{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:27QUISQHNGKQEMVHAJ3RF5RMTH","short_pith_number":"pith:27QUISQH","canonical_record":{"source":{"id":"1103.3817","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-19T23:00:07Z","cross_cats_sorted":["stat.AP","stat.ME","stat.TH"],"title_canon_sha256":"8292e8feff630b643f4350e3bfbdb71ed7c607cd95469533569ca9e52481a5eb","abstract_canon_sha256":"7b77cad97d2f58411089c74c17502180e1b0ca17c5b78b70b88dde01d1a3cf89"},"schema_version":"1.0"},"canonical_sha256":"d7e1444a0769950232a7027712f62c99cf8b96cd947ffc799c42e1e9e5838495","source":{"kind":"arxiv","id":"1103.3817","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3817","created_at":"2026-05-18T02:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3817v2","created_at":"2026-05-18T02:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3817","created_at":"2026-05-18T02:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"27QUISQHNGKQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"27QUISQHNGKQEMVH","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"27QUISQH","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:27QUISQHNGKQEMVHAJ3RF5RMTH","target":"record","payload":{"canonical_record":{"source":{"id":"1103.3817","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-19T23:00:07Z","cross_cats_sorted":["stat.AP","stat.ME","stat.TH"],"title_canon_sha256":"8292e8feff630b643f4350e3bfbdb71ed7c607cd95469533569ca9e52481a5eb","abstract_canon_sha256":"7b77cad97d2f58411089c74c17502180e1b0ca17c5b78b70b88dde01d1a3cf89"},"schema_version":"1.0"},"canonical_sha256":"d7e1444a0769950232a7027712f62c99cf8b96cd947ffc799c42e1e9e5838495","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:18.047495Z","signature_b64":"xP1a/FBjrBki3IeWxYE6Aye330TDKH4445flv7I+TvlrKKmfJgDwjwhCv/Ay6T8o01+FZYeGeehcwGpf6ip7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7e1444a0769950232a7027712f62c99cf8b96cd947ffc799c42e1e9e5838495","last_reissued_at":"2026-05-18T02:22:18.046937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:18.046937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.3817","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":"2026-05-18T02:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"79GByUpPETtPbGM/qMrdfosfjE0W8Hg3U7W3YQf9G0UKlJrCkgB+KKN2ZRy+HQyjbRvWCGVD1UcVkFFTDVvJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:33:43.693709Z"},"content_sha256":"6035cd4808a7affb4c3170c6b24d0acdf3dfdf6b53689b25375b1ec135376d4e","schema_version":"1.0","event_id":"sha256:6035cd4808a7affb4c3170c6b24d0acdf3dfdf6b53689b25375b1ec135376d4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:27QUISQHNGKQEMVHAJ3RF5RMTH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Registration of Functional Data Using Fisher-Rao Metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.AP","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Anuj Srivastava, Eric Klassen, J. S. Marron, Sebastian Kurtek, Wei Wu","submitted_at":"2011-03-19T23:00:07Z","abstract_excerpt":"We introduce a novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis. This framework uses the Fisher-Rao Riemannian metric to derive a proper distance on the quotient space of functions modulo the time-warping group. A convenient square-root velocity function (SRVF) representation transforms the Fisher-Rao metric into the standard $\\ltwo$ metric, simplifying the computations. This distance is then used to define a Karcher mean template and warp the individual functions to align them with the K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3817","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":"2026-05-18T02:22:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/BkPAa3UYz119npoKBL7ZFAUUnQj3ilt9b+ApjUzj6DxxZukH87lqXw/CDR1x5WHxG92uBlZ7wKxoKqnhsAKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:33:43.694340Z"},"content_sha256":"61d1395b58e2dbb70e20570ed9da47756b48bd4494bea3400aa25e0776739f72","schema_version":"1.0","event_id":"sha256:61d1395b58e2dbb70e20570ed9da47756b48bd4494bea3400aa25e0776739f72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/27QUISQHNGKQEMVHAJ3RF5RMTH/bundle.json","state_url":"https://pith.science/pith/27QUISQHNGKQEMVHAJ3RF5RMTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/27QUISQHNGKQEMVHAJ3RF5RMTH/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":"2026-05-26T11:33:43Z","links":{"resolver":"https://pith.science/pith/27QUISQHNGKQEMVHAJ3RF5RMTH","bundle":"https://pith.science/pith/27QUISQHNGKQEMVHAJ3RF5RMTH/bundle.json","state":"https://pith.science/pith/27QUISQHNGKQEMVHAJ3RF5RMTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/27QUISQHNGKQEMVHAJ3RF5RMTH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:27QUISQHNGKQEMVHAJ3RF5RMTH","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":"7b77cad97d2f58411089c74c17502180e1b0ca17c5b78b70b88dde01d1a3cf89","cross_cats_sorted":["stat.AP","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-19T23:00:07Z","title_canon_sha256":"8292e8feff630b643f4350e3bfbdb71ed7c607cd95469533569ca9e52481a5eb"},"schema_version":"1.0","source":{"id":"1103.3817","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3817","created_at":"2026-05-18T02:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3817v2","created_at":"2026-05-18T02:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3817","created_at":"2026-05-18T02:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"27QUISQHNGKQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"27QUISQHNGKQEMVH","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"27QUISQH","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:61d1395b58e2dbb70e20570ed9da47756b48bd4494bea3400aa25e0776739f72","target":"graph","created_at":"2026-05-18T02:22:18Z","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 introduce a novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis. This framework uses the Fisher-Rao Riemannian metric to derive a proper distance on the quotient space of functions modulo the time-warping group. A convenient square-root velocity function (SRVF) representation transforms the Fisher-Rao metric into the standard $\\ltwo$ metric, simplifying the computations. This distance is then used to define a Karcher mean template and warp the individual functions to align them with the K","authors_text":"Anuj Srivastava, Eric Klassen, J. S. Marron, Sebastian Kurtek, Wei Wu","cross_cats":["stat.AP","stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-19T23:00:07Z","title":"Registration of Functional Data Using Fisher-Rao Metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3817","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":"sha256:6035cd4808a7affb4c3170c6b24d0acdf3dfdf6b53689b25375b1ec135376d4e","target":"record","created_at":"2026-05-18T02:22:18Z","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":"7b77cad97d2f58411089c74c17502180e1b0ca17c5b78b70b88dde01d1a3cf89","cross_cats_sorted":["stat.AP","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-03-19T23:00:07Z","title_canon_sha256":"8292e8feff630b643f4350e3bfbdb71ed7c607cd95469533569ca9e52481a5eb"},"schema_version":"1.0","source":{"id":"1103.3817","kind":"arxiv","version":2}},"canonical_sha256":"d7e1444a0769950232a7027712f62c99cf8b96cd947ffc799c42e1e9e5838495","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7e1444a0769950232a7027712f62c99cf8b96cd947ffc799c42e1e9e5838495","first_computed_at":"2026-05-18T02:22:18.046937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:18.046937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xP1a/FBjrBki3IeWxYE6Aye330TDKH4445flv7I+TvlrKKmfJgDwjwhCv/Ay6T8o01+FZYeGeehcwGpf6ip7Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:18.047495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3817","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6035cd4808a7affb4c3170c6b24d0acdf3dfdf6b53689b25375b1ec135376d4e","sha256:61d1395b58e2dbb70e20570ed9da47756b48bd4494bea3400aa25e0776739f72"],"state_sha256":"f701ad7606c39bba80a8f508fcd9d226dd86a4f738c399d0850154dee007fea7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wRzyxGifyYhrbNdRK9dfjMIwonoLYK2PV4TkkpkxOPE9dmOyWQpmSHNpZBxFzuWLAqYcpR4nVjKdQOTSvrAFCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:33:43.697747Z","bundle_sha256":"050bc0f13d3758f7a06cf4197db755fbc36036d5f673a1e24a5f99c99a936046"}}