{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6IJTWCHPWQK5JYZHVFHFBEUNFO","short_pith_number":"pith:6IJTWCHP","canonical_record":{"source":{"id":"1803.06550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-03-17T18:31:49Z","cross_cats_sorted":[],"title_canon_sha256":"af2a7de591986486dbe4c76c6bcfc0d2606bad89a667bfd6d58bd0926e561bab","abstract_canon_sha256":"99d15192dfdb7d2522f28aace919b18587d9ac91ab5ebc4e0111c9dab319414b"},"schema_version":"1.0"},"canonical_sha256":"f2133b08efb415d4e327a94e50928d2b80916d732a5ed83254231551427ad521","source":{"kind":"arxiv","id":"1803.06550","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06550","created_at":"2026-05-18T00:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06550v1","created_at":"2026-05-18T00:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06550","created_at":"2026-05-18T00:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"6IJTWCHPWQK5","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6IJTWCHPWQK5JYZH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6IJTWCHP","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6IJTWCHPWQK5JYZHVFHFBEUNFO","target":"record","payload":{"canonical_record":{"source":{"id":"1803.06550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-03-17T18:31:49Z","cross_cats_sorted":[],"title_canon_sha256":"af2a7de591986486dbe4c76c6bcfc0d2606bad89a667bfd6d58bd0926e561bab","abstract_canon_sha256":"99d15192dfdb7d2522f28aace919b18587d9ac91ab5ebc4e0111c9dab319414b"},"schema_version":"1.0"},"canonical_sha256":"f2133b08efb415d4e327a94e50928d2b80916d732a5ed83254231551427ad521","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:45.631926Z","signature_b64":"5+NOI8b6aj3dS4yiVorC+bp3WEgpbJHfyrMt2u0XeXOYc6djCDlBw5O6PgxTzDbia0DAV/X6upmUT6aAe9blCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2133b08efb415d4e327a94e50928d2b80916d732a5ed83254231551427ad521","last_reissued_at":"2026-05-18T00:20:45.631398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:45.631398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.06550","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":"2026-05-18T00:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"izOQeRMacheOfMEGjumJeFjrKbnv4lVh7PcG3banPMdTOnbdrKdwEUKdicWod7y+6gZZjXCiJFKsT3kcgMNRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:38:38.258687Z"},"content_sha256":"016a4ead594700f064a391f95353897f3c8ef3db0d67ccbd6c4bbb9e52b18834","schema_version":"1.0","event_id":"sha256:016a4ead594700f064a391f95353897f3c8ef3db0d67ccbd6c4bbb9e52b18834"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6IJTWCHPWQK5JYZHVFHFBEUNFO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Mahalanobis distance in functional settings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Antonio Cuevas, Beatriz Bueno-Larraz, Jos\\'e R. Berrendero","submitted_at":"2018-03-17T18:31:49Z","abstract_excerpt":"Mahalanobis distance is a classical tool in multivariate analysis. We suggest here an extension of this concept to the case of functional data. More precisely, the proposed definition concerns those statistical problems where the sample data are real functions defined on a compact interval of the real line. The obvious difficulty for such a functional extension is the non-invertibility of the covariance operator in infinite-dimensional cases. Unlike other recent proposals, our definition is suggested and motivated in terms of the Reproducing Kernel Hilbert Space (RKHS) associated with the stoc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06550","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":""},"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":"2026-05-18T00:20:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iEJjHqs1PBRIqTFEuDTEE5qHB3qvwc12YXoeNwz/YFMbmSvFyCnpMDf1dchVr7oGEcVIK4UhXWrEYS75HXwlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T19:38:38.259027Z"},"content_sha256":"4a52edc5157b78f2e910edda3a7fd9bd488e690b9cfa104161ebc5e5db393c9c","schema_version":"1.0","event_id":"sha256:4a52edc5157b78f2e910edda3a7fd9bd488e690b9cfa104161ebc5e5db393c9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6IJTWCHPWQK5JYZHVFHFBEUNFO/bundle.json","state_url":"https://pith.science/pith/6IJTWCHPWQK5JYZHVFHFBEUNFO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6IJTWCHPWQK5JYZHVFHFBEUNFO/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":"2026-06-03T19:38:38Z","links":{"resolver":"https://pith.science/pith/6IJTWCHPWQK5JYZHVFHFBEUNFO","bundle":"https://pith.science/pith/6IJTWCHPWQK5JYZHVFHFBEUNFO/bundle.json","state":"https://pith.science/pith/6IJTWCHPWQK5JYZHVFHFBEUNFO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6IJTWCHPWQK5JYZHVFHFBEUNFO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6IJTWCHPWQK5JYZHVFHFBEUNFO","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":"99d15192dfdb7d2522f28aace919b18587d9ac91ab5ebc4e0111c9dab319414b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-03-17T18:31:49Z","title_canon_sha256":"af2a7de591986486dbe4c76c6bcfc0d2606bad89a667bfd6d58bd0926e561bab"},"schema_version":"1.0","source":{"id":"1803.06550","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06550","created_at":"2026-05-18T00:20:45Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06550v1","created_at":"2026-05-18T00:20:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06550","created_at":"2026-05-18T00:20:45Z"},{"alias_kind":"pith_short_12","alias_value":"6IJTWCHPWQK5","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6IJTWCHPWQK5JYZH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6IJTWCHP","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:4a52edc5157b78f2e910edda3a7fd9bd488e690b9cfa104161ebc5e5db393c9c","target":"graph","created_at":"2026-05-18T00:20:45Z","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":"Mahalanobis distance is a classical tool in multivariate analysis. We suggest here an extension of this concept to the case of functional data. More precisely, the proposed definition concerns those statistical problems where the sample data are real functions defined on a compact interval of the real line. The obvious difficulty for such a functional extension is the non-invertibility of the covariance operator in infinite-dimensional cases. Unlike other recent proposals, our definition is suggested and motivated in terms of the Reproducing Kernel Hilbert Space (RKHS) associated with the stoc","authors_text":"Antonio Cuevas, Beatriz Bueno-Larraz, Jos\\'e R. Berrendero","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-03-17T18:31:49Z","title":"On Mahalanobis distance in functional settings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06550","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":"sha256:016a4ead594700f064a391f95353897f3c8ef3db0d67ccbd6c4bbb9e52b18834","target":"record","created_at":"2026-05-18T00:20:45Z","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":"99d15192dfdb7d2522f28aace919b18587d9ac91ab5ebc4e0111c9dab319414b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-03-17T18:31:49Z","title_canon_sha256":"af2a7de591986486dbe4c76c6bcfc0d2606bad89a667bfd6d58bd0926e561bab"},"schema_version":"1.0","source":{"id":"1803.06550","kind":"arxiv","version":1}},"canonical_sha256":"f2133b08efb415d4e327a94e50928d2b80916d732a5ed83254231551427ad521","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2133b08efb415d4e327a94e50928d2b80916d732a5ed83254231551427ad521","first_computed_at":"2026-05-18T00:20:45.631398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:45.631398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5+NOI8b6aj3dS4yiVorC+bp3WEgpbJHfyrMt2u0XeXOYc6djCDlBw5O6PgxTzDbia0DAV/X6upmUT6aAe9blCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:45.631926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.06550","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:016a4ead594700f064a391f95353897f3c8ef3db0d67ccbd6c4bbb9e52b18834","sha256:4a52edc5157b78f2e910edda3a7fd9bd488e690b9cfa104161ebc5e5db393c9c"],"state_sha256":"ce8598c36d5d847a2da2bc18e7f7f39933f34d12c3a850e641cd9818830766e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ujRKDHr6V1SShDb4bu2rHohRgiqvKP70pVer0LLtuPzl3Q6bU2vByrHzWloTpF+zsbvQig0WIBT+jaPFwcjADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T19:38:38.260877Z","bundle_sha256":"a0e5236cb1de0979aa9ce557456a13f75c0bda015d3d72c57ab18d0c4f734ae3"}}