{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GVU2D4MV3572LTG3CKNBLSKYES","short_pith_number":"pith:GVU2D4MV","canonical_record":{"source":{"id":"1104.3074","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-04-15T14:41:41Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a3b17f04e91dbf917e65b68575fe4cab664d1a4e1d5b6c1fe03157fb7f842f12","abstract_canon_sha256":"cb5de2c081ca44297f7b909c20095c0b7eace9a5833414d849bc80d9bbb0eaef"},"schema_version":"1.0"},"canonical_sha256":"3569a1f195df7fa5ccdb129a15c95824b2c4e706eb7e23c9d48b96eed141d161","source":{"kind":"arxiv","id":"1104.3074","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3074","created_at":"2026-05-18T03:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3074v2","created_at":"2026-05-18T03:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3074","created_at":"2026-05-18T03:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"GVU2D4MV3572","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GVU2D4MV3572LTG3","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GVU2D4MV","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GVU2D4MV3572LTG3CKNBLSKYES","target":"record","payload":{"canonical_record":{"source":{"id":"1104.3074","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-04-15T14:41:41Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"a3b17f04e91dbf917e65b68575fe4cab664d1a4e1d5b6c1fe03157fb7f842f12","abstract_canon_sha256":"cb5de2c081ca44297f7b909c20095c0b7eace9a5833414d849bc80d9bbb0eaef"},"schema_version":"1.0"},"canonical_sha256":"3569a1f195df7fa5ccdb129a15c95824b2c4e706eb7e23c9d48b96eed141d161","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:07.845217Z","signature_b64":"eW3gLPxjN6x6smIUxRFWNp2HPE5xB1ho5Vdnxr5Resf3rtmj/E68eTv5fEj907PBSSz3ErEVxjHJXspABfwtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3569a1f195df7fa5ccdb129a15c95824b2c4e706eb7e23c9d48b96eed141d161","last_reissued_at":"2026-05-18T03:05:07.844574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:07.844574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.3074","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":"2026-05-18T03:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cnmd//26UEcO2ALuG3QlxcZwNs9IiUghAKgT/UNZmXJrH6zwfOfVj671jl/+N1zK22qFRE/Z00BeGEWrlptVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:21:47.869121Z"},"content_sha256":"41ca85340e8d7452e6f0b95138e086e3dfcde9dd5fc8a60befe8211156df387d","schema_version":"1.0","event_id":"sha256:41ca85340e8d7452e6f0b95138e086e3dfcde9dd5fc8a60befe8211156df387d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GVU2D4MV3572LTG3CKNBLSKYES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Consistency of the mean and the principal components of spatially distributed functional data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Piotr Kokoszka, Siegfried H\\\"ormann","submitted_at":"2011-04-15T14:41:41Z","abstract_excerpt":"This paper develops a framework for the estimation of the functional mean and the functional principal components when the functions form a random field. More specifically, the data we study consist of curves $X(\\mathbf{s}_k;t),t\\in[0,T]$, observed at spatial points $\\mathbf{s}_1,\\mathbf{s}_2,\\ldots,\\mathbf{s}_N$. We establish conditions for the sample average (in space) of the $X(\\mathbf{s}_k)$ to be a consistent estimator of the population mean function, and for the usual empirical covariance operator to be a consistent estimator of the population covariance operator. These conditions involv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3074","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":"2026-05-18T03:05:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8DvQ4KM5b754YdRa2g0vCdgwOvRWBf4NyJQJUR982pQrUiWt2wK7+BiwDAxSil6gHCg5G7wdEpezQTYfFKpyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:21:47.869491Z"},"content_sha256":"9945330aef9e4b597a25396baaa630a7f80e4040478a6b243cf081504c5801f1","schema_version":"1.0","event_id":"sha256:9945330aef9e4b597a25396baaa630a7f80e4040478a6b243cf081504c5801f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GVU2D4MV3572LTG3CKNBLSKYES/bundle.json","state_url":"https://pith.science/pith/GVU2D4MV3572LTG3CKNBLSKYES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GVU2D4MV3572LTG3CKNBLSKYES/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":"2026-06-03T13:21:47Z","links":{"resolver":"https://pith.science/pith/GVU2D4MV3572LTG3CKNBLSKYES","bundle":"https://pith.science/pith/GVU2D4MV3572LTG3CKNBLSKYES/bundle.json","state":"https://pith.science/pith/GVU2D4MV3572LTG3CKNBLSKYES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GVU2D4MV3572LTG3CKNBLSKYES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GVU2D4MV3572LTG3CKNBLSKYES","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":"cb5de2c081ca44297f7b909c20095c0b7eace9a5833414d849bc80d9bbb0eaef","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-04-15T14:41:41Z","title_canon_sha256":"a3b17f04e91dbf917e65b68575fe4cab664d1a4e1d5b6c1fe03157fb7f842f12"},"schema_version":"1.0","source":{"id":"1104.3074","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3074","created_at":"2026-05-18T03:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3074v2","created_at":"2026-05-18T03:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3074","created_at":"2026-05-18T03:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"GVU2D4MV3572","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GVU2D4MV3572LTG3","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GVU2D4MV","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:9945330aef9e4b597a25396baaa630a7f80e4040478a6b243cf081504c5801f1","target":"graph","created_at":"2026-05-18T03:05:07Z","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":"This paper develops a framework for the estimation of the functional mean and the functional principal components when the functions form a random field. More specifically, the data we study consist of curves $X(\\mathbf{s}_k;t),t\\in[0,T]$, observed at spatial points $\\mathbf{s}_1,\\mathbf{s}_2,\\ldots,\\mathbf{s}_N$. We establish conditions for the sample average (in space) of the $X(\\mathbf{s}_k)$ to be a consistent estimator of the population mean function, and for the usual empirical covariance operator to be a consistent estimator of the population covariance operator. These conditions involv","authors_text":"Piotr Kokoszka, Siegfried H\\\"ormann","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-04-15T14:41:41Z","title":"Consistency of the mean and the principal components of spatially distributed functional data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3074","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":"sha256:41ca85340e8d7452e6f0b95138e086e3dfcde9dd5fc8a60befe8211156df387d","target":"record","created_at":"2026-05-18T03:05:07Z","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":"cb5de2c081ca44297f7b909c20095c0b7eace9a5833414d849bc80d9bbb0eaef","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-04-15T14:41:41Z","title_canon_sha256":"a3b17f04e91dbf917e65b68575fe4cab664d1a4e1d5b6c1fe03157fb7f842f12"},"schema_version":"1.0","source":{"id":"1104.3074","kind":"arxiv","version":2}},"canonical_sha256":"3569a1f195df7fa5ccdb129a15c95824b2c4e706eb7e23c9d48b96eed141d161","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3569a1f195df7fa5ccdb129a15c95824b2c4e706eb7e23c9d48b96eed141d161","first_computed_at":"2026-05-18T03:05:07.844574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:07.844574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eW3gLPxjN6x6smIUxRFWNp2HPE5xB1ho5Vdnxr5Resf3rtmj/E68eTv5fEj907PBSSz3ErEVxjHJXspABfwtDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:07.845217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3074","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41ca85340e8d7452e6f0b95138e086e3dfcde9dd5fc8a60befe8211156df387d","sha256:9945330aef9e4b597a25396baaa630a7f80e4040478a6b243cf081504c5801f1"],"state_sha256":"70e954040162bb680788253b3e38e5b6f3fbf0702808665782bf58294e33a8c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fl8wYbYXx1/vA6frCWwJbnTwfKJwko2SYaU5bNO7OTc1mr3YIY1yylBxQEFaGkMWjl97RlSd6AMi7kFjcQwfAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T13:21:47.871402Z","bundle_sha256":"229d8349cacea7b5259e1261ceb964b3102ab3d77a4d52a7991e82999b99c948"}}