{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EQJ37KNZUPFYTGMQVUFBSABCKZ","short_pith_number":"pith:EQJ37KNZ","canonical_record":{"source":{"id":"1607.07771","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-26T15:59:50Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"96a44b1874cbc2e3ad7f9bfe7908bae914ad7386e77e050e28e0cb7f91f79d09","abstract_canon_sha256":"f8d23c28415c5e4f1a47ee3d8d64897d06e45769d7b2b18401c95814075cd571"},"schema_version":"1.0"},"canonical_sha256":"2413bfa9b9a3cb899990ad0a190022567bea911271c8b73d888a2d595741db16","source":{"kind":"arxiv","id":"1607.07771","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07771","created_at":"2026-05-18T01:09:30Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07771v2","created_at":"2026-05-18T01:09:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07771","created_at":"2026-05-18T01:09:30Z"},{"alias_kind":"pith_short_12","alias_value":"EQJ37KNZUPFY","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EQJ37KNZUPFYTGMQ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EQJ37KNZ","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EQJ37KNZUPFYTGMQVUFBSABCKZ","target":"record","payload":{"canonical_record":{"source":{"id":"1607.07771","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-26T15:59:50Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"96a44b1874cbc2e3ad7f9bfe7908bae914ad7386e77e050e28e0cb7f91f79d09","abstract_canon_sha256":"f8d23c28415c5e4f1a47ee3d8d64897d06e45769d7b2b18401c95814075cd571"},"schema_version":"1.0"},"canonical_sha256":"2413bfa9b9a3cb899990ad0a190022567bea911271c8b73d888a2d595741db16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:30.670077Z","signature_b64":"PYszQ6r6bAqyQ0pQX6SyG8HrutF5r6ootG7iDukn4umEYoZHjW+P5tTIOcJlejVtViXcr198yB++aW7vRH8cCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2413bfa9b9a3cb899990ad0a190022567bea911271c8b73d888a2d595741db16","last_reissued_at":"2026-05-18T01:09:30.669662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:30.669662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.07771","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":"2026-05-18T01:09:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0jJTT8hW7ihy03ITRz1O9YXohlDy1hy78+HkhcUnW5HKK55iCx9YE4u5pzYk4j0moKc5pkuU+BSOUqoF+ik8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:24:00.873630Z"},"content_sha256":"b3894d3ab3bf0bad2fc40364ab91c3f5854916662296347ca2b279a78968677a","schema_version":"1.0","event_id":"sha256:b3894d3ab3bf0bad2fc40364ab91c3f5854916662296347ca2b279a78968677a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EQJ37KNZUPFYTGMQVUFBSABCKZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Geometric Approach to Confidence Regions and Bands for Functional Parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Hyunphil Choi, Matthew Reimherr","submitted_at":"2016-07-26T15:59:50Z","abstract_excerpt":"Functional data analysis, FDA, is now a well established discipline of statistics, with its core concepts and perspectives in place. Despite this, there are still fundamental statistical questions which have received relatively little attention. One of these is the systematic construction of confidence regions for functional parameters. This work is concerned with developing, understanding, and visualizing such regions. We provide a general strategy for constructing confidence regions in a real separable Hilbert space using hyper-ellipsoids and hyper-rectangles. We then propose specific implem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07771","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":"2026-05-18T01:09:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kzFAERszms9zHkh1UZCWT9s7Lo1uwqpY9EQwY9e/YlzTfb3MMBfdJSIImn9LW92a9d/3AEnvJNB3pWsjjz+bAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:24:00.874209Z"},"content_sha256":"c22ce439a68dde93bc8c2979720733a42c3cc0fcb13380f549b9de426083a592","schema_version":"1.0","event_id":"sha256:c22ce439a68dde93bc8c2979720733a42c3cc0fcb13380f549b9de426083a592"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQJ37KNZUPFYTGMQVUFBSABCKZ/bundle.json","state_url":"https://pith.science/pith/EQJ37KNZUPFYTGMQVUFBSABCKZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQJ37KNZUPFYTGMQVUFBSABCKZ/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":"2026-05-26T08:24:00Z","links":{"resolver":"https://pith.science/pith/EQJ37KNZUPFYTGMQVUFBSABCKZ","bundle":"https://pith.science/pith/EQJ37KNZUPFYTGMQVUFBSABCKZ/bundle.json","state":"https://pith.science/pith/EQJ37KNZUPFYTGMQVUFBSABCKZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQJ37KNZUPFYTGMQVUFBSABCKZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EQJ37KNZUPFYTGMQVUFBSABCKZ","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":"f8d23c28415c5e4f1a47ee3d8d64897d06e45769d7b2b18401c95814075cd571","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-26T15:59:50Z","title_canon_sha256":"96a44b1874cbc2e3ad7f9bfe7908bae914ad7386e77e050e28e0cb7f91f79d09"},"schema_version":"1.0","source":{"id":"1607.07771","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07771","created_at":"2026-05-18T01:09:30Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07771v2","created_at":"2026-05-18T01:09:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07771","created_at":"2026-05-18T01:09:30Z"},{"alias_kind":"pith_short_12","alias_value":"EQJ37KNZUPFY","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EQJ37KNZUPFYTGMQ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EQJ37KNZ","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:c22ce439a68dde93bc8c2979720733a42c3cc0fcb13380f549b9de426083a592","target":"graph","created_at":"2026-05-18T01:09:30Z","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":"Functional data analysis, FDA, is now a well established discipline of statistics, with its core concepts and perspectives in place. Despite this, there are still fundamental statistical questions which have received relatively little attention. One of these is the systematic construction of confidence regions for functional parameters. This work is concerned with developing, understanding, and visualizing such regions. We provide a general strategy for constructing confidence regions in a real separable Hilbert space using hyper-ellipsoids and hyper-rectangles. We then propose specific implem","authors_text":"Hyunphil Choi, Matthew Reimherr","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-26T15:59:50Z","title":"A Geometric Approach to Confidence Regions and Bands for Functional Parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07771","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:b3894d3ab3bf0bad2fc40364ab91c3f5854916662296347ca2b279a78968677a","target":"record","created_at":"2026-05-18T01:09:30Z","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":"f8d23c28415c5e4f1a47ee3d8d64897d06e45769d7b2b18401c95814075cd571","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-07-26T15:59:50Z","title_canon_sha256":"96a44b1874cbc2e3ad7f9bfe7908bae914ad7386e77e050e28e0cb7f91f79d09"},"schema_version":"1.0","source":{"id":"1607.07771","kind":"arxiv","version":2}},"canonical_sha256":"2413bfa9b9a3cb899990ad0a190022567bea911271c8b73d888a2d595741db16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2413bfa9b9a3cb899990ad0a190022567bea911271c8b73d888a2d595741db16","first_computed_at":"2026-05-18T01:09:30.669662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:30.669662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PYszQ6r6bAqyQ0pQX6SyG8HrutF5r6ootG7iDukn4umEYoZHjW+P5tTIOcJlejVtViXcr198yB++aW7vRH8cCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:30.670077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07771","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3894d3ab3bf0bad2fc40364ab91c3f5854916662296347ca2b279a78968677a","sha256:c22ce439a68dde93bc8c2979720733a42c3cc0fcb13380f549b9de426083a592"],"state_sha256":"0e72c9ca69f7c270642d20aa82f33d26d2e0800db29f6f698313d3be5e4d7491"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xOApDPQ3uNpMPDjlsw2J/CyHkMFKgyCCijEQ6y/ZGnewgPnTGJFe6ybPdhu+TMZwtkSmHnpuDQZhR7ry2qqsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:24:00.877636Z","bundle_sha256":"fee0210bd678f7e3e9cda46bdf08e62ae3928ab111618ba27705d7f8a6eb228b"}}