{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P25BR67KDGVLRD4SEA6SRIXOE3","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":"effea1e0970498c542cd5aa755e601adb7a563495686829764a03a1572df25c7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-23T12:49:16Z","title_canon_sha256":"c673e5e1b6c1d8a03832ed8c13b8c4fbff0004ae89e548d8c2a984ba2b505180"},"schema_version":"1.0","source":{"id":"1509.06947","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06947","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06947v2","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06947","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"P25BR67KDGVL","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P25BR67KDGVLRD4S","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P25BR67K","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:c1466a4f272f21ddde3da571df65692076e00c100d7e2b915ec6602dc2864d46","target":"graph","created_at":"2026-05-18T00:52:44Z","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":"We consider the problem of constructing a linear map from a Hilbert space $\\mathcal{H}$ (possibly infinite dimensional) to $\\mathbb{R}^m$ that satisfies a restricted isometry property (RIP) on an arbitrary signal model $\\mathcal{S} \\subset \\mathcal{H}$. We present a generic framework that handles a large class of low-dimensional subsets but also unstructured and structured linear maps. We provide a simple recipe to prove that a random linear map satisfies a general RIP on $\\mathcal{S}$ with high probability. We also describe a generic technique to construct linear maps that satisfy the RIP. Fi","authors_text":"Gilles Puy, Mike Davies, R\\'emi Gribonval","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-23T12:49:16Z","title":"Recipes for stable linear embeddings from Hilbert spaces to R^m"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06947","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":"sha256:564b0cae452e6b9035ea51e24a117ea0a8316c417151f33e54b52f7d57d7acfe","target":"record","created_at":"2026-05-18T00:52:44Z","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":"effea1e0970498c542cd5aa755e601adb7a563495686829764a03a1572df25c7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-23T12:49:16Z","title_canon_sha256":"c673e5e1b6c1d8a03832ed8c13b8c4fbff0004ae89e548d8c2a984ba2b505180"},"schema_version":"1.0","source":{"id":"1509.06947","kind":"arxiv","version":2}},"canonical_sha256":"7eba18fbea19aab88f92203d28a2ee26f32a0cd0de86e1440c73ebbca7759a38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7eba18fbea19aab88f92203d28a2ee26f32a0cd0de86e1440c73ebbca7759a38","first_computed_at":"2026-05-18T00:52:44.448113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:44.448113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ozz6qKlqZghrgWvcn5AupKMLC33H926pKPBHpEFfPBfmo5VPhXbbsWMlR/TeVWKv8KfBuHRmc7yNCMzR+b5YBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:44.448521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06947","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:564b0cae452e6b9035ea51e24a117ea0a8316c417151f33e54b52f7d57d7acfe","sha256:c1466a4f272f21ddde3da571df65692076e00c100d7e2b915ec6602dc2864d46"],"state_sha256":"246393c7d8b204a667b180f78b1a6ec627c2b146ebf20408b2ca0dcdcf4b89fc"}