{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BRSCL7ILCG3YV36ICXXEEJVF2J","short_pith_number":"pith:BRSCL7IL","canonical_record":{"source":{"id":"1908.10744","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-08-28T14:24:03Z","cross_cats_sorted":["cs.LG","eess.SP","math.IT","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"1fa68ad026dbd242a0fdd957d1d18942c2ecdc959b51cb9029fb4b1940a70e55","abstract_canon_sha256":"41e14f729338d7410af908b618aa746a33d2b867281db967ef27a4ef281c77ab"},"schema_version":"1.0"},"canonical_sha256":"0c6425fd0b11b78aefc815ee4226a5d260392a100762abe4d89e0dc678738fb1","source":{"kind":"arxiv","id":"1908.10744","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.10744","created_at":"2026-07-05T00:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1908.10744v2","created_at":"2026-07-05T00:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10744","created_at":"2026-07-05T00:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"BRSCL7ILCG3Y","created_at":"2026-07-05T00:46:48Z"},{"alias_kind":"pith_short_16","alias_value":"BRSCL7ILCG3YV36I","created_at":"2026-07-05T00:46:48Z"},{"alias_kind":"pith_short_8","alias_value":"BRSCL7IL","created_at":"2026-07-05T00:46:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BRSCL7ILCG3YV36ICXXEEJVF2J","target":"record","payload":{"canonical_record":{"source":{"id":"1908.10744","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-08-28T14:24:03Z","cross_cats_sorted":["cs.LG","eess.SP","math.IT","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"1fa68ad026dbd242a0fdd957d1d18942c2ecdc959b51cb9029fb4b1940a70e55","abstract_canon_sha256":"41e14f729338d7410af908b618aa746a33d2b867281db967ef27a4ef281c77ab"},"schema_version":"1.0"},"canonical_sha256":"0c6425fd0b11b78aefc815ee4226a5d260392a100762abe4d89e0dc678738fb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:46:48.142486Z","signature_b64":"sWvdVs+0EHgNrbUXQRpvmtksmezmMOdOp4V6oNKaJMjkA9W94u+RnAt/Cal2YnLGiKU0PUBTkTd5sLAmvovJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c6425fd0b11b78aefc815ee4226a5d260392a100762abe4d89e0dc678738fb1","last_reissued_at":"2026-07-05T00:46:48.142016Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:46:48.142016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.10744","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":"2026-07-05T00:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"86XsTacUZv8+01mCgOYC3mwsGlmPHjpXJRYzv1M+qTbsaEbyRh8gcFx+1PrWmJnr6IHeuHz9EJtTpJA1IzHSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:26:48.714528Z"},"content_sha256":"1786c1651146e485bd5aee4d436242c10bac37142276f3e337500e02d3afacb8","schema_version":"1.0","event_id":"sha256:1786c1651146e485bd5aee4d436242c10bac37142276f3e337500e02d3afacb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BRSCL7ILCG3YV36ICXXEEJVF2J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Information-Theoretic Lower Bounds for Compressive Sensing with Generative Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","eess.SP","math.IT","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.IT","authors_text":"Jonathan Scarlett, Zhaoqiang Liu","submitted_at":"2019-08-28T14:24:03Z","abstract_excerpt":"It has recently been shown that for compressive sensing, significantly fewer measurements may be required if the sparsity assumption is replaced by the assumption the unknown vector lies near the range of a suitably-chosen generative model. In particular, in (Bora {\\em et al.}, 2017) it was shown roughly $O(k\\log L)$ random Gaussian measurements suffice for accurate recovery when the generative model is an $L$-Lipschitz function with bounded $k$-dimensional inputs, and $O(kd \\log w)$ measurements suffice when the generative model is a $k$-input ReLU network with depth $d$ and width $w$. In thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10744","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.10744/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":"2026-07-05T00:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1JDsND3pZAcnQ9QuAQLSBhUpLPiXI6v4vlPYHYCU9VAcI753kOED0MlTuJ//nNlps5i088B5caG/3YsD270Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:26:48.715140Z"},"content_sha256":"bd1725f1b03aabf9e56661af3c7e7887843ada2f02f342d8dd8d7baff5bee474","schema_version":"1.0","event_id":"sha256:bd1725f1b03aabf9e56661af3c7e7887843ada2f02f342d8dd8d7baff5bee474"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BRSCL7ILCG3YV36ICXXEEJVF2J/bundle.json","state_url":"https://pith.science/pith/BRSCL7ILCG3YV36ICXXEEJVF2J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BRSCL7ILCG3YV36ICXXEEJVF2J/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":"2026-08-16T20:26:48Z","links":{"resolver":"https://pith.science/pith/BRSCL7ILCG3YV36ICXXEEJVF2J","bundle":"https://pith.science/pith/BRSCL7ILCG3YV36ICXXEEJVF2J/bundle.json","state":"https://pith.science/pith/BRSCL7ILCG3YV36ICXXEEJVF2J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BRSCL7ILCG3YV36ICXXEEJVF2J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BRSCL7ILCG3YV36ICXXEEJVF2J","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":"41e14f729338d7410af908b618aa746a33d2b867281db967ef27a4ef281c77ab","cross_cats_sorted":["cs.LG","eess.SP","math.IT","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-08-28T14:24:03Z","title_canon_sha256":"1fa68ad026dbd242a0fdd957d1d18942c2ecdc959b51cb9029fb4b1940a70e55"},"schema_version":"1.0","source":{"id":"1908.10744","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.10744","created_at":"2026-07-05T00:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1908.10744v2","created_at":"2026-07-05T00:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10744","created_at":"2026-07-05T00:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"BRSCL7ILCG3Y","created_at":"2026-07-05T00:46:48Z"},{"alias_kind":"pith_short_16","alias_value":"BRSCL7ILCG3YV36I","created_at":"2026-07-05T00:46:48Z"},{"alias_kind":"pith_short_8","alias_value":"BRSCL7IL","created_at":"2026-07-05T00:46:48Z"}],"graph_snapshots":[{"event_id":"sha256:bd1725f1b03aabf9e56661af3c7e7887843ada2f02f342d8dd8d7baff5bee474","target":"graph","created_at":"2026-07-05T00:46:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.10744/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It has recently been shown that for compressive sensing, significantly fewer measurements may be required if the sparsity assumption is replaced by the assumption the unknown vector lies near the range of a suitably-chosen generative model. In particular, in (Bora {\\em et al.}, 2017) it was shown roughly $O(k\\log L)$ random Gaussian measurements suffice for accurate recovery when the generative model is an $L$-Lipschitz function with bounded $k$-dimensional inputs, and $O(kd \\log w)$ measurements suffice when the generative model is a $k$-input ReLU network with depth $d$ and width $w$. In thi","authors_text":"Jonathan Scarlett, Zhaoqiang Liu","cross_cats":["cs.LG","eess.SP","math.IT","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-08-28T14:24:03Z","title":"Information-Theoretic Lower Bounds for Compressive Sensing with Generative Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10744","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":"sha256:1786c1651146e485bd5aee4d436242c10bac37142276f3e337500e02d3afacb8","target":"record","created_at":"2026-07-05T00:46:48Z","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":"41e14f729338d7410af908b618aa746a33d2b867281db967ef27a4ef281c77ab","cross_cats_sorted":["cs.LG","eess.SP","math.IT","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-08-28T14:24:03Z","title_canon_sha256":"1fa68ad026dbd242a0fdd957d1d18942c2ecdc959b51cb9029fb4b1940a70e55"},"schema_version":"1.0","source":{"id":"1908.10744","kind":"arxiv","version":2}},"canonical_sha256":"0c6425fd0b11b78aefc815ee4226a5d260392a100762abe4d89e0dc678738fb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c6425fd0b11b78aefc815ee4226a5d260392a100762abe4d89e0dc678738fb1","first_computed_at":"2026-07-05T00:46:48.142016Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:46:48.142016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sWvdVs+0EHgNrbUXQRpvmtksmezmMOdOp4V6oNKaJMjkA9W94u+RnAt/Cal2YnLGiKU0PUBTkTd5sLAmvovJBA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:46:48.142486Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.10744","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1786c1651146e485bd5aee4d436242c10bac37142276f3e337500e02d3afacb8","sha256:bd1725f1b03aabf9e56661af3c7e7887843ada2f02f342d8dd8d7baff5bee474"],"state_sha256":"6a9d453a071b88671de00d748dd60e9ce8cf2cd2f520ae200f11295378259ad1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dTR3/gaNkkrJMKQtpAF+6wdsZPDE5XqnHr+SNPJfJXHSUENf62BTAk0+uZk6T8lZQ/JqiTSy2/TauA0ejdVBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T20:26:48.719248Z","bundle_sha256":"7d6a657febc9af9f06bf66719c0d4d37a1ba2ca45df5541ed1b72479e8d2d791"}}