{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3VJF2ZVP2RCQJ32CZHXNTFMUCJ","short_pith_number":"pith:3VJF2ZVP","canonical_record":{"source":{"id":"1801.09729","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-01-29T19:41:18Z","cross_cats_sorted":[],"title_canon_sha256":"10ba1fe8bf464de7ede879a555949dd6e278ac93960d3e1a660ee7be6719455c","abstract_canon_sha256":"929f59c5034e0bbda7bde4f96ef49438b9bdc494fd88675d17fab8034430d02b"},"schema_version":"1.0"},"canonical_sha256":"dd525d66afd44504ef42c9eed99594125882a8184a640ab80fe4b428fdd02a1d","source":{"kind":"arxiv","id":"1801.09729","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09729","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09729v2","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09729","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"3VJF2ZVP2RCQ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"3VJF2ZVP2RCQJ32C","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"3VJF2ZVP","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3VJF2ZVP2RCQJ32CZHXNTFMUCJ","target":"record","payload":{"canonical_record":{"source":{"id":"1801.09729","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-01-29T19:41:18Z","cross_cats_sorted":[],"title_canon_sha256":"10ba1fe8bf464de7ede879a555949dd6e278ac93960d3e1a660ee7be6719455c","abstract_canon_sha256":"929f59c5034e0bbda7bde4f96ef49438b9bdc494fd88675d17fab8034430d02b"},"schema_version":"1.0"},"canonical_sha256":"dd525d66afd44504ef42c9eed99594125882a8184a640ab80fe4b428fdd02a1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:39.637534Z","signature_b64":"dBEiKObrhalvvbpzc9eAR6tfPNwpmAXSLoWneXGWN0LtfMF41YDPWyM6HLfbMidq8eLlzZyZ5FrVu+HWyzTvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd525d66afd44504ef42c9eed99594125882a8184a640ab80fe4b428fdd02a1d","last_reissued_at":"2026-05-18T00:04:39.636701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:39.636701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.09729","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":"2026-05-18T00:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q1OmaG7HlMBJpWEyoHnoLNTKX436nbslQOGzO3IJQ1a2Gl0MTIPZ/omCKGyrzxlZAaUfg518ESQhq4+cbHyhCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:52:52.920921Z"},"content_sha256":"9d1d27fda3bbe91d4a08431b0e9995eb9f53495b1d2588b2f0cd94bc65ca382f","schema_version":"1.0","event_id":"sha256:9d1d27fda3bbe91d4a08431b0e9995eb9f53495b1d2588b2f0cd94bc65ca382f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3VJF2ZVP2RCQJ32CZHXNTFMUCJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerically Modelling Stochastic Lie Transport in Fluid Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Colin J. Cotter, Dan Crisan, Darryl D. Holm, Igor Shevchenko, Wei Pan","submitted_at":"2018-01-29T19:41:18Z","abstract_excerpt":"We present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a physically meaningful, data-driven approach for decomposing the fluid transport velocity into its drift and stochastic parts, for a certain class of fluid flows. In the current paper, we develop new methodology to implement this velocity decomposition and then numerically integrate the resulting stochastic partial differential equation using a finite element dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09729","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":"2026-05-18T00:04:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6giLFR3DOYF+rb13eiGJKxtTwKvknbUEC8uRgwCT7zrK4Hg9qNogncM53BopY7t2wnBEQVdscEZ5KlUOkk/7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:52:52.921601Z"},"content_sha256":"c154248c6e165dc35d6d5f8ac3b0b55af5bd853b8cc6632b8058b52270cd9a93","schema_version":"1.0","event_id":"sha256:c154248c6e165dc35d6d5f8ac3b0b55af5bd853b8cc6632b8058b52270cd9a93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VJF2ZVP2RCQJ32CZHXNTFMUCJ/bundle.json","state_url":"https://pith.science/pith/3VJF2ZVP2RCQJ32CZHXNTFMUCJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VJF2ZVP2RCQJ32CZHXNTFMUCJ/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":"2026-06-05T04:52:52Z","links":{"resolver":"https://pith.science/pith/3VJF2ZVP2RCQJ32CZHXNTFMUCJ","bundle":"https://pith.science/pith/3VJF2ZVP2RCQJ32CZHXNTFMUCJ/bundle.json","state":"https://pith.science/pith/3VJF2ZVP2RCQJ32CZHXNTFMUCJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VJF2ZVP2RCQJ32CZHXNTFMUCJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3VJF2ZVP2RCQJ32CZHXNTFMUCJ","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":"929f59c5034e0bbda7bde4f96ef49438b9bdc494fd88675d17fab8034430d02b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-01-29T19:41:18Z","title_canon_sha256":"10ba1fe8bf464de7ede879a555949dd6e278ac93960d3e1a660ee7be6719455c"},"schema_version":"1.0","source":{"id":"1801.09729","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09729","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09729v2","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09729","created_at":"2026-05-18T00:04:39Z"},{"alias_kind":"pith_short_12","alias_value":"3VJF2ZVP2RCQ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"3VJF2ZVP2RCQJ32C","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"3VJF2ZVP","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:c154248c6e165dc35d6d5f8ac3b0b55af5bd853b8cc6632b8058b52270cd9a93","target":"graph","created_at":"2026-05-18T00:04:39Z","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 present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a physically meaningful, data-driven approach for decomposing the fluid transport velocity into its drift and stochastic parts, for a certain class of fluid flows. In the current paper, we develop new methodology to implement this velocity decomposition and then numerically integrate the resulting stochastic partial differential equation using a finite element dis","authors_text":"Colin J. Cotter, Dan Crisan, Darryl D. Holm, Igor Shevchenko, Wei Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-01-29T19:41:18Z","title":"Numerically Modelling Stochastic Lie Transport in Fluid Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09729","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":"sha256:9d1d27fda3bbe91d4a08431b0e9995eb9f53495b1d2588b2f0cd94bc65ca382f","target":"record","created_at":"2026-05-18T00:04:39Z","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":"929f59c5034e0bbda7bde4f96ef49438b9bdc494fd88675d17fab8034430d02b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-01-29T19:41:18Z","title_canon_sha256":"10ba1fe8bf464de7ede879a555949dd6e278ac93960d3e1a660ee7be6719455c"},"schema_version":"1.0","source":{"id":"1801.09729","kind":"arxiv","version":2}},"canonical_sha256":"dd525d66afd44504ef42c9eed99594125882a8184a640ab80fe4b428fdd02a1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd525d66afd44504ef42c9eed99594125882a8184a640ab80fe4b428fdd02a1d","first_computed_at":"2026-05-18T00:04:39.636701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:39.636701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dBEiKObrhalvvbpzc9eAR6tfPNwpmAXSLoWneXGWN0LtfMF41YDPWyM6HLfbMidq8eLlzZyZ5FrVu+HWyzTvBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:39.637534Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09729","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d1d27fda3bbe91d4a08431b0e9995eb9f53495b1d2588b2f0cd94bc65ca382f","sha256:c154248c6e165dc35d6d5f8ac3b0b55af5bd853b8cc6632b8058b52270cd9a93"],"state_sha256":"834069af69e687c909a75bed6e8de8a27bd24577fdd9c02c27ec66e41c0bf48a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A5Ubip4fa421WfzdDs1RjkzPtCDnlDKmRXBkdiIRYvJH2yfpLZGlRoYm3Vkebr67m07mUWZGnI6l4MNpxB48BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T04:52:52.924867Z","bundle_sha256":"8abe5ce21026fb119f549b9aaa9aa0fb4cca3a0542b0223abe094324c102b2bf"}}