{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:P25BR67KDGVLRD4SEA6SRIXOE3","short_pith_number":"pith:P25BR67K","canonical_record":{"source":{"id":"1509.06947","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-23T12:49:16Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c673e5e1b6c1d8a03832ed8c13b8c4fbff0004ae89e548d8c2a984ba2b505180","abstract_canon_sha256":"effea1e0970498c542cd5aa755e601adb7a563495686829764a03a1572df25c7"},"schema_version":"1.0"},"canonical_sha256":"7eba18fbea19aab88f92203d28a2ee26f32a0cd0de86e1440c73ebbca7759a38","source":{"kind":"arxiv","id":"1509.06947","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:P25BR67KDGVLRD4SEA6SRIXOE3","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06947","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-23T12:49:16Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c673e5e1b6c1d8a03832ed8c13b8c4fbff0004ae89e548d8c2a984ba2b505180","abstract_canon_sha256":"effea1e0970498c542cd5aa755e601adb7a563495686829764a03a1572df25c7"},"schema_version":"1.0"},"canonical_sha256":"7eba18fbea19aab88f92203d28a2ee26f32a0cd0de86e1440c73ebbca7759a38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:44.448521Z","signature_b64":"ozz6qKlqZghrgWvcn5AupKMLC33H926pKPBHpEFfPBfmo5VPhXbbsWMlR/TeVWKv8KfBuHRmc7yNCMzR+b5YBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7eba18fbea19aab88f92203d28a2ee26f32a0cd0de86e1440c73ebbca7759a38","last_reissued_at":"2026-05-18T00:52:44.448113Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:44.448113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06947","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/c9pgFppfUJF1PFOl0GttjSxVPv/RrSWC+4uy8p71Jyuc15CuFreX59YQPZSttFSlVDHQWn5WyeHeLWC4YXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:29:37.599765Z"},"content_sha256":"564b0cae452e6b9035ea51e24a117ea0a8316c417151f33e54b52f7d57d7acfe","schema_version":"1.0","event_id":"sha256:564b0cae452e6b9035ea51e24a117ea0a8316c417151f33e54b52f7d57d7acfe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:P25BR67KDGVLRD4SEA6SRIXOE3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recipes for stable linear embeddings from Hilbert spaces to R^m","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Gilles Puy, Mike Davies, R\\'emi Gribonval","submitted_at":"2015-09-23T12:49:16Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06947","kind":"arxiv","version":2},"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":"2026-05-18T00:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rglWrGvB9e57OmYwgsVvLbN95r0JIAmBlKgbJ6vMCM/7Dlrp3lKF18hgOVOmB624GQRWLf8pLqxKYRAYAB3XDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:29:37.600107Z"},"content_sha256":"c1466a4f272f21ddde3da571df65692076e00c100d7e2b915ec6602dc2864d46","schema_version":"1.0","event_id":"sha256:c1466a4f272f21ddde3da571df65692076e00c100d7e2b915ec6602dc2864d46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P25BR67KDGVLRD4SEA6SRIXOE3/bundle.json","state_url":"https://pith.science/pith/P25BR67KDGVLRD4SEA6SRIXOE3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P25BR67KDGVLRD4SEA6SRIXOE3/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":"2026-06-01T08:29:37Z","links":{"resolver":"https://pith.science/pith/P25BR67KDGVLRD4SEA6SRIXOE3","bundle":"https://pith.science/pith/P25BR67KDGVLRD4SEA6SRIXOE3/bundle.json","state":"https://pith.science/pith/P25BR67KDGVLRD4SEA6SRIXOE3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P25BR67KDGVLRD4SEA6SRIXOE3/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+PAv5rEWD2/0cDsz6STv1pD4ZQRjABn9Ja/imjpTG3fBR45wdcxsqBtZsQRy1xvwUL1pmn2hXCze9QT72CwtDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:29:37.602159Z","bundle_sha256":"a74ddeccb257f91307aaa8a4be065ba67f60da6c7d45551f9472ac6ead16defc"}}