{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:MVQLEQA3EQJP63YXBG4Q6VLQTG","short_pith_number":"pith:MVQLEQA3","canonical_record":{"source":{"id":"math/0508073","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.ST","submitted_at":"2005-08-03T11:19:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"2c008eb52f4f08777a87c159d42e5c7aac2d0cd27cfeaab6e3ab458f76af5102","abstract_canon_sha256":"fa68703494c99c8815c7cb8baccc4b158d5d806dfb0b14c6c729827706bdabfb"},"schema_version":"1.0"},"canonical_sha256":"6560b2401b2412ff6f1709b90f5570998e8f4d957247a719e880b38df06b85d5","source":{"kind":"arxiv","id":"math/0508073","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508073","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508073v1","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508073","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"pith_short_12","alias_value":"MVQLEQA3EQJP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"MVQLEQA3EQJP63YX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"MVQLEQA3","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:MVQLEQA3EQJP63YXBG4Q6VLQTG","target":"record","payload":{"canonical_record":{"source":{"id":"math/0508073","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.ST","submitted_at":"2005-08-03T11:19:34Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"2c008eb52f4f08777a87c159d42e5c7aac2d0cd27cfeaab6e3ab458f76af5102","abstract_canon_sha256":"fa68703494c99c8815c7cb8baccc4b158d5d806dfb0b14c6c729827706bdabfb"},"schema_version":"1.0"},"canonical_sha256":"6560b2401b2412ff6f1709b90f5570998e8f4d957247a719e880b38df06b85d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:50.958400Z","signature_b64":"VdyJMbFAI3a2GUxF0PK6qtMPiVhukHm79JnAsd613i5maj6dUcjGXesmekuGe6z1R8LvaN4tkjGH2QOykb07BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6560b2401b2412ff6f1709b90f5570998e8f4d957247a719e880b38df06b85d5","last_reissued_at":"2026-05-18T01:08:50.957726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:50.957726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0508073","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":"2026-05-18T01:08:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vbOxKto2vfkTyprYcJElPPr5WBmXbv62VnSAk0nqJcmy8I9WP7zz0TxY3LXJdwPdYMZGvjA1+6d/5zPSaMMcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:22:31.963993Z"},"content_sha256":"e0f5302db39972b1ccd5f28b15620014606fd714c9578b44ecc58fc1d2426002","schema_version":"1.0","event_id":"sha256:e0f5302db39972b1ccd5f28b15620014606fd714c9578b44ecc58fc1d2426002"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:MVQLEQA3EQJP63YXBG4Q6VLQTG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"CLT in Functional Linear Regression Models","license":"","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Andr\\'e Mas (I3M), BIA), Herv\\'e Cardot (INRA Toulouse, Pascal Sarda (GRIMM)","submitted_at":"2005-08-03T11:19:34Z","abstract_excerpt":"We propose in this work to derive a CLT in the functional linear regression model to get confidence sets for prediction based on functional linear regression. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill-posed inverse problem. We consider estimators that belong to a large class of regularizing methods and we first show that, contrary to the multivariate case, it is not possible to state a CLT in the topology of the considered functional space. However, we show that we can get a CLT for the weak topology under mild hypotheses and in p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508073","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":"2026-05-18T01:08:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8qCHfLeQlprbAzXd/SOG8D/ZDTg6HmyzD9eds1z+tDfQAao88nLFgBX5MLURJ0rCk3I5pVpeZHPsnS1c9xvRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:22:31.964343Z"},"content_sha256":"0d84ed72dae5a83cdd3e4992c419fa0cdbab4ba107b2d714a4b4846b9968118c","schema_version":"1.0","event_id":"sha256:0d84ed72dae5a83cdd3e4992c419fa0cdbab4ba107b2d714a4b4846b9968118c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVQLEQA3EQJP63YXBG4Q6VLQTG/bundle.json","state_url":"https://pith.science/pith/MVQLEQA3EQJP63YXBG4Q6VLQTG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVQLEQA3EQJP63YXBG4Q6VLQTG/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":"2026-06-03T08:22:31Z","links":{"resolver":"https://pith.science/pith/MVQLEQA3EQJP63YXBG4Q6VLQTG","bundle":"https://pith.science/pith/MVQLEQA3EQJP63YXBG4Q6VLQTG/bundle.json","state":"https://pith.science/pith/MVQLEQA3EQJP63YXBG4Q6VLQTG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVQLEQA3EQJP63YXBG4Q6VLQTG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:MVQLEQA3EQJP63YXBG4Q6VLQTG","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":"fa68703494c99c8815c7cb8baccc4b158d5d806dfb0b14c6c729827706bdabfb","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2005-08-03T11:19:34Z","title_canon_sha256":"2c008eb52f4f08777a87c159d42e5c7aac2d0cd27cfeaab6e3ab458f76af5102"},"schema_version":"1.0","source":{"id":"math/0508073","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508073","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508073v1","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508073","created_at":"2026-05-18T01:08:50Z"},{"alias_kind":"pith_short_12","alias_value":"MVQLEQA3EQJP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"MVQLEQA3EQJP63YX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"MVQLEQA3","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:0d84ed72dae5a83cdd3e4992c419fa0cdbab4ba107b2d714a4b4846b9968118c","target":"graph","created_at":"2026-05-18T01:08:50Z","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 propose in this work to derive a CLT in the functional linear regression model to get confidence sets for prediction based on functional linear regression. The main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill-posed inverse problem. We consider estimators that belong to a large class of regularizing methods and we first show that, contrary to the multivariate case, it is not possible to state a CLT in the topology of the considered functional space. However, we show that we can get a CLT for the weak topology under mild hypotheses and in p","authors_text":"Andr\\'e Mas (I3M), BIA), Herv\\'e Cardot (INRA Toulouse, Pascal Sarda (GRIMM)","cross_cats":["stat.TH"],"headline":"","license":"","primary_cat":"math.ST","submitted_at":"2005-08-03T11:19:34Z","title":"CLT in Functional Linear Regression Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508073","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:e0f5302db39972b1ccd5f28b15620014606fd714c9578b44ecc58fc1d2426002","target":"record","created_at":"2026-05-18T01:08:50Z","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":"fa68703494c99c8815c7cb8baccc4b158d5d806dfb0b14c6c729827706bdabfb","cross_cats_sorted":["stat.TH"],"license":"","primary_cat":"math.ST","submitted_at":"2005-08-03T11:19:34Z","title_canon_sha256":"2c008eb52f4f08777a87c159d42e5c7aac2d0cd27cfeaab6e3ab458f76af5102"},"schema_version":"1.0","source":{"id":"math/0508073","kind":"arxiv","version":1}},"canonical_sha256":"6560b2401b2412ff6f1709b90f5570998e8f4d957247a719e880b38df06b85d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6560b2401b2412ff6f1709b90f5570998e8f4d957247a719e880b38df06b85d5","first_computed_at":"2026-05-18T01:08:50.957726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:50.957726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VdyJMbFAI3a2GUxF0PK6qtMPiVhukHm79JnAsd613i5maj6dUcjGXesmekuGe6z1R8LvaN4tkjGH2QOykb07BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:50.958400Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0508073","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0f5302db39972b1ccd5f28b15620014606fd714c9578b44ecc58fc1d2426002","sha256:0d84ed72dae5a83cdd3e4992c419fa0cdbab4ba107b2d714a4b4846b9968118c"],"state_sha256":"8f5ad35ed517a3f11a2eea287f96342ded857699cc91fb5d200a772bddab6cfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n4NIZd/cM2jjM1OLR+osLAOxElGtmGnC2N/sgmT47kNExmc8h0/BMKHZGtNHv5xtEyn6AJtL0YgEIrNyBfUnAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:22:31.966228Z","bundle_sha256":"38e16e1332e5dc869eda870c8ceac36087284ccb2f89545e0c9a9c2a5d4fabb5"}}