{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YGPWQB2L2BBQBGW6Y765ROGHKX","short_pith_number":"pith:YGPWQB2L","canonical_record":{"source":{"id":"1202.5122","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-23T09:15:04Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"d0b2d017ede6629297dc1de10ad34e0a9f6e782ca7e174c9b081f717df727621","abstract_canon_sha256":"7f09bbb54c2014e232e54f744cea73a38796247c0dcd49b399cfd4ddc2e01eb2"},"schema_version":"1.0"},"canonical_sha256":"c19f68074bd043009adec7fdd8b8c755f825f4a11e5f79eae3b10074a8a23523","source":{"kind":"arxiv","id":"1202.5122","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5122","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5122v4","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5122","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"YGPWQB2L2BBQ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YGPWQB2L2BBQBGW6","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YGPWQB2L","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YGPWQB2L2BBQBGW6Y765ROGHKX","target":"record","payload":{"canonical_record":{"source":{"id":"1202.5122","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-23T09:15:04Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"d0b2d017ede6629297dc1de10ad34e0a9f6e782ca7e174c9b081f717df727621","abstract_canon_sha256":"7f09bbb54c2014e232e54f744cea73a38796247c0dcd49b399cfd4ddc2e01eb2"},"schema_version":"1.0"},"canonical_sha256":"c19f68074bd043009adec7fdd8b8c755f825f4a11e5f79eae3b10074a8a23523","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:43.375908Z","signature_b64":"PpbjAWkmIrdkPvEqXFbGq9/EI1e0h0RPyXMzIJDnMwrdfNoYEtbuCxiIsQh1kff3Giy4YJbW/glycWYx4iFyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c19f68074bd043009adec7fdd8b8c755f825f4a11e5f79eae3b10074a8a23523","last_reissued_at":"2026-05-18T02:41:43.375244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:43.375244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.5122","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T5d2SudE40BvJsUllyfWDr+UO+E3hi4NaPO+gB4s+mg8/Ocnv9ITPHluul5MGqM7Zq83m9mmCEYYOxdWL7UhBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:28:27.070389Z"},"content_sha256":"9d82adc7c1157d8fe044e04831eb435523ebe3917d9dbe3fe4437049c94cb832","schema_version":"1.0","event_id":"sha256:9d82adc7c1157d8fe044e04831eb435523ebe3917d9dbe3fe4437049c94cb832"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YGPWQB2L2BBQBGW6Y765ROGHKX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Boris Kolev (I2M), Joachim Escher (IFAM)","submitted_at":"2012-02-23T09:15:04Z","abstract_excerpt":"In this paper, we study the geodesic flow of a right-invariant metric induced by a general Fourier multiplier on the diffeomorphism group of the circle and on some of its homogeneous spaces. This study covers in particular right-invariant metrics induced by Sobolev norms of fractional order. We show that, under a certain condition on the symbol of the inertia operator (which is satisfied for the fractional Sobolev norm $H^{s}$ for $s \\ge 1/2$), the corresponding initial value problem is well-posed in the smooth category and that the Riemannian exponential map is a smooth local diffeomorphism. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5122","kind":"arxiv","version":4},"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":"2026-05-18T02:41:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LDTgHU1dpR3ynoUmvC4jOXCdJ3TE8lkd/lLVlrFu0dPAKr5tcpgv2/FslidyrNYpe39ph1hvCIV64FAlkSFbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:28:27.071075Z"},"content_sha256":"a8c6f4fded163fdcc1c820994153a14561a79b8ed1566f83676d5c67ecbd24fb","schema_version":"1.0","event_id":"sha256:a8c6f4fded163fdcc1c820994153a14561a79b8ed1566f83676d5c67ecbd24fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YGPWQB2L2BBQBGW6Y765ROGHKX/bundle.json","state_url":"https://pith.science/pith/YGPWQB2L2BBQBGW6Y765ROGHKX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YGPWQB2L2BBQBGW6Y765ROGHKX/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":"2026-06-10T01:28:27Z","links":{"resolver":"https://pith.science/pith/YGPWQB2L2BBQBGW6Y765ROGHKX","bundle":"https://pith.science/pith/YGPWQB2L2BBQBGW6Y765ROGHKX/bundle.json","state":"https://pith.science/pith/YGPWQB2L2BBQBGW6Y765ROGHKX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YGPWQB2L2BBQBGW6Y765ROGHKX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YGPWQB2L2BBQBGW6Y765ROGHKX","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":"7f09bbb54c2014e232e54f744cea73a38796247c0dcd49b399cfd4ddc2e01eb2","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-23T09:15:04Z","title_canon_sha256":"d0b2d017ede6629297dc1de10ad34e0a9f6e782ca7e174c9b081f717df727621"},"schema_version":"1.0","source":{"id":"1202.5122","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5122","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5122v4","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5122","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"YGPWQB2L2BBQ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YGPWQB2L2BBQBGW6","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YGPWQB2L","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:a8c6f4fded163fdcc1c820994153a14561a79b8ed1566f83676d5c67ecbd24fb","target":"graph","created_at":"2026-05-18T02:41:43Z","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 this paper, we study the geodesic flow of a right-invariant metric induced by a general Fourier multiplier on the diffeomorphism group of the circle and on some of its homogeneous spaces. This study covers in particular right-invariant metrics induced by Sobolev norms of fractional order. We show that, under a certain condition on the symbol of the inertia operator (which is satisfied for the fractional Sobolev norm $H^{s}$ for $s \\ge 1/2$), the corresponding initial value problem is well-posed in the smooth category and that the Riemannian exponential map is a smooth local diffeomorphism. ","authors_text":"Boris Kolev (I2M), Joachim Escher (IFAM)","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-23T09:15:04Z","title":"Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5122","kind":"arxiv","version":4},"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":"sha256:9d82adc7c1157d8fe044e04831eb435523ebe3917d9dbe3fe4437049c94cb832","target":"record","created_at":"2026-05-18T02:41:43Z","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":"7f09bbb54c2014e232e54f744cea73a38796247c0dcd49b399cfd4ddc2e01eb2","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-02-23T09:15:04Z","title_canon_sha256":"d0b2d017ede6629297dc1de10ad34e0a9f6e782ca7e174c9b081f717df727621"},"schema_version":"1.0","source":{"id":"1202.5122","kind":"arxiv","version":4}},"canonical_sha256":"c19f68074bd043009adec7fdd8b8c755f825f4a11e5f79eae3b10074a8a23523","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c19f68074bd043009adec7fdd8b8c755f825f4a11e5f79eae3b10074a8a23523","first_computed_at":"2026-05-18T02:41:43.375244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:43.375244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PpbjAWkmIrdkPvEqXFbGq9/EI1e0h0RPyXMzIJDnMwrdfNoYEtbuCxiIsQh1kff3Giy4YJbW/glycWYx4iFyAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:43.375908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5122","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d82adc7c1157d8fe044e04831eb435523ebe3917d9dbe3fe4437049c94cb832","sha256:a8c6f4fded163fdcc1c820994153a14561a79b8ed1566f83676d5c67ecbd24fb"],"state_sha256":"14d4bd98ba1c103ad95a580d1289f903ad872f67f01af5f5f9c2e271bd2f535a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CL2iDF1EB74ZORtdNHKesfLVBY51hc+cANaqX9ZZSk29VziEoi9pgjq1OX2eQ8xR3ICTleP9hCnD0fqSXn3zBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:28:27.075302Z","bundle_sha256":"e4593ab7eb8514fb02c2273f31610d33e1c342f550d8b327837e309cf9ab723d"}}