{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YBVTNNDOROW2D5SDXERF22UUJB","short_pith_number":"pith:YBVTNNDO","canonical_record":{"source":{"id":"1705.01603","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2017-05-03T20:11:13Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"6da2e21b67f184f85e57cdbe725dffee7932b79e424a3326696826d2d1dee039","abstract_canon_sha256":"fbf36edf46a8f80dd099d5161e2a4167e8795a7ef822ece2efde0b0bd9d6be7b"},"schema_version":"1.0"},"canonical_sha256":"c06b36b46e8bada1f643b9225d6a944841e931ce9d25a7e214444cae71d4ba25","source":{"kind":"arxiv","id":"1705.01603","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01603","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01603v2","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01603","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"YBVTNNDOROW2","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YBVTNNDOROW2D5SD","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YBVTNNDO","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YBVTNNDOROW2D5SDXERF22UUJB","target":"record","payload":{"canonical_record":{"source":{"id":"1705.01603","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2017-05-03T20:11:13Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"6da2e21b67f184f85e57cdbe725dffee7932b79e424a3326696826d2d1dee039","abstract_canon_sha256":"fbf36edf46a8f80dd099d5161e2a4167e8795a7ef822ece2efde0b0bd9d6be7b"},"schema_version":"1.0"},"canonical_sha256":"c06b36b46e8bada1f643b9225d6a944841e931ce9d25a7e214444cae71d4ba25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:41.908713Z","signature_b64":"JIy2K85mbkNW0MGqGbEaUACPP5kN4qsd3XANwX4LUJHVvO+e8FCjBrLJpLFyoVOT8YltUoWXU9fNKbT6vPJvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c06b36b46e8bada1f643b9225d6a944841e931ce9d25a7e214444cae71d4ba25","last_reissued_at":"2026-05-18T00:06:41.908099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:41.908099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.01603","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":"2026-05-18T00:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P+iOxEK77guuvRWO0t3VXAa8YwuoYN4VvC3CMlynQPAZ7Ul7XnUu1gLQP8aHX0dvMhW0tWCYwQAfXKJL4ANADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T20:54:14.938632Z"},"content_sha256":"f9b91d68ac56cbc9ec0e70b7c0d85d6cfc32c99935b2d57c5bb9b0be8c4ad3a4","schema_version":"1.0","event_id":"sha256:f9b91d68ac56cbc9ec0e70b7c0d85d6cfc32c99935b2d57c5bb9b0be8c4ad3a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YBVTNNDOROW2D5SDXERF22UUJB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vortex sheets and diffeomorphism groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SG","authors_text":"Anton Izosimov, Boris Khesin","submitted_at":"2017-05-03T20:11:13Z","abstract_excerpt":"In 1966 V.Arnold suggested a group-theoretic approach to ideal hydrodynamics in which the motion of an inviscid incompressible fluid is described as the geodesic flow of the right-invariant $L^2$-metric on the group of volume-preserving diffeomorphisms of the flow domain. Here we propose geodesic, group-theoretic, and Hamiltonian frameworks to include fluid flows with vortex sheets. It turns out that the corresponding dynamics is related to a certain groupoid of pairs of volume-preserving diffeomorphisms with common interface. We also develop a general framework for Euler-Arnold equations for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01603","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":"2026-05-18T00:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"omJ0Eyl1OmXivhmv5S2epx8MF/vbB4r9TV+pcbMru48+KqOgXMJFxZlgvaPrphxCJGQMQlRI0bZcgOFjKxKpDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T20:54:14.939302Z"},"content_sha256":"85685ff4053e6908864c7b122c712724549d8620398b79add89487a38e8f8a6b","schema_version":"1.0","event_id":"sha256:85685ff4053e6908864c7b122c712724549d8620398b79add89487a38e8f8a6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YBVTNNDOROW2D5SDXERF22UUJB/bundle.json","state_url":"https://pith.science/pith/YBVTNNDOROW2D5SDXERF22UUJB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YBVTNNDOROW2D5SDXERF22UUJB/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":"2026-05-21T20:54:14Z","links":{"resolver":"https://pith.science/pith/YBVTNNDOROW2D5SDXERF22UUJB","bundle":"https://pith.science/pith/YBVTNNDOROW2D5SDXERF22UUJB/bundle.json","state":"https://pith.science/pith/YBVTNNDOROW2D5SDXERF22UUJB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YBVTNNDOROW2D5SDXERF22UUJB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YBVTNNDOROW2D5SDXERF22UUJB","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":"fbf36edf46a8f80dd099d5161e2a4167e8795a7ef822ece2efde0b0bd9d6be7b","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2017-05-03T20:11:13Z","title_canon_sha256":"6da2e21b67f184f85e57cdbe725dffee7932b79e424a3326696826d2d1dee039"},"schema_version":"1.0","source":{"id":"1705.01603","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01603","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01603v2","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01603","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"YBVTNNDOROW2","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YBVTNNDOROW2D5SD","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YBVTNNDO","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:85685ff4053e6908864c7b122c712724549d8620398b79add89487a38e8f8a6b","target":"graph","created_at":"2026-05-18T00:06:41Z","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 1966 V.Arnold suggested a group-theoretic approach to ideal hydrodynamics in which the motion of an inviscid incompressible fluid is described as the geodesic flow of the right-invariant $L^2$-metric on the group of volume-preserving diffeomorphisms of the flow domain. Here we propose geodesic, group-theoretic, and Hamiltonian frameworks to include fluid flows with vortex sheets. It turns out that the corresponding dynamics is related to a certain groupoid of pairs of volume-preserving diffeomorphisms with common interface. We also develop a general framework for Euler-Arnold equations for ","authors_text":"Anton Izosimov, Boris Khesin","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2017-05-03T20:11:13Z","title":"Vortex sheets and diffeomorphism groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01603","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:f9b91d68ac56cbc9ec0e70b7c0d85d6cfc32c99935b2d57c5bb9b0be8c4ad3a4","target":"record","created_at":"2026-05-18T00:06:41Z","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":"fbf36edf46a8f80dd099d5161e2a4167e8795a7ef822ece2efde0b0bd9d6be7b","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2017-05-03T20:11:13Z","title_canon_sha256":"6da2e21b67f184f85e57cdbe725dffee7932b79e424a3326696826d2d1dee039"},"schema_version":"1.0","source":{"id":"1705.01603","kind":"arxiv","version":2}},"canonical_sha256":"c06b36b46e8bada1f643b9225d6a944841e931ce9d25a7e214444cae71d4ba25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c06b36b46e8bada1f643b9225d6a944841e931ce9d25a7e214444cae71d4ba25","first_computed_at":"2026-05-18T00:06:41.908099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:41.908099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JIy2K85mbkNW0MGqGbEaUACPP5kN4qsd3XANwX4LUJHVvO+e8FCjBrLJpLFyoVOT8YltUoWXU9fNKbT6vPJvCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:41.908713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01603","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9b91d68ac56cbc9ec0e70b7c0d85d6cfc32c99935b2d57c5bb9b0be8c4ad3a4","sha256:85685ff4053e6908864c7b122c712724549d8620398b79add89487a38e8f8a6b"],"state_sha256":"ecd2d1c3106cc8835cf705ece64954792d19d43953d8d65ed7126314526f904b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yEFgTD0Bp40gsXSZjWebLHWBCvVnyvv51Yj7uHqe8xREJPKgdfWCiR0+6aaOuVmnW6q4qnWViEU4HzMK+Z0qBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T20:54:14.941779Z","bundle_sha256":"3ad7ddc12f323e1326e8ab9d6fc7554cb2dce9fa91502c77ca051b4711fd7573"}}