{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HADWAIHLB2VLB6P4OII5NAK75R","short_pith_number":"pith:HADWAIHL","canonical_record":{"source":{"id":"1208.2895","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-08-14T15:17:05Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"614e108599789b354cbd2fe983bf49a09ad6a9e98f1d4659071f88e77437fb00","abstract_canon_sha256":"a3ea5e446f9f840e83064ccb0e9cb119337edf194e44b45261f3d30f6bc09dd6"},"schema_version":"1.0"},"canonical_sha256":"38076020eb0eaab0f9fc7211d6815fec68aa5eada8c5d85f1d3f42a2146b7402","source":{"kind":"arxiv","id":"1208.2895","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2895","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2895v3","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2895","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"pith_short_12","alias_value":"HADWAIHLB2VL","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HADWAIHLB2VLB6P4","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HADWAIHL","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HADWAIHLB2VLB6P4OII5NAK75R","target":"record","payload":{"canonical_record":{"source":{"id":"1208.2895","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-08-14T15:17:05Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"614e108599789b354cbd2fe983bf49a09ad6a9e98f1d4659071f88e77437fb00","abstract_canon_sha256":"a3ea5e446f9f840e83064ccb0e9cb119337edf194e44b45261f3d30f6bc09dd6"},"schema_version":"1.0"},"canonical_sha256":"38076020eb0eaab0f9fc7211d6815fec68aa5eada8c5d85f1d3f42a2146b7402","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:12.922594Z","signature_b64":"0iQ9Et6fxX1inkArVHvvPASpPnLUE69HIoFvapm14QKuW3FsuDckCB3oARJuDeIhx3CniXpX2CV2oHZ4E2PhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38076020eb0eaab0f9fc7211d6815fec68aa5eada8c5d85f1d3f42a2146b7402","last_reissued_at":"2026-05-18T02:54:12.921893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:12.921893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.2895","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":"2026-05-18T02:54:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ppKkU3YdLcym08DWeSfU5/kEKHo5ib42qEA8OgGYR2S4e5o1cDBDLF7qJ4HZGa4x7shWMQQ664hTPpfg4MyVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:51:56.992846Z"},"content_sha256":"5e214138b170cad95fdf58791dd2458f840c53dec890e2a2e2ee5b30f6a37295","schema_version":"1.0","event_id":"sha256:5e214138b170cad95fdf58791dd2458f840c53dec890e2a2e2ee5b30f6a37295"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HADWAIHLB2VLB6P4OII5NAK75R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on estimation in Hilbertian linear models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"{\\L}ukasz Kidzi\\'nski, Siegfried H\\\"ormann","submitted_at":"2012-08-14T15:17:05Z","abstract_excerpt":"We study estimation and prediction in linear models where the response and the regressor variable both take values in some Hilbert space. Our main objective is to obtain consistency of a principal components based estimator for the regression operator under minimal assumptions. In particular, we avoid some inconvenient technical restrictions that have been used throughout the literature. We develop our theory in a time dependent setup which comprises as important special case the autoregressive Hilbertian model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2895","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":"2026-05-18T02:54:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xG+CyiC+2TbeuEQ3736RDOoDaoS2lDigMkjM3s5Z/7cHTSYxZ4iY2IHidQMj6Y6T87HpfkrTmEb17M5B07TjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:51:56.993611Z"},"content_sha256":"819b80c66e4f9a40d969dfe761281d935ed5975187402bb4233de2872e22755a","schema_version":"1.0","event_id":"sha256:819b80c66e4f9a40d969dfe761281d935ed5975187402bb4233de2872e22755a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HADWAIHLB2VLB6P4OII5NAK75R/bundle.json","state_url":"https://pith.science/pith/HADWAIHLB2VLB6P4OII5NAK75R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HADWAIHLB2VLB6P4OII5NAK75R/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":"2026-06-11T16:51:56Z","links":{"resolver":"https://pith.science/pith/HADWAIHLB2VLB6P4OII5NAK75R","bundle":"https://pith.science/pith/HADWAIHLB2VLB6P4OII5NAK75R/bundle.json","state":"https://pith.science/pith/HADWAIHLB2VLB6P4OII5NAK75R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HADWAIHLB2VLB6P4OII5NAK75R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HADWAIHLB2VLB6P4OII5NAK75R","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":"a3ea5e446f9f840e83064ccb0e9cb119337edf194e44b45261f3d30f6bc09dd6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-08-14T15:17:05Z","title_canon_sha256":"614e108599789b354cbd2fe983bf49a09ad6a9e98f1d4659071f88e77437fb00"},"schema_version":"1.0","source":{"id":"1208.2895","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2895","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2895v3","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2895","created_at":"2026-05-18T02:54:12Z"},{"alias_kind":"pith_short_12","alias_value":"HADWAIHLB2VL","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HADWAIHLB2VLB6P4","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HADWAIHL","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:819b80c66e4f9a40d969dfe761281d935ed5975187402bb4233de2872e22755a","target":"graph","created_at":"2026-05-18T02:54:12Z","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":"We study estimation and prediction in linear models where the response and the regressor variable both take values in some Hilbert space. Our main objective is to obtain consistency of a principal components based estimator for the regression operator under minimal assumptions. In particular, we avoid some inconvenient technical restrictions that have been used throughout the literature. We develop our theory in a time dependent setup which comprises as important special case the autoregressive Hilbertian model.","authors_text":"{\\L}ukasz Kidzi\\'nski, Siegfried H\\\"ormann","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-08-14T15:17:05Z","title":"A note on estimation in Hilbertian linear models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2895","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":"sha256:5e214138b170cad95fdf58791dd2458f840c53dec890e2a2e2ee5b30f6a37295","target":"record","created_at":"2026-05-18T02:54:12Z","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":"a3ea5e446f9f840e83064ccb0e9cb119337edf194e44b45261f3d30f6bc09dd6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-08-14T15:17:05Z","title_canon_sha256":"614e108599789b354cbd2fe983bf49a09ad6a9e98f1d4659071f88e77437fb00"},"schema_version":"1.0","source":{"id":"1208.2895","kind":"arxiv","version":3}},"canonical_sha256":"38076020eb0eaab0f9fc7211d6815fec68aa5eada8c5d85f1d3f42a2146b7402","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38076020eb0eaab0f9fc7211d6815fec68aa5eada8c5d85f1d3f42a2146b7402","first_computed_at":"2026-05-18T02:54:12.921893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:12.921893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0iQ9Et6fxX1inkArVHvvPASpPnLUE69HIoFvapm14QKuW3FsuDckCB3oARJuDeIhx3CniXpX2CV2oHZ4E2PhCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:12.922594Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2895","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e214138b170cad95fdf58791dd2458f840c53dec890e2a2e2ee5b30f6a37295","sha256:819b80c66e4f9a40d969dfe761281d935ed5975187402bb4233de2872e22755a"],"state_sha256":"b828043bc3700070428dd040fdcfcf1f5da75c7550dab4bd3b49a4c323cfc575"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gjfIk103Yx3Plni9UApGlFhYUNyC20fARk8ZpcTB8YRJuNhdi5yM6nw4ku5TEvveSgjJToqFNntTiwgIxXU+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:51:56.998110Z","bundle_sha256":"c5ee45ceaac8a16de9d97179e68eff94d4442482c0eec72688909d1a416b1210"}}