{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LWAJQ7YX34HK6AR5M3WT2J2RHL","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":"c5b7543f8d010fc38cb4a3ac05dad0b2397f16d2a69af590bac7ca24d6457abc","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-10T19:15:24Z","title_canon_sha256":"cee30d1e8249b6d688c901133d612a4f84366e17a37f547577972ff90376c938"},"schema_version":"1.0","source":{"id":"1907.04895","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04895","created_at":"2026-05-17T23:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04895v1","created_at":"2026-05-17T23:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04895","created_at":"2026-05-17T23:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"LWAJQ7YX34HK","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LWAJQ7YX34HK6AR5","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LWAJQ7YX","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:7806986aeaec24936757862302d17ef8f2d2ccac993ef58bdfedcaad4c39b18c","target":"graph","created_at":"2026-05-17T23:40:54Z","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":"The problem of super-resolution in general terms is to recuperate a finitely supported measure $\\mu$ given finitely many of its coefficients $\\hat{\\mu}(k)$ with respect to some orthonormal system. The interesting case concerns situations, where the number of coefficients required is substantially smaller than a power of the reciprocal of the minimal separation among the points in the support of $\\mu$. In this paper, we consider the more severe problem of recuperating $\\mu$ approximately without any assumption on $\\mu$ beyond having a finite total variation. In particular, $\\mu$ may be supporte","authors_text":"H. N. Mhaskar","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-10T19:15:24Z","title":"Super-resolution meets machine learning: approximation of measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04895","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":"sha256:3145f1164a7ca7b8fcff46a42e572dd52b2f37aa260186b63d9b0a7c6d3d929c","target":"record","created_at":"2026-05-17T23:40:54Z","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":"c5b7543f8d010fc38cb4a3ac05dad0b2397f16d2a69af590bac7ca24d6457abc","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-07-10T19:15:24Z","title_canon_sha256":"cee30d1e8249b6d688c901133d612a4f84366e17a37f547577972ff90376c938"},"schema_version":"1.0","source":{"id":"1907.04895","kind":"arxiv","version":1}},"canonical_sha256":"5d80987f17df0eaf023d66ed3d27513aebf4214b30a78243ab9c0e0340e608ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d80987f17df0eaf023d66ed3d27513aebf4214b30a78243ab9c0e0340e608ff","first_computed_at":"2026-05-17T23:40:54.651002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:54.651002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"scJ12IVRUTuy+HnyOOSUEwmh0HLyMLZRuMv5PZ0ICmf5GZJ6IaA8TfxvvlyV9fGyul+8ir2gMZRL4X730HuwCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:54.651665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.04895","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3145f1164a7ca7b8fcff46a42e572dd52b2f37aa260186b63d9b0a7c6d3d929c","sha256:7806986aeaec24936757862302d17ef8f2d2ccac993ef58bdfedcaad4c39b18c"],"state_sha256":"27d7790f687d59742cc2462bdf20f42cc12731c3f2169bda7030854a02f66691"}