{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:A4QLHEXSPPRYHO3CDMWEJ5TJHI","short_pith_number":"pith:A4QLHEXS","canonical_record":{"source":{"id":"1412.4732","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-15T19:29:39Z","cross_cats_sorted":[],"title_canon_sha256":"b749504096571c03b68c5d0fda6db67e1e66f2746a1282b5a6dfeed1c70910ad","abstract_canon_sha256":"72a6f1305545601ccc2188a98b2650b1dfa684efed3952c332191f1073a9bf04"},"schema_version":"1.0"},"canonical_sha256":"0720b392f27be383bb621b2c44f6693a20b00da31516f809f8ea82b094d89f9f","source":{"kind":"arxiv","id":"1412.4732","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4732","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4732v2","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4732","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"A4QLHEXSPPRY","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A4QLHEXSPPRYHO3C","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A4QLHEXS","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:A4QLHEXSPPRYHO3CDMWEJ5TJHI","target":"record","payload":{"canonical_record":{"source":{"id":"1412.4732","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-15T19:29:39Z","cross_cats_sorted":[],"title_canon_sha256":"b749504096571c03b68c5d0fda6db67e1e66f2746a1282b5a6dfeed1c70910ad","abstract_canon_sha256":"72a6f1305545601ccc2188a98b2650b1dfa684efed3952c332191f1073a9bf04"},"schema_version":"1.0"},"canonical_sha256":"0720b392f27be383bb621b2c44f6693a20b00da31516f809f8ea82b094d89f9f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:06.792065Z","signature_b64":"MzMpGQVJFyFuYfqH2fAGn83VPxnjUmYhhA2T/DgwhAcCOJHzmKMPXgbZ/Kf6qrC3mNpghIbHdJ2AE/LDcI7LAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0720b392f27be383bb621b2c44f6693a20b00da31516f809f8ea82b094d89f9f","last_reissued_at":"2026-05-18T01:28:06.791560Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:06.791560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.4732","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":"2026-05-18T01:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WPA/ATTY0Bz3h6Hr8xFJfLBLEk8BfnjElADUCSKLez/LBqus+iKchEYuMV7QslcFbjLuBz2f9A81uVJv41uHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:47:52.280780Z"},"content_sha256":"a5b9527c4399e53fcc6529afaa3ab4faaba896116df5eb2f05ab968e386d0a08","schema_version":"1.0","event_id":"sha256:a5b9527c4399e53fcc6529afaa3ab4faaba896116df5eb2f05ab968e386d0a08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:A4QLHEXSPPRYHO3CDMWEJ5TJHI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Groups of Asymptotic Diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Peter Topalov, Robert McOwen","submitted_at":"2014-12-15T19:29:39Z","abstract_excerpt":"We consider classes of diffeomorphisms of Euclidean space with partial asymptotic expansions at infinity; the remainder term lies in a weighted Sobolev space whose properties at infinity fit with the desired application. We show that two such classes of asymptotic diffeomorphisms form topological groups under composition. As such, they can be used in the study of fluid dynamics according to the method of V. Arnold. Specific applications have been obtained for the Camassa-Holm equation and the Euler equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4732","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":"2026-05-18T01:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"awNSpRrEnqRsC/Z/rXKTDzlVBQ3feuZQdYkDtJMaEl/9Q7y7rhxh/PcufTgHXLnvLd7z15bfre5PYtkELGtaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:47:52.281431Z"},"content_sha256":"591840f3c18e3f73b10e6c545684d91a612b206d9347de9e834d9c717139fa95","schema_version":"1.0","event_id":"sha256:591840f3c18e3f73b10e6c545684d91a612b206d9347de9e834d9c717139fa95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4QLHEXSPPRYHO3CDMWEJ5TJHI/bundle.json","state_url":"https://pith.science/pith/A4QLHEXSPPRYHO3CDMWEJ5TJHI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4QLHEXSPPRYHO3CDMWEJ5TJHI/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":"2026-05-27T15:47:52Z","links":{"resolver":"https://pith.science/pith/A4QLHEXSPPRYHO3CDMWEJ5TJHI","bundle":"https://pith.science/pith/A4QLHEXSPPRYHO3CDMWEJ5TJHI/bundle.json","state":"https://pith.science/pith/A4QLHEXSPPRYHO3CDMWEJ5TJHI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4QLHEXSPPRYHO3CDMWEJ5TJHI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:A4QLHEXSPPRYHO3CDMWEJ5TJHI","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":"72a6f1305545601ccc2188a98b2650b1dfa684efed3952c332191f1073a9bf04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-15T19:29:39Z","title_canon_sha256":"b749504096571c03b68c5d0fda6db67e1e66f2746a1282b5a6dfeed1c70910ad"},"schema_version":"1.0","source":{"id":"1412.4732","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4732","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4732v2","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4732","created_at":"2026-05-18T01:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"A4QLHEXSPPRY","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A4QLHEXSPPRYHO3C","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A4QLHEXS","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:591840f3c18e3f73b10e6c545684d91a612b206d9347de9e834d9c717139fa95","target":"graph","created_at":"2026-05-18T01:28:06Z","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 consider classes of diffeomorphisms of Euclidean space with partial asymptotic expansions at infinity; the remainder term lies in a weighted Sobolev space whose properties at infinity fit with the desired application. We show that two such classes of asymptotic diffeomorphisms form topological groups under composition. As such, they can be used in the study of fluid dynamics according to the method of V. Arnold. Specific applications have been obtained for the Camassa-Holm equation and the Euler equations.","authors_text":"Peter Topalov, Robert McOwen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-15T19:29:39Z","title":"Groups of Asymptotic Diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4732","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:a5b9527c4399e53fcc6529afaa3ab4faaba896116df5eb2f05ab968e386d0a08","target":"record","created_at":"2026-05-18T01:28:06Z","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":"72a6f1305545601ccc2188a98b2650b1dfa684efed3952c332191f1073a9bf04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-15T19:29:39Z","title_canon_sha256":"b749504096571c03b68c5d0fda6db67e1e66f2746a1282b5a6dfeed1c70910ad"},"schema_version":"1.0","source":{"id":"1412.4732","kind":"arxiv","version":2}},"canonical_sha256":"0720b392f27be383bb621b2c44f6693a20b00da31516f809f8ea82b094d89f9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0720b392f27be383bb621b2c44f6693a20b00da31516f809f8ea82b094d89f9f","first_computed_at":"2026-05-18T01:28:06.791560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:06.791560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MzMpGQVJFyFuYfqH2fAGn83VPxnjUmYhhA2T/DgwhAcCOJHzmKMPXgbZ/Kf6qrC3mNpghIbHdJ2AE/LDcI7LAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:06.792065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4732","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5b9527c4399e53fcc6529afaa3ab4faaba896116df5eb2f05ab968e386d0a08","sha256:591840f3c18e3f73b10e6c545684d91a612b206d9347de9e834d9c717139fa95"],"state_sha256":"1a35df1b3991d397a5fe4079a6d8ed88777fb5d39dff4736075a9af5737edec4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4xOop+4J563fAQDw4KSOWfMUg232E/mwVJzZLmXuSLw8AavSsqK2eH0s2dIJ9eoc4RnK0GvLcG+Z+1bC/JeDAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:47:52.284801Z","bundle_sha256":"3e49cb906d10de936b4c98569f103722b709650b255de7d61639ae55f2ac3b53"}}