{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:K674QA5COSQHKYPX2I3L7QBW4E","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":"43570425f40a49fdc16fd2f798ddc35b89e0642a50013559f991b817a00e59a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-06T21:39:56Z","title_canon_sha256":"c3a54a07f987867a8e1cf603391aff27fb2e70d9de8b8f39dad2871c1e51f942"},"schema_version":"1.0","source":{"id":"1004.0978","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0978","created_at":"2026-05-18T04:23:03Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0978v2","created_at":"2026-05-18T04:23:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0978","created_at":"2026-05-18T04:23:03Z"},{"alias_kind":"pith_short_12","alias_value":"K674QA5COSQH","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"K674QA5COSQHKYPX","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"K674QA5C","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:7b528c5a2b8cc9051b46f1e702f1c36f992a95ae92b1fba2d09fc3d0fc7f0635","target":"graph","created_at":"2026-05-18T04:23:03Z","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 the periodic $\\muDP$ equation (a modified version of the Degasperis-Procesi equation) as the geodesic flow of a right-invariant affine connection $\\nabla$ on the Fr\\'echet Lie group $\\Diff^{\\infty}(\\S^1)$ of all smooth and orientation-preserving diffeomorphisms of the circle $\\S^1=\\R/\\Z$. On the Lie algebra $\\C^{\\infty}(\\S^1)$ of $\\Diff^{\\infty}(\\S^1)$, this connection is canonically given by the sum of the Lie bracket and a bilinear operator. For smooth initial data, we show the short time existence of a smooth solution of $\\muDP$ which depends smoothly on time and on the initial ","authors_text":"Boris Kolev, Joachim Escher, Martin Kohlmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-06T21:39:56Z","title":"Geometric aspects of the periodic $\\mu$-Degasperis-Procesi equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0978","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:d82f512fb1ffb7d1a0e89f35cd6c94f970e629f66699bf49cc581b151804907e","target":"record","created_at":"2026-05-18T04:23:03Z","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":"43570425f40a49fdc16fd2f798ddc35b89e0642a50013559f991b817a00e59a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-06T21:39:56Z","title_canon_sha256":"c3a54a07f987867a8e1cf603391aff27fb2e70d9de8b8f39dad2871c1e51f942"},"schema_version":"1.0","source":{"id":"1004.0978","kind":"arxiv","version":2}},"canonical_sha256":"57bfc803a274a07561f7d236bfc036e12cd27037054a19c7f76d19577bca2b8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57bfc803a274a07561f7d236bfc036e12cd27037054a19c7f76d19577bca2b8b","first_computed_at":"2026-05-18T04:23:03.121807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:03.121807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fhPu+Ete6NYzv/BK4ACsXqdAgngtmOvFcKe3tyUsYFleUoXVfEozgthL9Mo87pGX/D3RXRPIhSQRrDu9vkhtAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:03.122418Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0978","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d82f512fb1ffb7d1a0e89f35cd6c94f970e629f66699bf49cc581b151804907e","sha256:7b528c5a2b8cc9051b46f1e702f1c36f992a95ae92b1fba2d09fc3d0fc7f0635"],"state_sha256":"ed37eeb57d669e396a4039dd8dd2672ec384e8486ef04fef433def6dfde79158"}