{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SFHUCAXP5ZAK54OKFNQO67UWBW","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":"93c3093a353af4caa273be2e230eca10dda434eb3fc2f45c658288aaba0cb601","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-18T12:51:48Z","title_canon_sha256":"bd7416281668195daaac3718beabaf0d4d4320059cf3e72c4485d5e605dd79f8"},"schema_version":"1.0","source":{"id":"1712.06373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06373","created_at":"2026-05-18T00:27:48Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06373v1","created_at":"2026-05-18T00:27:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06373","created_at":"2026-05-18T00:27:48Z"},{"alias_kind":"pith_short_12","alias_value":"SFHUCAXP5ZAK","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SFHUCAXP5ZAK54OK","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SFHUCAXP","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:5e66f78529360f8d67a42b60f65077e2aeec691aa85df245cb8849c2ec52378d","target":"graph","created_at":"2026-05-18T00:27:48Z","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":"In a recent article, Schiebinger et al. provided sufficient conditions for the noiseless recovery of a signal made of M Dirac masses given 2M + 1 observations of, e.g. , its convolution with a Gaussian filter, using the Basis Pursuit for measures. In the present work, we show that a variant of their criterion provides a necessary and sufficient condition for the Non-Degenerate Source Condition (NDSC) which was introduced by Duval and Peyr{\\'e} to ensure support stability in super-resolution. We provide sufficient conditions which, for instance, hold unconditionally for the Laplace kernel provi","authors_text":"Vincent Duval (MOKAPLAN)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-18T12:51:48Z","title":"A characterization of the Non-Degenerate Source Condition in Super-Resolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06373","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":"sha256:4e9b44c087fe650d564b9355418a0e0e05b90853e9a7f7c126dea677763358b8","target":"record","created_at":"2026-05-18T00:27:48Z","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":"93c3093a353af4caa273be2e230eca10dda434eb3fc2f45c658288aaba0cb601","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-12-18T12:51:48Z","title_canon_sha256":"bd7416281668195daaac3718beabaf0d4d4320059cf3e72c4485d5e605dd79f8"},"schema_version":"1.0","source":{"id":"1712.06373","kind":"arxiv","version":1}},"canonical_sha256":"914f4102efee40aef1ca2b60ef7e960d928c1bb57ef7055643502e0b5656fab4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"914f4102efee40aef1ca2b60ef7e960d928c1bb57ef7055643502e0b5656fab4","first_computed_at":"2026-05-18T00:27:48.001905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:48.001905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4iMX9Wsq6RkY7qhgdgDkYtGH6XZ2wiIFeA/JAJIStxACYLsXn12dC74gKKJlAUEa6gsE3nTMXwFc7sFDmB1wCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:48.002424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.06373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e9b44c087fe650d564b9355418a0e0e05b90853e9a7f7c126dea677763358b8","sha256:5e66f78529360f8d67a42b60f65077e2aeec691aa85df245cb8849c2ec52378d"],"state_sha256":"3c7b5aebf6a9d267548944fa23f48074cc4caaaec3ce01d62ac0059cc9cf66d4"}