:20.084030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13b278475f9a55774d3ecd6247548a9ff8352ddc70d39b6909631d7a2b29fe1c","sha256:e1637f3d4d341846b1c8e925c4c8c8c0b551c573112f302ab5e2c61ee2bf232d"],"state_sha256":"840ca83b1cc9390f0cc3eece04abc31ab2effa62f91efca00a69ac8d82c6e265"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EaJOiXILv+ZRsXDN7unvwa8n/Y2IMd5qj/12nCj5aXk6RlCEDgZg5klmwONDuCGHBHaC7q9tnliDuKYGHMnjBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:52:48.781199Z","bundle_sha256":"bf3d0c4ae67aac1f6c6b3b3a622d746fcff0dd5a9d69ffc7747af54034359592"}}