{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:CTUQB5SIOYNVPD27TTNR67DECA","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":"a9a86e17d5d1a9000ef631f86fb95ab3ac7de69d5600177f7b433c41eb030638","cross_cats_sorted":["math.AP","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2003-05-07T15:07:31Z","title_canon_sha256":"99f17c00eecb3bf4b51ef4b60671a67b2a9dcbcd9a4742f27fdf9ba8ca9a3e22"},"schema_version":"1.0","source":{"id":"math-ph/0305013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0305013","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0305013v1","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0305013","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"pith_short_12","alias_value":"CTUQB5SIOYNV","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"CTUQB5SIOYNVPD27","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"CTUQB5SI","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:0a87cd89474f3f502bb61951cee8e0d529ea5e0e3592be8d8b7886cfce13a212","target":"graph","created_at":"2026-05-18T01:38:33Z","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 show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to prove infinite-dimensional counterparts of results from classical Riemannian geometry: the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of the geodesics holds.","authors_text":"Adrian Constantin, Boris Kolev","cross_cats":["math.AP","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2003-05-07T15:07:31Z","title":"Geodesic Flow on the Diffeomorphism Group of the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0305013","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":"sha256:8d76c345984a78209c66818582795ca5dd18935902eb18e1f39935e9ecb72a94","target":"record","created_at":"2026-05-18T01:38:33Z","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":"a9a86e17d5d1a9000ef631f86fb95ab3ac7de69d5600177f7b433c41eb030638","cross_cats_sorted":["math.AP","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2003-05-07T15:07:31Z","title_canon_sha256":"99f17c00eecb3bf4b51ef4b60671a67b2a9dcbcd9a4742f27fdf9ba8ca9a3e22"},"schema_version":"1.0","source":{"id":"math-ph/0305013","kind":"arxiv","version":1}},"canonical_sha256":"14e900f648761b578f5f9cdb1f7c641001be514b909322efd66a30a7a9973ccd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14e900f648761b578f5f9cdb1f7c641001be514b909322efd66a30a7a9973ccd","first_computed_at":"2026-05-18T01:38:33.802837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:33.802837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e5iBHya3ZbK9PgjdRe7q1Ue3kLOs8kZ2EkSAmEAkMIbquuXZMxg/I9fkYo5guFyj1R8bs/DuUGbsOi9Re1u7Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:33.803361Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0305013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d76c345984a78209c66818582795ca5dd18935902eb18e1f39935e9ecb72a94","sha256:0a87cd89474f3f502bb61951cee8e0d529ea5e0e3592be8d8b7886cfce13a212"],"state_sha256":"bc5dcb33ab43a04730a0757cbd3d0dcc9dd8609287c528508cbc1d12d164c688"}