{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:L5OM73YEGSWMYFY5IRDNGEQL7V","short_pith_number":"pith:L5OM73YE","canonical_record":{"source":{"id":"2004.07829","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-04-16T09:59:24Z","cross_cats_sorted":["math.DS","math.PR","physics.flu-dyn"],"title_canon_sha256":"3584d8264358ba55887afb7a32e1f666647ca8292ee96cce8ee51d9b36947885","abstract_canon_sha256":"daae680fa2364f55ef36e38e0adc5c1749ee9e21d94c7da9abf0eea7c321b8ac"},"schema_version":"1.0"},"canonical_sha256":"5f5ccfef0434accc171d4446d3120bfd78b04b5598b82a55f5c96b2e52b43e9f","source":{"kind":"arxiv","id":"2004.07829","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.07829","created_at":"2026-07-05T03:44:27Z"},{"alias_kind":"arxiv_version","alias_value":"2004.07829v2","created_at":"2026-07-05T03:44:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.07829","created_at":"2026-07-05T03:44:27Z"},{"alias_kind":"pith_short_12","alias_value":"L5OM73YEGSWM","created_at":"2026-07-05T03:44:27Z"},{"alias_kind":"pith_short_16","alias_value":"L5OM73YEGSWMYFY5","created_at":"2026-07-05T03:44:27Z"},{"alias_kind":"pith_short_8","alias_value":"L5OM73YE","created_at":"2026-07-05T03:44:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:L5OM73YEGSWMYFY5IRDNGEQL7V","target":"record","payload":{"canonical_record":{"source":{"id":"2004.07829","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-04-16T09:59:24Z","cross_cats_sorted":["math.DS","math.PR","physics.flu-dyn"],"title_canon_sha256":"3584d8264358ba55887afb7a32e1f666647ca8292ee96cce8ee51d9b36947885","abstract_canon_sha256":"daae680fa2364f55ef36e38e0adc5c1749ee9e21d94c7da9abf0eea7c321b8ac"},"schema_version":"1.0"},"canonical_sha256":"5f5ccfef0434accc171d4446d3120bfd78b04b5598b82a55f5c96b2e52b43e9f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:44:27.431452Z","signature_b64":"U8z6mviEw/O3QaA0OjSOuI4yR0ek0pxW/4cemFINNsgkereJvqXWMcc6hG9C+WMmW6j5ezbw85i9vkXeLtLaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f5ccfef0434accc171d4446d3120bfd78b04b5598b82a55f5c96b2e52b43e9f","last_reissued_at":"2026-07-05T03:44:27.430933Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:44:27.430933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.07829","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":"2026-07-05T03:44:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uV4171S/I3LuWd1RPq5Gjhqibs9t2e3BR9CsF249XytKAWJ6d3C+xoZN7zuJfXpDLobdccUtc7pzVQqb9C4nCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:28:31.308672Z"},"content_sha256":"46fb3b0c743002d03f286ff90ca75f3dfb9f089e11e02754a32e4de7eb933b5d","schema_version":"1.0","event_id":"sha256:46fb3b0c743002d03f286ff90ca75f3dfb9f089e11e02754a32e4de7eb933b5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:L5OM73YEGSWMYFY5IRDNGEQL7V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational principles for fluid dynamics on rough paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Dan Crisan, Darryl D. Holm, James-Michael Leahy, Torstein Nilssen","submitted_at":"2020-04-16T09:59:24Z","abstract_excerpt":"In this paper, we introduce a new framework for parametrization schemes (PS) in GFD. Using the theory of controlled rough paths, we derive a class of rough geophysical fluid dynamics (RGFD) models as critical points of rough action functionals. These RGFD models characterize Lagrangian trajectories in fluid dynamics as geometric rough paths (GRP) on the manifold of diffeomorphic maps. Three constrained variational approaches are formulated for the derivation of these models. The first is the Clebsch formulation, in which the constraints are imposed as rough advection laws. The second is the Ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.07829","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.07829/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:44:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oodQ2xZzxFOzr8CsU0bS1ajjaycd9vrryVubGPov17LXBU+i9g4Yfu/uuI2AO3jxMJdsprrXLgOVob3Ixc9aDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T14:28:31.309188Z"},"content_sha256":"9c64f7109e61c0eed4ae5aec48ad143a586a264041e99cb140b62108b6742d47","schema_version":"1.0","event_id":"sha256:9c64f7109e61c0eed4ae5aec48ad143a586a264041e99cb140b62108b6742d47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5OM73YEGSWMYFY5IRDNGEQL7V/bundle.json","state_url":"https://pith.science/pith/L5OM73YEGSWMYFY5IRDNGEQL7V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5OM73YEGSWMYFY5IRDNGEQL7V/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":"2026-08-08T14:28:31Z","links":{"resolver":"https://pith.science/pith/L5OM73YEGSWMYFY5IRDNGEQL7V","bundle":"https://pith.science/pith/L5OM73YEGSWMYFY5IRDNGEQL7V/bundle.json","state":"https://pith.science/pith/L5OM73YEGSWMYFY5IRDNGEQL7V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5OM73YEGSWMYFY5IRDNGEQL7V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:L5OM73YEGSWMYFY5IRDNGEQL7V","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":"daae680fa2364f55ef36e38e0adc5c1749ee9e21d94c7da9abf0eea7c321b8ac","cross_cats_sorted":["math.DS","math.PR","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-04-16T09:59:24Z","title_canon_sha256":"3584d8264358ba55887afb7a32e1f666647ca8292ee96cce8ee51d9b36947885"},"schema_version":"1.0","source":{"id":"2004.07829","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.07829","created_at":"2026-07-05T03:44:27Z"},{"alias_kind":"arxiv_version","alias_value":"2004.07829v2","created_at":"2026-07-05T03:44:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.07829","created_at":"2026-07-05T03:44:27Z"},{"alias_kind":"pith_short_12","alias_value":"L5OM73YEGSWM","created_at":"2026-07-05T03:44:27Z"},{"alias_kind":"pith_short_16","alias_value":"L5OM73YEGSWMYFY5","created_at":"2026-07-05T03:44:27Z"},{"alias_kind":"pith_short_8","alias_value":"L5OM73YE","created_at":"2026-07-05T03:44:27Z"}],"graph_snapshots":[{"event_id":"sha256:9c64f7109e61c0eed4ae5aec48ad143a586a264041e99cb140b62108b6742d47","target":"graph","created_at":"2026-07-05T03:44:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2004.07829/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce a new framework for parametrization schemes (PS) in GFD. Using the theory of controlled rough paths, we derive a class of rough geophysical fluid dynamics (RGFD) models as critical points of rough action functionals. These RGFD models characterize Lagrangian trajectories in fluid dynamics as geometric rough paths (GRP) on the manifold of diffeomorphic maps. Three constrained variational approaches are formulated for the derivation of these models. The first is the Clebsch formulation, in which the constraints are imposed as rough advection laws. The second is the Ha","authors_text":"Dan Crisan, Darryl D. Holm, James-Michael Leahy, Torstein Nilssen","cross_cats":["math.DS","math.PR","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-04-16T09:59:24Z","title":"Variational principles for fluid dynamics on rough paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.07829","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":"sha256:46fb3b0c743002d03f286ff90ca75f3dfb9f089e11e02754a32e4de7eb933b5d","target":"record","created_at":"2026-07-05T03:44:27Z","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":"daae680fa2364f55ef36e38e0adc5c1749ee9e21d94c7da9abf0eea7c321b8ac","cross_cats_sorted":["math.DS","math.PR","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-04-16T09:59:24Z","title_canon_sha256":"3584d8264358ba55887afb7a32e1f666647ca8292ee96cce8ee51d9b36947885"},"schema_version":"1.0","source":{"id":"2004.07829","kind":"arxiv","version":2}},"canonical_sha256":"5f5ccfef0434accc171d4446d3120bfd78b04b5598b82a55f5c96b2e52b43e9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f5ccfef0434accc171d4446d3120bfd78b04b5598b82a55f5c96b2e52b43e9f","first_computed_at":"2026-07-05T03:44:27.430933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:44:27.430933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U8z6mviEw/O3QaA0OjSOuI4yR0ek0pxW/4cemFINNsgkereJvqXWMcc6hG9C+WMmW6j5ezbw85i9vkXeLtLaBw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:44:27.431452Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.07829","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46fb3b0c743002d03f286ff90ca75f3dfb9f089e11e02754a32e4de7eb933b5d","sha256:9c64f7109e61c0eed4ae5aec48ad143a586a264041e99cb140b62108b6742d47"],"state_sha256":"b5dd49f9ce1c89590e16f2c1add59ee8b1003aff16c772f8a3d0d315e46475bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZFUMeQFXrnedttAuGsi89YojNHnFT2HHCt+FYr8A6JFvXA+K1b3VJaPxcSjJ6PfUHgMGBQcGX10ieQr6HuflBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T14:28:31.314190Z","bundle_sha256":"6b3128cced2602a0b5cf75fbd0bd15d18b76670bed986e6fcd080e037bc78247"}}