{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:KHNDB7MDAW5TO3BERHEQKQ47YA","short_pith_number":"pith:KHNDB7MD","canonical_record":{"source":{"id":"2502.01995","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-02-04T04:16:00Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"91fe4d90448841a050480b0a1446a358b44f162d259bb086ae23fda5628ec54a","abstract_canon_sha256":"f2796a4e0b4dc9f863888a7913f54f4c4c632021a346304f1d0e8d2e47a22d49"},"schema_version":"1.0"},"canonical_sha256":"51da30fd8305bb376c2489c905439fc00cd9fc27d673cc07ecf755a7607d312b","source":{"kind":"arxiv","id":"2502.01995","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.01995","created_at":"2026-07-05T10:09:22Z"},{"alias_kind":"arxiv_version","alias_value":"2502.01995v1","created_at":"2026-07-05T10:09:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.01995","created_at":"2026-07-05T10:09:22Z"},{"alias_kind":"pith_short_12","alias_value":"KHNDB7MDAW5T","created_at":"2026-07-05T10:09:22Z"},{"alias_kind":"pith_short_16","alias_value":"KHNDB7MDAW5TO3BE","created_at":"2026-07-05T10:09:22Z"},{"alias_kind":"pith_short_8","alias_value":"KHNDB7MD","created_at":"2026-07-05T10:09:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:KHNDB7MDAW5TO3BERHEQKQ47YA","target":"record","payload":{"canonical_record":{"source":{"id":"2502.01995","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-02-04T04:16:00Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"91fe4d90448841a050480b0a1446a358b44f162d259bb086ae23fda5628ec54a","abstract_canon_sha256":"f2796a4e0b4dc9f863888a7913f54f4c4c632021a346304f1d0e8d2e47a22d49"},"schema_version":"1.0"},"canonical_sha256":"51da30fd8305bb376c2489c905439fc00cd9fc27d673cc07ecf755a7607d312b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:09:22.120249Z","signature_b64":"9iiEoPfevo2ap++L5xJT7KufzRAbfxrCQKtO0luS41Ux29ZKky6flE7WVuyDsY0D1b6WuAEq6pAosLxlfJhtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51da30fd8305bb376c2489c905439fc00cd9fc27d673cc07ecf755a7607d312b","last_reissued_at":"2026-07-05T10:09:22.119852Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:09:22.119852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.01995","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:09:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dnwzOH1Mzheszg7Yo7WTSNGacB39FuzsFHJlrSXV52/c+y+j0KhW99gUQ/52z3Ng5FF4hjyFHCI3BKokjnYiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T14:26:33.950409Z"},"content_sha256":"8c0746f26a7a5615a2be04dd1119f35cb3f67fba2cfc8ca8bde490a522ebcecf","schema_version":"1.0","event_id":"sha256:8c0746f26a7a5615a2be04dd1119f35cb3f67fba2cfc8ca8bde490a522ebcecf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:KHNDB7MDAW5TO3BERHEQKQ47YA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theoretical and Practical Analysis of Fr\\'echet Regression via Comparison Geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"stat.ML","authors_text":"Howard Bondell, Masanari Kimura","submitted_at":"2025-02-04T04:16:00Z","abstract_excerpt":"Fr\\'echet regression extends classical regression methods to non-Euclidean metric spaces, enabling the analysis of data relationships on complex structures such as manifolds and graphs. This work establishes a rigorous theoretical analysis for Fr\\'echet regression through the lens of comparison geometry which leads to important considerations for its use in practice. The analysis provides key results on the existence, uniqueness, and stability of the Fr\\'echet mean, along with statistical guarantees for nonparametric regression, including exponential concentration bounds and convergence rates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01995","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.01995/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:09:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2I0Bnq6qbT0fENz0JKevxbw6a54BKC8CuD/CSZWORtHuGGt3N84OY5JZng6lWYyD1Foju4SQfTXu+tIlVvMHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T14:26:33.950793Z"},"content_sha256":"71dd3114257af81f6b2020880d22d873f40901c822906f528be042a0f3415aa3","schema_version":"1.0","event_id":"sha256:71dd3114257af81f6b2020880d22d873f40901c822906f528be042a0f3415aa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KHNDB7MDAW5TO3BERHEQKQ47YA/bundle.json","state_url":"https://pith.science/pith/KHNDB7MDAW5TO3BERHEQKQ47YA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KHNDB7MDAW5TO3BERHEQKQ47YA/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":"2026-07-12T14:26:33Z","links":{"resolver":"https://pith.science/pith/KHNDB7MDAW5TO3BERHEQKQ47YA","bundle":"https://pith.science/pith/KHNDB7MDAW5TO3BERHEQKQ47YA/bundle.json","state":"https://pith.science/pith/KHNDB7MDAW5TO3BERHEQKQ47YA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KHNDB7MDAW5TO3BERHEQKQ47YA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KHNDB7MDAW5TO3BERHEQKQ47YA","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":"f2796a4e0b4dc9f863888a7913f54f4c4c632021a346304f1d0e8d2e47a22d49","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-02-04T04:16:00Z","title_canon_sha256":"91fe4d90448841a050480b0a1446a358b44f162d259bb086ae23fda5628ec54a"},"schema_version":"1.0","source":{"id":"2502.01995","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.01995","created_at":"2026-07-05T10:09:22Z"},{"alias_kind":"arxiv_version","alias_value":"2502.01995v1","created_at":"2026-07-05T10:09:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.01995","created_at":"2026-07-05T10:09:22Z"},{"alias_kind":"pith_short_12","alias_value":"KHNDB7MDAW5T","created_at":"2026-07-05T10:09:22Z"},{"alias_kind":"pith_short_16","alias_value":"KHNDB7MDAW5TO3BE","created_at":"2026-07-05T10:09:22Z"},{"alias_kind":"pith_short_8","alias_value":"KHNDB7MD","created_at":"2026-07-05T10:09:22Z"}],"graph_snapshots":[{"event_id":"sha256:71dd3114257af81f6b2020880d22d873f40901c822906f528be042a0f3415aa3","target":"graph","created_at":"2026-07-05T10:09:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.01995/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fr\\'echet regression extends classical regression methods to non-Euclidean metric spaces, enabling the analysis of data relationships on complex structures such as manifolds and graphs. This work establishes a rigorous theoretical analysis for Fr\\'echet regression through the lens of comparison geometry which leads to important considerations for its use in practice. The analysis provides key results on the existence, uniqueness, and stability of the Fr\\'echet mean, along with statistical guarantees for nonparametric regression, including exponential concentration bounds and convergence rates.","authors_text":"Howard Bondell, Masanari Kimura","cross_cats":["cs.AI","cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-02-04T04:16:00Z","title":"Theoretical and Practical Analysis of Fr\\'echet Regression via Comparison Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01995","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":"sha256:8c0746f26a7a5615a2be04dd1119f35cb3f67fba2cfc8ca8bde490a522ebcecf","target":"record","created_at":"2026-07-05T10:09:22Z","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":"f2796a4e0b4dc9f863888a7913f54f4c4c632021a346304f1d0e8d2e47a22d49","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2025-02-04T04:16:00Z","title_canon_sha256":"91fe4d90448841a050480b0a1446a358b44f162d259bb086ae23fda5628ec54a"},"schema_version":"1.0","source":{"id":"2502.01995","kind":"arxiv","version":1}},"canonical_sha256":"51da30fd8305bb376c2489c905439fc00cd9fc27d673cc07ecf755a7607d312b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51da30fd8305bb376c2489c905439fc00cd9fc27d673cc07ecf755a7607d312b","first_computed_at":"2026-07-05T10:09:22.119852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:09:22.119852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9iiEoPfevo2ap++L5xJT7KufzRAbfxrCQKtO0luS41Ux29ZKky6flE7WVuyDsY0D1b6WuAEq6pAosLxlfJhtAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:09:22.120249Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.01995","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c0746f26a7a5615a2be04dd1119f35cb3f67fba2cfc8ca8bde490a522ebcecf","sha256:71dd3114257af81f6b2020880d22d873f40901c822906f528be042a0f3415aa3"],"state_sha256":"30987a837acea46c96ff387eb4d462e234ea71a6565218eb44238a5912a86b86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"njn/0LnrpUzseVZWAO9ZK8pgo4tUe0bmRaKuX4gd5pj2R3kbNkEuCeburYIVpCWFhUZ113vcJDVMtLQBZ61kBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T14:26:33.953421Z","bundle_sha256":"b0e26951bac49bac3c15d4da690a1f0db5d76d1b1de7ab9f6a0735a80f3a1257"}}