{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RN33O5KSSZ5SFIOAODXLPWYRCB","short_pith_number":"pith:RN33O5KS","canonical_record":{"source":{"id":"1709.03039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-08-29T00:57:48Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"5f3abbd7e2b6f10533ab341e3512ec466412632ac988220d952974e66ff81afb","abstract_canon_sha256":"7bb066b1feda8a023bd32800cc319c91fbc130a0a567fa8b132ffa0b880fb7cd"},"schema_version":"1.0"},"canonical_sha256":"8b77b77552967b22a1c070eeb7db1110775366a395e910ff60f78d4b49b44f7d","source":{"kind":"arxiv","id":"1709.03039","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03039","created_at":"2026-05-18T00:35:39Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03039v1","created_at":"2026-05-18T00:35:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03039","created_at":"2026-05-18T00:35:39Z"},{"alias_kind":"pith_short_12","alias_value":"RN33O5KSSZ5S","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RN33O5KSSZ5SFIOA","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RN33O5KS","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RN33O5KSSZ5SFIOAODXLPWYRCB","target":"record","payload":{"canonical_record":{"source":{"id":"1709.03039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-08-29T00:57:48Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"5f3abbd7e2b6f10533ab341e3512ec466412632ac988220d952974e66ff81afb","abstract_canon_sha256":"7bb066b1feda8a023bd32800cc319c91fbc130a0a567fa8b132ffa0b880fb7cd"},"schema_version":"1.0"},"canonical_sha256":"8b77b77552967b22a1c070eeb7db1110775366a395e910ff60f78d4b49b44f7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:39.593137Z","signature_b64":"o9q8/IEDBfSD6xEGfEl0t19oVol4KOxQFq4a39daYZRNMJDXjcdfvjvcwg7/rwlJuP3xAIl2K/3acOa6xZ6RBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b77b77552967b22a1c070eeb7db1110775366a395e910ff60f78d4b49b44f7d","last_reissued_at":"2026-05-18T00:35:39.592405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:39.592405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.03039","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":"2026-05-18T00:35:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ao7wKPS2rZ/EwN/ARDXsKgy4fdMed6/kZnRyj2gtgTcu93KXTEM1nMYs/9OaCjWOp5kE3x9VT9F3ObGQE4/ACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:13:34.150828Z"},"content_sha256":"7317a489f6613fffb8c8691fd269738fed7e5b748d556ee70b769913b5bfa337","schema_version":"1.0","event_id":"sha256:7317a489f6613fffb8c8691fd269738fed7e5b748d556ee70b769913b5bfa337"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RN33O5KSSZ5SFIOAODXLPWYRCB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An estimate of the root mean square error incurred when approximating an $f \\in L^2({\\mathbb{R}})$ by a partial sum of its Hermite series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Mei Ling Huang, Ron Kerman, Susanna Spektor","submitted_at":"2017-08-29T00:57:48Z","abstract_excerpt":"Let $f$ be a band-limited function in $L^2({\\mathbb{R}})$. Fix $T >0$ and suppose $f^{\\prime}$ exists and is integrable on $[-T, T]$. This paper gives a concrete estimate of the error incurred when approximating $f$ in the root mean square by a partial sum of its Hermite series.\n  Specifically, we show, for $K=2n, \\quad n \\in Z_+,$\n  $$\n  \\left[\\frac{1}{2T}\\int_{-T}^T[f(t)-(S_Kf)(t)]^2dt\\right]^{1/2}\\leq \\left(1+\\frac 1K\\right)\\left(\\left[ \\frac{1}{2T}\\int_{|t|> T}f(t)^2dt\\right]^{1/2} +\\left[\\frac{1}{2T} \\int_{|\\omega|>N}|\\hat f(\\omega)|^2d\\omega\\right]^{1/2} \\right) +\\frac{1}{K}\\left[\\frac{1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03039","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":"2026-05-18T00:35:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Nm1WCZ+9nPv1eyHhptRpWQwsvwuUs7JEtrE3mRaGxHrVQWgsXV5OV19MPmeuD2QSykS2u7EF/Ku8DxY+RN1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:13:34.151181Z"},"content_sha256":"48e90176bf4df0fd3df4254781686b26870aa65dd92ced780671f1305262d5d7","schema_version":"1.0","event_id":"sha256:48e90176bf4df0fd3df4254781686b26870aa65dd92ced780671f1305262d5d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RN33O5KSSZ5SFIOAODXLPWYRCB/bundle.json","state_url":"https://pith.science/pith/RN33O5KSSZ5SFIOAODXLPWYRCB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RN33O5KSSZ5SFIOAODXLPWYRCB/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":"2026-05-30T07:13:34Z","links":{"resolver":"https://pith.science/pith/RN33O5KSSZ5SFIOAODXLPWYRCB","bundle":"https://pith.science/pith/RN33O5KSSZ5SFIOAODXLPWYRCB/bundle.json","state":"https://pith.science/pith/RN33O5KSSZ5SFIOAODXLPWYRCB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RN33O5KSSZ5SFIOAODXLPWYRCB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RN33O5KSSZ5SFIOAODXLPWYRCB","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":"7bb066b1feda8a023bd32800cc319c91fbc130a0a567fa8b132ffa0b880fb7cd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-08-29T00:57:48Z","title_canon_sha256":"5f3abbd7e2b6f10533ab341e3512ec466412632ac988220d952974e66ff81afb"},"schema_version":"1.0","source":{"id":"1709.03039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03039","created_at":"2026-05-18T00:35:39Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03039v1","created_at":"2026-05-18T00:35:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03039","created_at":"2026-05-18T00:35:39Z"},{"alias_kind":"pith_short_12","alias_value":"RN33O5KSSZ5S","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RN33O5KSSZ5SFIOA","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RN33O5KS","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:48e90176bf4df0fd3df4254781686b26870aa65dd92ced780671f1305262d5d7","target":"graph","created_at":"2026-05-18T00:35:39Z","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":"Let $f$ be a band-limited function in $L^2({\\mathbb{R}})$. Fix $T >0$ and suppose $f^{\\prime}$ exists and is integrable on $[-T, T]$. This paper gives a concrete estimate of the error incurred when approximating $f$ in the root mean square by a partial sum of its Hermite series.\n  Specifically, we show, for $K=2n, \\quad n \\in Z_+,$\n  $$\n  \\left[\\frac{1}{2T}\\int_{-T}^T[f(t)-(S_Kf)(t)]^2dt\\right]^{1/2}\\leq \\left(1+\\frac 1K\\right)\\left(\\left[ \\frac{1}{2T}\\int_{|t|> T}f(t)^2dt\\right]^{1/2} +\\left[\\frac{1}{2T} \\int_{|\\omega|>N}|\\hat f(\\omega)|^2d\\omega\\right]^{1/2} \\right) +\\frac{1}{K}\\left[\\frac{1","authors_text":"Mei Ling Huang, Ron Kerman, Susanna Spektor","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-08-29T00:57:48Z","title":"An estimate of the root mean square error incurred when approximating an $f \\in L^2({\\mathbb{R}})$ by a partial sum of its Hermite series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03039","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":"sha256:7317a489f6613fffb8c8691fd269738fed7e5b748d556ee70b769913b5bfa337","target":"record","created_at":"2026-05-18T00:35:39Z","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":"7bb066b1feda8a023bd32800cc319c91fbc130a0a567fa8b132ffa0b880fb7cd","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-08-29T00:57:48Z","title_canon_sha256":"5f3abbd7e2b6f10533ab341e3512ec466412632ac988220d952974e66ff81afb"},"schema_version":"1.0","source":{"id":"1709.03039","kind":"arxiv","version":1}},"canonical_sha256":"8b77b77552967b22a1c070eeb7db1110775366a395e910ff60f78d4b49b44f7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b77b77552967b22a1c070eeb7db1110775366a395e910ff60f78d4b49b44f7d","first_computed_at":"2026-05-18T00:35:39.592405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:39.592405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o9q8/IEDBfSD6xEGfEl0t19oVol4KOxQFq4a39daYZRNMJDXjcdfvjvcwg7/rwlJuP3xAIl2K/3acOa6xZ6RBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:39.593137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7317a489f6613fffb8c8691fd269738fed7e5b748d556ee70b769913b5bfa337","sha256:48e90176bf4df0fd3df4254781686b26870aa65dd92ced780671f1305262d5d7"],"state_sha256":"0cb8775b99a0cee69e8793cd444bf9ae8ae858c05273d2713bcfd86a47e1988c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CIj5OUDoLTrGwC8JKiylkEft3e+rRWB09PjnvcVrz6cylu60yxtcdQwxTgBi2wW6Ig5t80jphSZSBKSWyTKPBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:13:34.153299Z","bundle_sha256":"f68942160658ac84efefeb84fb4d84469eace6d37abdb756829ebfc920bcb36a"}}