{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:E6BEUTIDPIYGPWTLFTNMJJCYJ6","short_pith_number":"pith:E6BEUTID","canonical_record":{"source":{"id":"1602.05823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-18T14:59:41Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"76cbf0481336fee2e3dbf8f5c16c60e135e3686a16a164255910335eccf052ef","abstract_canon_sha256":"c988ddceaddd4d39fa1ffdb6fbc0f7ecb0e926d547c66dac57946e5ea8de17bb"},"schema_version":"1.0"},"canonical_sha256":"27824a4d037a3067da6b2cdac4a4584f8375b0b2c9745ec75d5df8217d7bf7cd","source":{"kind":"arxiv","id":"1602.05823","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05823","created_at":"2026-06-04T17:10:02Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05823v1","created_at":"2026-06-04T17:10:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05823","created_at":"2026-06-04T17:10:02Z"},{"alias_kind":"pith_short_12","alias_value":"E6BEUTIDPIYG","created_at":"2026-06-04T17:10:02Z"},{"alias_kind":"pith_short_16","alias_value":"E6BEUTIDPIYGPWTL","created_at":"2026-06-04T17:10:02Z"},{"alias_kind":"pith_short_8","alias_value":"E6BEUTID","created_at":"2026-06-04T17:10:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:E6BEUTIDPIYGPWTLFTNMJJCYJ6","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05823","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-18T14:59:41Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"76cbf0481336fee2e3dbf8f5c16c60e135e3686a16a164255910335eccf052ef","abstract_canon_sha256":"c988ddceaddd4d39fa1ffdb6fbc0f7ecb0e926d547c66dac57946e5ea8de17bb"},"schema_version":"1.0"},"canonical_sha256":"27824a4d037a3067da6b2cdac4a4584f8375b0b2c9745ec75d5df8217d7bf7cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T17:10:02.188759Z","signature_b64":"Q7qE0Ob5H6fLC4b34bwvMyoloSP5MpzkRlNGCeEIFeZZgAQwxMz2iizgZrh1yL9gm57kzlKf6Ds6WQna8u10Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27824a4d037a3067da6b2cdac4a4584f8375b0b2c9745ec75d5df8217d7bf7cd","last_reissued_at":"2026-06-04T17:10:02.188324Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T17:10:02.188324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05823","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":"2026-06-04T17:10:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RALoRCFGLDYkQWQgjomQdrNu3p8WnP6pcoFyaf69eSQADyB7BGN+HBUTr7k39xblZV9ot42hmTL2AcVeUkDnBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:29:35.029586Z"},"content_sha256":"f7147ecd47a9454915f244b3cdbba28f262be39550d34d5cca28ebec8d0f579f","schema_version":"1.0","event_id":"sha256:f7147ecd47a9454915f244b3cdbba28f262be39550d34d5cca28ebec8d0f579f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:E6BEUTIDPIYGPWTLFTNMJJCYJ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial approximation via compressed sensing of high-dimensional functions on lower sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Abdellah Chkifa, Clayton G. Webster, Hoang Tran, Nick Dexter","submitted_at":"2016-02-18T14:59:41Z","abstract_excerpt":"This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly decaying orthonormal expansion, whose most important terms are captured by a lower (or downward closed) set. By exploiting this fact, we present an innovative weighted $\\ell_1$ minimization procedure with a precise choice of weights, and a new iterative hard thresholding method, for imposing the downward closed preference. Theoretical results reveal that our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05823","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1602.05823/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-04T17:10:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CtTQDp3wrUo9r1FCzERKEgPFLOkrg7/tsP92Oafb2EJym8vt8RrK+OITOUFiYbTf0uWbFZP+yvfHDpIVuKpXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:29:35.029974Z"},"content_sha256":"15722a07a20d21e4ed14751273d8aed3e32ede63a2d9b402b3fad68141be1fa9","schema_version":"1.0","event_id":"sha256:15722a07a20d21e4ed14751273d8aed3e32ede63a2d9b402b3fad68141be1fa9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E6BEUTIDPIYGPWTLFTNMJJCYJ6/bundle.json","state_url":"https://pith.science/pith/E6BEUTIDPIYGPWTLFTNMJJCYJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E6BEUTIDPIYGPWTLFTNMJJCYJ6/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":"2026-06-20T05:29:35Z","links":{"resolver":"https://pith.science/pith/E6BEUTIDPIYGPWTLFTNMJJCYJ6","bundle":"https://pith.science/pith/E6BEUTIDPIYGPWTLFTNMJJCYJ6/bundle.json","state":"https://pith.science/pith/E6BEUTIDPIYGPWTLFTNMJJCYJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E6BEUTIDPIYGPWTLFTNMJJCYJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E6BEUTIDPIYGPWTLFTNMJJCYJ6","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":"c988ddceaddd4d39fa1ffdb6fbc0f7ecb0e926d547c66dac57946e5ea8de17bb","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-18T14:59:41Z","title_canon_sha256":"76cbf0481336fee2e3dbf8f5c16c60e135e3686a16a164255910335eccf052ef"},"schema_version":"1.0","source":{"id":"1602.05823","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05823","created_at":"2026-06-04T17:10:02Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05823v1","created_at":"2026-06-04T17:10:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05823","created_at":"2026-06-04T17:10:02Z"},{"alias_kind":"pith_short_12","alias_value":"E6BEUTIDPIYG","created_at":"2026-06-04T17:10:02Z"},{"alias_kind":"pith_short_16","alias_value":"E6BEUTIDPIYGPWTL","created_at":"2026-06-04T17:10:02Z"},{"alias_kind":"pith_short_8","alias_value":"E6BEUTID","created_at":"2026-06-04T17:10:02Z"}],"graph_snapshots":[{"event_id":"sha256:15722a07a20d21e4ed14751273d8aed3e32ede63a2d9b402b3fad68141be1fa9","target":"graph","created_at":"2026-06-04T17:10:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1602.05823/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly decaying orthonormal expansion, whose most important terms are captured by a lower (or downward closed) set. By exploiting this fact, we present an innovative weighted $\\ell_1$ minimization procedure with a precise choice of weights, and a new iterative hard thresholding method, for imposing the downward closed preference. Theoretical results reveal that our","authors_text":"Abdellah Chkifa, Clayton G. Webster, Hoang Tran, Nick Dexter","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-18T14:59:41Z","title":"Polynomial approximation via compressed sensing of high-dimensional functions on lower sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05823","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:f7147ecd47a9454915f244b3cdbba28f262be39550d34d5cca28ebec8d0f579f","target":"record","created_at":"2026-06-04T17:10:02Z","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":"c988ddceaddd4d39fa1ffdb6fbc0f7ecb0e926d547c66dac57946e5ea8de17bb","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-18T14:59:41Z","title_canon_sha256":"76cbf0481336fee2e3dbf8f5c16c60e135e3686a16a164255910335eccf052ef"},"schema_version":"1.0","source":{"id":"1602.05823","kind":"arxiv","version":1}},"canonical_sha256":"27824a4d037a3067da6b2cdac4a4584f8375b0b2c9745ec75d5df8217d7bf7cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27824a4d037a3067da6b2cdac4a4584f8375b0b2c9745ec75d5df8217d7bf7cd","first_computed_at":"2026-06-04T17:10:02.188324Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T17:10:02.188324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q7qE0Ob5H6fLC4b34bwvMyoloSP5MpzkRlNGCeEIFeZZgAQwxMz2iizgZrh1yL9gm57kzlKf6Ds6WQna8u10Dg==","signature_status":"signed_v1","signed_at":"2026-06-04T17:10:02.188759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05823","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7147ecd47a9454915f244b3cdbba28f262be39550d34d5cca28ebec8d0f579f","sha256:15722a07a20d21e4ed14751273d8aed3e32ede63a2d9b402b3fad68141be1fa9"],"state_sha256":"d66e311ab1c24a8862572c85d5886f6ebf54ba8f10df3e0fc1be0a08e5dfc500"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vocs/H/ZC35bVB4IDpRGdE4E7YWJomXw5gSeeMZlCggAiYDZ90uBlgeIQOTM3X1CY2d+QYh+RVyqIpDCRAVdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:29:35.032091Z","bundle_sha256":"2e46568dc5da7bee94e23512e92413086b1338aef626971bb03e171aa285ffc4"}}