{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AHVVL3QTDN553JV77DY37QJVRJ","short_pith_number":"pith:AHVVL3QT","canonical_record":{"source":{"id":"1010.0427","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-10-03T18:29:15Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c1d1d54bb9fab6b2cdaaa42d1a00b7ca4d89635b48f4a6c7fd7d7bca7c62d9ab","abstract_canon_sha256":"f01de26a562c6e83802e0cf1b495e2a640256b94e78eea95340703a7f51947b8"},"schema_version":"1.0"},"canonical_sha256":"01eb55ee131b7bdda6bff8f1bfc1358a5f741c11fc478cbfa3177965d7cc2a2c","source":{"kind":"arxiv","id":"1010.0427","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0427","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0427v4","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0427","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"AHVVL3QTDN55","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AHVVL3QTDN553JV7","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AHVVL3QT","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AHVVL3QTDN553JV77DY37QJVRJ","target":"record","payload":{"canonical_record":{"source":{"id":"1010.0427","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-10-03T18:29:15Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c1d1d54bb9fab6b2cdaaa42d1a00b7ca4d89635b48f4a6c7fd7d7bca7c62d9ab","abstract_canon_sha256":"f01de26a562c6e83802e0cf1b495e2a640256b94e78eea95340703a7f51947b8"},"schema_version":"1.0"},"canonical_sha256":"01eb55ee131b7bdda6bff8f1bfc1358a5f741c11fc478cbfa3177965d7cc2a2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:55.176366Z","signature_b64":"0tiPzE0vzSzcncXBx054Ry1/lMftwAYHmGdp56dppWPgv2RbqmbCHARBN4uFKFp3fcuM6G6W+y5ikIA56wAUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01eb55ee131b7bdda6bff8f1bfc1358a5f741c11fc478cbfa3177965d7cc2a2c","last_reissued_at":"2026-05-18T04:14:55.175959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:55.175959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.0427","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":"2026-05-18T04:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FMbpbK8dsLGeTRc+09F6UZhiZzEuIybSTAWe0ahqwZfem4IB2jwta0FB0K4Amy6IjqWKFdosOg12rwnpSib0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:16:27.786990Z"},"content_sha256":"fc28cdeb246628ce58f1148f42e0b2e0c4ff395a9fcab7f3a48b633584f26c72","schema_version":"1.0","event_id":"sha256:fc28cdeb246628ce58f1148f42e0b2e0c4ff395a9fcab7f3a48b633584f26c72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AHVVL3QTDN553JV77DY37QJVRJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the consistency of Fr\\'echet means in deformable models for curve and image analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Benjamin Charlier (IMT), J\\'er\\'emie Bigot (IMT)","submitted_at":"2010-10-03T18:29:15Z","abstract_excerpt":"A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual variations in intensity around a mean pattern. It is shown that an appropriate tool for statistical inference in such models is the notion of sample Fr\\'echet means, which leads to estimators of the deformation parameters and the mean pattern. The main contribution of this paper is to study how the behavior of these estimators depends on the number n of design points"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0427","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":"2026-05-18T04:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J94R17i+uoI//ddv3sXWQDMt8VB2SrctKi9kOSsdR81FODAJMwhf5FSxtmjEtZOHZU1GwdOiioGTBNa3B9iaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T05:16:27.787733Z"},"content_sha256":"343679bce8ec1e4fe74305ea92760f0901a80a8fd564a127131689cd169b828e","schema_version":"1.0","event_id":"sha256:343679bce8ec1e4fe74305ea92760f0901a80a8fd564a127131689cd169b828e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AHVVL3QTDN553JV77DY37QJVRJ/bundle.json","state_url":"https://pith.science/pith/AHVVL3QTDN553JV77DY37QJVRJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AHVVL3QTDN553JV77DY37QJVRJ/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":"2026-06-08T05:16:27Z","links":{"resolver":"https://pith.science/pith/AHVVL3QTDN553JV77DY37QJVRJ","bundle":"https://pith.science/pith/AHVVL3QTDN553JV77DY37QJVRJ/bundle.json","state":"https://pith.science/pith/AHVVL3QTDN553JV77DY37QJVRJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AHVVL3QTDN553JV77DY37QJVRJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AHVVL3QTDN553JV77DY37QJVRJ","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":"f01de26a562c6e83802e0cf1b495e2a640256b94e78eea95340703a7f51947b8","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-10-03T18:29:15Z","title_canon_sha256":"c1d1d54bb9fab6b2cdaaa42d1a00b7ca4d89635b48f4a6c7fd7d7bca7c62d9ab"},"schema_version":"1.0","source":{"id":"1010.0427","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0427","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0427v4","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0427","created_at":"2026-05-18T04:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"AHVVL3QTDN55","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AHVVL3QTDN553JV7","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AHVVL3QT","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:343679bce8ec1e4fe74305ea92760f0901a80a8fd564a127131689cd169b828e","target":"graph","created_at":"2026-05-18T04:14:55Z","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":"A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual variations in intensity around a mean pattern. It is shown that an appropriate tool for statistical inference in such models is the notion of sample Fr\\'echet means, which leads to estimators of the deformation parameters and the mean pattern. The main contribution of this paper is to study how the behavior of these estimators depends on the number n of design points","authors_text":"Benjamin Charlier (IMT), J\\'er\\'emie Bigot (IMT)","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-10-03T18:29:15Z","title":"On the consistency of Fr\\'echet means in deformable models for curve and image analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0427","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:fc28cdeb246628ce58f1148f42e0b2e0c4ff395a9fcab7f3a48b633584f26c72","target":"record","created_at":"2026-05-18T04:14:55Z","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":"f01de26a562c6e83802e0cf1b495e2a640256b94e78eea95340703a7f51947b8","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-10-03T18:29:15Z","title_canon_sha256":"c1d1d54bb9fab6b2cdaaa42d1a00b7ca4d89635b48f4a6c7fd7d7bca7c62d9ab"},"schema_version":"1.0","source":{"id":"1010.0427","kind":"arxiv","version":4}},"canonical_sha256":"01eb55ee131b7bdda6bff8f1bfc1358a5f741c11fc478cbfa3177965d7cc2a2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01eb55ee131b7bdda6bff8f1bfc1358a5f741c11fc478cbfa3177965d7cc2a2c","first_computed_at":"2026-05-18T04:14:55.175959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:55.175959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tiPzE0vzSzcncXBx054Ry1/lMftwAYHmGdp56dppWPgv2RbqmbCHARBN4uFKFp3fcuM6G6W+y5ikIA56wAUAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:55.176366Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0427","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc28cdeb246628ce58f1148f42e0b2e0c4ff395a9fcab7f3a48b633584f26c72","sha256:343679bce8ec1e4fe74305ea92760f0901a80a8fd564a127131689cd169b828e"],"state_sha256":"4f428566ccc6e0ee8c049fc659ba00d652649653a1227dec2e9ad0a5bbc3df75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/DZSi2RLkxL+aGbZUH9jpP4Ohvgb7uxBiLEus7xRYDp9ScIAPr3Y6cYGo0l8P6gAzIGt+CCJqseq9pWENtLDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T05:16:27.791497Z","bundle_sha256":"ec2ebf4deeddd6d3ff2d3877f003ff93a04408b7a4d49741b2374a77d87c5f7d"}}