{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6FXVWLJTNDOZSKW72HTG7JAYR5","short_pith_number":"pith:6FXVWLJT","canonical_record":{"source":{"id":"1208.1981","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-08-09T17:46:11Z","cross_cats_sorted":[],"title_canon_sha256":"71ed5d42648fb8f8d146b033e67c35a72395cbd14fdfb029135eec688c25adc5","abstract_canon_sha256":"d5b1b77cc7ae120f55c7de81aa4fa5cc70a7b76918f24130f449b79f936415af"},"schema_version":"1.0"},"canonical_sha256":"f16f5b2d3368dd992adfd1e66fa4188f533bc059d07dcae20192a40848a4d90f","source":{"kind":"arxiv","id":"1208.1981","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1981","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1981v3","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1981","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"6FXVWLJTNDOZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6FXVWLJTNDOZSKW7","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6FXVWLJT","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6FXVWLJTNDOZSKW72HTG7JAYR5","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1981","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-08-09T17:46:11Z","cross_cats_sorted":[],"title_canon_sha256":"71ed5d42648fb8f8d146b033e67c35a72395cbd14fdfb029135eec688c25adc5","abstract_canon_sha256":"d5b1b77cc7ae120f55c7de81aa4fa5cc70a7b76918f24130f449b79f936415af"},"schema_version":"1.0"},"canonical_sha256":"f16f5b2d3368dd992adfd1e66fa4188f533bc059d07dcae20192a40848a4d90f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:53.593214Z","signature_b64":"a51UmKNTOXvDN7ZUNw+B9mqYuZ3pEjNjD9xZ/hBmtbdzEmLcQIEl7u8Sl/LH8LLwn1mhC5iZwQHi3bINgLwbDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f16f5b2d3368dd992adfd1e66fa4188f533bc059d07dcae20192a40848a4d90f","last_reissued_at":"2026-05-18T00:24:53.592531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:53.592531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1981","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sao/896lUpsiG+TikdPcR2uhtejliZbrEk4qpxwdW1BpuNbgjaM8KM/JNP9a6Kkh7HGOjb0tTjM+hE1MJc8AAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:18:40.293401Z"},"content_sha256":"4aa730156183584053a034d582b8e5e09990e7101eb932c00816a1c71269668f","schema_version":"1.0","event_id":"sha256:4aa730156183584053a034d582b8e5e09990e7101eb932c00816a1c71269668f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6FXVWLJTNDOZSKW72HTG7JAYR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"General notions of depth for functional data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Karl Mosler, Yulia Polyakova","submitted_at":"2012-08-09T17:46:11Z","abstract_excerpt":"A data depth measures the centrality of a point with respect to an empirical distribution. Postulates are formulated, which a depth for functional data should satisfy, and a general approach is proposed to construct multivariate data depths in Banach spaces. The new approach, mentioned as Phi-depth, is based on depth infima over a proper set Phi of R^d-valued linear functions. Several desirable properties are established for the Phi-depth and a generalized version of it. The general notions include many new depths as special cases. In particular a location-slope depth and a principal component"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1981","kind":"arxiv","version":3},"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":"2026-05-18T00:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mJWVXZwsdvkvI8VAndEhqynPcj/8EYFpc7/kyCpMuddJkBtwkoZ0K0aLUbUwQHQBziKpy56LYft1G1ClsfjtAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:18:40.293749Z"},"content_sha256":"797fe76cd468ff23cb228361d3a9427b9215bea23056b1558694feacfc36e5aa","schema_version":"1.0","event_id":"sha256:797fe76cd468ff23cb228361d3a9427b9215bea23056b1558694feacfc36e5aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6FXVWLJTNDOZSKW72HTG7JAYR5/bundle.json","state_url":"https://pith.science/pith/6FXVWLJTNDOZSKW72HTG7JAYR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6FXVWLJTNDOZSKW72HTG7JAYR5/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":"2026-06-25T06:18:40Z","links":{"resolver":"https://pith.science/pith/6FXVWLJTNDOZSKW72HTG7JAYR5","bundle":"https://pith.science/pith/6FXVWLJTNDOZSKW72HTG7JAYR5/bundle.json","state":"https://pith.science/pith/6FXVWLJTNDOZSKW72HTG7JAYR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6FXVWLJTNDOZSKW72HTG7JAYR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6FXVWLJTNDOZSKW72HTG7JAYR5","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":"d5b1b77cc7ae120f55c7de81aa4fa5cc70a7b76918f24130f449b79f936415af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-08-09T17:46:11Z","title_canon_sha256":"71ed5d42648fb8f8d146b033e67c35a72395cbd14fdfb029135eec688c25adc5"},"schema_version":"1.0","source":{"id":"1208.1981","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1981","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1981v3","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1981","created_at":"2026-05-18T00:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"6FXVWLJTNDOZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6FXVWLJTNDOZSKW7","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6FXVWLJT","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:797fe76cd468ff23cb228361d3a9427b9215bea23056b1558694feacfc36e5aa","target":"graph","created_at":"2026-05-18T00:24:53Z","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 data depth measures the centrality of a point with respect to an empirical distribution. Postulates are formulated, which a depth for functional data should satisfy, and a general approach is proposed to construct multivariate data depths in Banach spaces. The new approach, mentioned as Phi-depth, is based on depth infima over a proper set Phi of R^d-valued linear functions. Several desirable properties are established for the Phi-depth and a generalized version of it. The general notions include many new depths as special cases. In particular a location-slope depth and a principal component","authors_text":"Karl Mosler, Yulia Polyakova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-08-09T17:46:11Z","title":"General notions of depth for functional data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1981","kind":"arxiv","version":3},"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":"sha256:4aa730156183584053a034d582b8e5e09990e7101eb932c00816a1c71269668f","target":"record","created_at":"2026-05-18T00:24:53Z","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":"d5b1b77cc7ae120f55c7de81aa4fa5cc70a7b76918f24130f449b79f936415af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-08-09T17:46:11Z","title_canon_sha256":"71ed5d42648fb8f8d146b033e67c35a72395cbd14fdfb029135eec688c25adc5"},"schema_version":"1.0","source":{"id":"1208.1981","kind":"arxiv","version":3}},"canonical_sha256":"f16f5b2d3368dd992adfd1e66fa4188f533bc059d07dcae20192a40848a4d90f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f16f5b2d3368dd992adfd1e66fa4188f533bc059d07dcae20192a40848a4d90f","first_computed_at":"2026-05-18T00:24:53.592531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:53.592531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a51UmKNTOXvDN7ZUNw+B9mqYuZ3pEjNjD9xZ/hBmtbdzEmLcQIEl7u8Sl/LH8LLwn1mhC5iZwQHi3bINgLwbDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:53.593214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1981","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4aa730156183584053a034d582b8e5e09990e7101eb932c00816a1c71269668f","sha256:797fe76cd468ff23cb228361d3a9427b9215bea23056b1558694feacfc36e5aa"],"state_sha256":"96ec7ec1d4fa7d7a61fc92598e0dcebcc416585b0b6253678c94bc14b8de12f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WISMxyrcHmDT2D6qKOT2vUF9kGaV9dO5mMFOvD/2c6ofSU15NdlEMUj0aZSeo0IVncp8QLFq0EuyCenEwl78Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T06:18:40.295697Z","bundle_sha256":"ee60a9283c9c74fb8579f13eba338bf8afba3defecb5a5202a79ad3073cf0d58"}}