{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HJ6UALVWD6VZ4BHUAKFTDX6L3E","short_pith_number":"pith:HJ6UALVW","canonical_record":{"source":{"id":"1205.1650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-08T10:03:20Z","cross_cats_sorted":["math.IT","math.OC"],"title_canon_sha256":"a70cafb9876fc96de633b4e538903240afa6a711b792f3b9b3763d7fd8c1aede","abstract_canon_sha256":"70c0ce6727049946008e2f61beb28c1198346f696aa43d79b5af85762aa9cddc"},"schema_version":"1.0"},"canonical_sha256":"3a7d402eb61fab9e04f4028b31dfcbd91d72e95e49a5e8e314ac258126638c27","source":{"kind":"arxiv","id":"1205.1650","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1650","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1650v1","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1650","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"HJ6UALVWD6VZ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HJ6UALVWD6VZ4BHU","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HJ6UALVW","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HJ6UALVWD6VZ4BHUAKFTDX6L3E","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-08T10:03:20Z","cross_cats_sorted":["math.IT","math.OC"],"title_canon_sha256":"a70cafb9876fc96de633b4e538903240afa6a711b792f3b9b3763d7fd8c1aede","abstract_canon_sha256":"70c0ce6727049946008e2f61beb28c1198346f696aa43d79b5af85762aa9cddc"},"schema_version":"1.0"},"canonical_sha256":"3a7d402eb61fab9e04f4028b31dfcbd91d72e95e49a5e8e314ac258126638c27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:09.594655Z","signature_b64":"zw40oquNq9OJCuI7RJAD3FuVB6kHfCpYSMCTvgxD+rMo8hdodnMBmz7fKjQnV6JQZwp4POfvh1RkZf9TPODuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a7d402eb61fab9e04f4028b31dfcbd91d72e95e49a5e8e314ac258126638c27","last_reissued_at":"2026-05-18T03:56:09.593833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:09.593833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1650","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CbgRKUHefGXfzhAlZRFx83qyNYqbG15MiDAHAHbcHXcxM42cdR4BAHzeggmpxqwPGQsjCOhXhkblNTgqoCKjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:18:11.923325Z"},"content_sha256":"95733ae8c395cba5cf97797a25987930f090ca355c587e33e85ce0eda5327245","schema_version":"1.0","event_id":"sha256:95733ae8c395cba5cf97797a25987930f090ca355c587e33e85ce0eda5327245"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HJ6UALVWD6VZ4BHUAKFTDX6L3E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compressed Sensing with Nonlinear Observations and Related Nonlinear Optimisation Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.OC"],"primary_cat":"cs.IT","authors_text":"Thomas Blumensath","submitted_at":"2012-05-08T10:03:20Z","abstract_excerpt":"Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured signals to be sampled far below the rate traditionally prescribed.\n  Nearly all of the theory developed for Compressed Sensing signal recovery assumes that samples are taken using linear measurements. In this paper we instead address the Compressed Sensing recovery problem in a setting where the observations are non-linear. We show that, under conditions simi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1650","kind":"arxiv","version":1},"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":"2026-05-18T03:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ywz8bgzBlGraS6+a+t+f6eH/L0Yp/jvkAXX/M41E7xlsbYTRn9PYf72FWWo5GysRb+uQgWVzt6kzHLOT+CNBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:18:11.923671Z"},"content_sha256":"3c3fc081a52bad240ac8af865984fcfc9370543d650140ef185c39667fc8e598","schema_version":"1.0","event_id":"sha256:3c3fc081a52bad240ac8af865984fcfc9370543d650140ef185c39667fc8e598"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HJ6UALVWD6VZ4BHUAKFTDX6L3E/bundle.json","state_url":"https://pith.science/pith/HJ6UALVWD6VZ4BHUAKFTDX6L3E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HJ6UALVWD6VZ4BHUAKFTDX6L3E/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":"2026-07-04T23:18:11Z","links":{"resolver":"https://pith.science/pith/HJ6UALVWD6VZ4BHUAKFTDX6L3E","bundle":"https://pith.science/pith/HJ6UALVWD6VZ4BHUAKFTDX6L3E/bundle.json","state":"https://pith.science/pith/HJ6UALVWD6VZ4BHUAKFTDX6L3E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HJ6UALVWD6VZ4BHUAKFTDX6L3E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HJ6UALVWD6VZ4BHUAKFTDX6L3E","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":"70c0ce6727049946008e2f61beb28c1198346f696aa43d79b5af85762aa9cddc","cross_cats_sorted":["math.IT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-08T10:03:20Z","title_canon_sha256":"a70cafb9876fc96de633b4e538903240afa6a711b792f3b9b3763d7fd8c1aede"},"schema_version":"1.0","source":{"id":"1205.1650","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1650","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1650v1","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1650","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"HJ6UALVWD6VZ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HJ6UALVWD6VZ4BHU","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HJ6UALVW","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:3c3fc081a52bad240ac8af865984fcfc9370543d650140ef185c39667fc8e598","target":"graph","created_at":"2026-05-18T03:56:09Z","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":"Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured signals to be sampled far below the rate traditionally prescribed.\n  Nearly all of the theory developed for Compressed Sensing signal recovery assumes that samples are taken using linear measurements. In this paper we instead address the Compressed Sensing recovery problem in a setting where the observations are non-linear. We show that, under conditions simi","authors_text":"Thomas Blumensath","cross_cats":["math.IT","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-08T10:03:20Z","title":"Compressed Sensing with Nonlinear Observations and Related Nonlinear Optimisation Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1650","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":"sha256:95733ae8c395cba5cf97797a25987930f090ca355c587e33e85ce0eda5327245","target":"record","created_at":"2026-05-18T03:56:09Z","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":"70c0ce6727049946008e2f61beb28c1198346f696aa43d79b5af85762aa9cddc","cross_cats_sorted":["math.IT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-08T10:03:20Z","title_canon_sha256":"a70cafb9876fc96de633b4e538903240afa6a711b792f3b9b3763d7fd8c1aede"},"schema_version":"1.0","source":{"id":"1205.1650","kind":"arxiv","version":1}},"canonical_sha256":"3a7d402eb61fab9e04f4028b31dfcbd91d72e95e49a5e8e314ac258126638c27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a7d402eb61fab9e04f4028b31dfcbd91d72e95e49a5e8e314ac258126638c27","first_computed_at":"2026-05-18T03:56:09.593833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:09.593833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zw40oquNq9OJCuI7RJAD3FuVB6kHfCpYSMCTvgxD+rMo8hdodnMBmz7fKjQnV6JQZwp4POfvh1RkZf9TPODuAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:09.594655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1650","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95733ae8c395cba5cf97797a25987930f090ca355c587e33e85ce0eda5327245","sha256:3c3fc081a52bad240ac8af865984fcfc9370543d650140ef185c39667fc8e598"],"state_sha256":"e51421f8ad34aa75af27c380eda26c7bf94eebb6b657f3f2496e0005a31495d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rm215OeN+ghjccpaFMI821Jp6msLhjqOZFZa/WHKMYoTawy6dPuauNOX/0KrMeIju270nGui5AhY/sAIsYMJAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T23:18:11.925489Z","bundle_sha256":"fdeaf33d9834d09a01858599fd937bda0cc51715543208313bad483bcfd735c5"}}