{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KP4TLCYLAHC6JDX55PPWRVMPSN","short_pith_number":"pith:KP4TLCYL","canonical_record":{"source":{"id":"1012.2736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-13T14:28:41Z","cross_cats_sorted":[],"title_canon_sha256":"a35d6b96d37db1497da1cb426c6bf217a5a4384191635a0527686d8700c71c86","abstract_canon_sha256":"18a31e311d8982e9cf9371da4ca7e65e053f0098540a022ea9094048475e820f"},"schema_version":"1.0"},"canonical_sha256":"53f9358b0b01c5e48efdebdf68d58f9368eb35e1b9483ff4044285738cd4fa3c","source":{"kind":"arxiv","id":"1012.2736","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2736","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2736v1","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2736","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"pith_short_12","alias_value":"KP4TLCYLAHC6","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KP4TLCYLAHC6JDX5","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KP4TLCYL","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KP4TLCYLAHC6JDX55PPWRVMPSN","target":"record","payload":{"canonical_record":{"source":{"id":"1012.2736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-13T14:28:41Z","cross_cats_sorted":[],"title_canon_sha256":"a35d6b96d37db1497da1cb426c6bf217a5a4384191635a0527686d8700c71c86","abstract_canon_sha256":"18a31e311d8982e9cf9371da4ca7e65e053f0098540a022ea9094048475e820f"},"schema_version":"1.0"},"canonical_sha256":"53f9358b0b01c5e48efdebdf68d58f9368eb35e1b9483ff4044285738cd4fa3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:04.017851Z","signature_b64":"Ff6RgN0mlXHr/uS5dsXbe8cFsPLRCj2Yz6I3JC7xS6I4NCB2N6vRMNpWpPNWKRclEORnILCys/yEHUWjBYS2CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53f9358b0b01c5e48efdebdf68d58f9368eb35e1b9483ff4044285738cd4fa3c","last_reissued_at":"2026-05-18T03:29:04.017312Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:04.017312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.2736","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":"2026-05-18T03:29:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4o79blHicrsLoG0RelrYB9WMybyESby9p1g2UWL4gov6L1if/DA0E9Jr9xUJCyt6zBZqfgtsuX20YURvx6jgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:23:53.641866Z"},"content_sha256":"2ca8379cb213d4de567247c128d44358f617eca3f5773616b771746c871ad4a6","schema_version":"1.0","event_id":"sha256:2ca8379cb213d4de567247c128d44358f617eca3f5773616b771746c871ad4a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KP4TLCYLAHC6JDX55PPWRVMPSN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local structure of the set of steady-state solutions to the 2D incompressible Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antoine Choffrut, Vladim\\'ir \\v{S}ver\\'ak","submitted_at":"2010-12-13T14:28:41Z","abstract_excerpt":"It is well known that the incompressible Euler equations can be formulated in a very geometric language. The geometric structures provide very valuable insights into the properties of the solutions. Analogies with the finite-dimensional model of geodesics on a Lie group with left-invariant metric can be very instructive, but it is often difficult to prove analogues of finite-dimensional results in the infinite-dimensional setting of Euler's equations. In this paper we establish a result in this direction in the simple case of steady-state solutions in two dimensions, under some non-degeneracy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2736","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":"2026-05-18T03:29:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QwgAEzP1gcqvoi4Xg8saYDuE5olfU6gUGEiTZJFixG//MquLsNCXB8mN3xREPq8Hsohe067wTsuwxofeoboVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:23:53.642206Z"},"content_sha256":"5eef8ab989a4f8f13fa6e81304010c80d0e323f5af6bf7ab43bd2125d043d57f","schema_version":"1.0","event_id":"sha256:5eef8ab989a4f8f13fa6e81304010c80d0e323f5af6bf7ab43bd2125d043d57f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KP4TLCYLAHC6JDX55PPWRVMPSN/bundle.json","state_url":"https://pith.science/pith/KP4TLCYLAHC6JDX55PPWRVMPSN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KP4TLCYLAHC6JDX55PPWRVMPSN/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":"2026-06-03T14:23:53Z","links":{"resolver":"https://pith.science/pith/KP4TLCYLAHC6JDX55PPWRVMPSN","bundle":"https://pith.science/pith/KP4TLCYLAHC6JDX55PPWRVMPSN/bundle.json","state":"https://pith.science/pith/KP4TLCYLAHC6JDX55PPWRVMPSN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KP4TLCYLAHC6JDX55PPWRVMPSN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KP4TLCYLAHC6JDX55PPWRVMPSN","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":"18a31e311d8982e9cf9371da4ca7e65e053f0098540a022ea9094048475e820f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-13T14:28:41Z","title_canon_sha256":"a35d6b96d37db1497da1cb426c6bf217a5a4384191635a0527686d8700c71c86"},"schema_version":"1.0","source":{"id":"1012.2736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2736","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2736v1","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2736","created_at":"2026-05-18T03:29:04Z"},{"alias_kind":"pith_short_12","alias_value":"KP4TLCYLAHC6","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KP4TLCYLAHC6JDX5","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KP4TLCYL","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:5eef8ab989a4f8f13fa6e81304010c80d0e323f5af6bf7ab43bd2125d043d57f","target":"graph","created_at":"2026-05-18T03:29:04Z","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":"It is well known that the incompressible Euler equations can be formulated in a very geometric language. The geometric structures provide very valuable insights into the properties of the solutions. Analogies with the finite-dimensional model of geodesics on a Lie group with left-invariant metric can be very instructive, but it is often difficult to prove analogues of finite-dimensional results in the infinite-dimensional setting of Euler's equations. In this paper we establish a result in this direction in the simple case of steady-state solutions in two dimensions, under some non-degeneracy ","authors_text":"Antoine Choffrut, Vladim\\'ir \\v{S}ver\\'ak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-13T14:28:41Z","title":"Local structure of the set of steady-state solutions to the 2D incompressible Euler equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2736","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":"sha256:2ca8379cb213d4de567247c128d44358f617eca3f5773616b771746c871ad4a6","target":"record","created_at":"2026-05-18T03:29:04Z","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":"18a31e311d8982e9cf9371da4ca7e65e053f0098540a022ea9094048475e820f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-13T14:28:41Z","title_canon_sha256":"a35d6b96d37db1497da1cb426c6bf217a5a4384191635a0527686d8700c71c86"},"schema_version":"1.0","source":{"id":"1012.2736","kind":"arxiv","version":1}},"canonical_sha256":"53f9358b0b01c5e48efdebdf68d58f9368eb35e1b9483ff4044285738cd4fa3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53f9358b0b01c5e48efdebdf68d58f9368eb35e1b9483ff4044285738cd4fa3c","first_computed_at":"2026-05-18T03:29:04.017312Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:04.017312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ff6RgN0mlXHr/uS5dsXbe8cFsPLRCj2Yz6I3JC7xS6I4NCB2N6vRMNpWpPNWKRclEORnILCys/yEHUWjBYS2CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:04.017851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ca8379cb213d4de567247c128d44358f617eca3f5773616b771746c871ad4a6","sha256:5eef8ab989a4f8f13fa6e81304010c80d0e323f5af6bf7ab43bd2125d043d57f"],"state_sha256":"e71f80d662a3823e0b2632447d84dd2073e8064de35114d8fecb5d390e3ab14a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uSSRa0zzmmmquYe9shiiou3WYUgLHBqMDx35TI/XYnwMxcCNPZBhQFWECHLqgDzFwJPcR9Mzk1vAYb/U+2EbBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:23:53.644130Z","bundle_sha256":"26261f1c75a7f5aab8692cc3569946e9749b3371ac5b6c2c1962b53b61a9522d"}}