{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NNCQQY6ELAFHAYAYWCNFBTQQ4O","short_pith_number":"pith:NNCQQY6E","canonical_record":{"source":{"id":"1203.2309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-03-11T03:51:05Z","cross_cats_sorted":["math-ph","math.MP","math.OC"],"title_canon_sha256":"1f7cab13273d814a9f675fd9550946485c4913b95ea722158e2e5fc6c6e5c0e7","abstract_canon_sha256":"3d673bd7095147461c610c668c44fd3b407c6e652b78c7a396eb80b572adbcb9"},"schema_version":"1.0"},"canonical_sha256":"6b450863c4580a706018b09a50ce10e392bed4fcf43e14171c03e75cfe2636f4","source":{"kind":"arxiv","id":"1203.2309","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2309","created_at":"2026-05-18T01:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2309v1","created_at":"2026-05-18T01:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2309","created_at":"2026-05-18T01:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"NNCQQY6ELAFH","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NNCQQY6ELAFHAYAY","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NNCQQY6E","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NNCQQY6ELAFHAYAYWCNFBTQQ4O","target":"record","payload":{"canonical_record":{"source":{"id":"1203.2309","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-03-11T03:51:05Z","cross_cats_sorted":["math-ph","math.MP","math.OC"],"title_canon_sha256":"1f7cab13273d814a9f675fd9550946485c4913b95ea722158e2e5fc6c6e5c0e7","abstract_canon_sha256":"3d673bd7095147461c610c668c44fd3b407c6e652b78c7a396eb80b572adbcb9"},"schema_version":"1.0"},"canonical_sha256":"6b450863c4580a706018b09a50ce10e392bed4fcf43e14171c03e75cfe2636f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:10.253237Z","signature_b64":"wcgwx64P5j2LUg2QCr+pRlH8JZIpufh+CjwiBWIIkxyazXDTs/Y0s8sjqYmPYBhlpxdq9xbp6RU9gzMDEBXQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b450863c4580a706018b09a50ce10e392bed4fcf43e14171c03e75cfe2636f4","last_reissued_at":"2026-05-18T01:58:10.252728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:10.252728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.2309","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":"2026-05-18T01:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PXNmOhki++Ja988sJYWsojLLfVc4ZGiCLNUMoatBiBFSOhdkyoxSIjCMDGZ7Zyt1I9nUSE5JVN4bJ2VaSz51DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:50:20.625148Z"},"content_sha256":"ff28c113c7b6b7a88a89bdec976b98f566177d477aee6ffd0cc4bf47f8d81412","schema_version":"1.0","event_id":"sha256:ff28c113c7b6b7a88a89bdec976b98f566177d477aee6ffd0cc4bf47f8d81412"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NNCQQY6ELAFHAYAYWCNFBTQQ4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A differential equations approach to $l_1$-minimization with applications to array imaging","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OC"],"primary_cat":"math.NA","authors_text":"Alexei Novikov, George Papanicolaou, Lenya Ryzhik, Miguel Moscoso","submitted_at":"2012-03-11T03:51:05Z","abstract_excerpt":"We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is independent of the relaxation parameter. An advantage of using the ordinary differential equations is that energy methods can be used to prove convergence. The connection to the discrete algorithms is provided by the Crandall-Liggett theory of monotone nonlinear semigroups. We illustrate the effectiveness of the discrete optimization algorithm in some sparse ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2309","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":"2026-05-18T01:58:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y8jn6LMnZO6r84I1SxAYhDoM4CCGO6zXsBRc6g3lL6pXhoxbTVA4vFBo1uVpYr8+eOQktymnRJeWgSxGxtg3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:50:20.625515Z"},"content_sha256":"8ab1fd019ba21cd98fba799caff623c99b3b1da80a8c1fce67d09b7da1d560b6","schema_version":"1.0","event_id":"sha256:8ab1fd019ba21cd98fba799caff623c99b3b1da80a8c1fce67d09b7da1d560b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNCQQY6ELAFHAYAYWCNFBTQQ4O/bundle.json","state_url":"https://pith.science/pith/NNCQQY6ELAFHAYAYWCNFBTQQ4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNCQQY6ELAFHAYAYWCNFBTQQ4O/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":"2026-06-01T06:50:20Z","links":{"resolver":"https://pith.science/pith/NNCQQY6ELAFHAYAYWCNFBTQQ4O","bundle":"https://pith.science/pith/NNCQQY6ELAFHAYAYWCNFBTQQ4O/bundle.json","state":"https://pith.science/pith/NNCQQY6ELAFHAYAYWCNFBTQQ4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNCQQY6ELAFHAYAYWCNFBTQQ4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NNCQQY6ELAFHAYAYWCNFBTQQ4O","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":"3d673bd7095147461c610c668c44fd3b407c6e652b78c7a396eb80b572adbcb9","cross_cats_sorted":["math-ph","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-03-11T03:51:05Z","title_canon_sha256":"1f7cab13273d814a9f675fd9550946485c4913b95ea722158e2e5fc6c6e5c0e7"},"schema_version":"1.0","source":{"id":"1203.2309","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2309","created_at":"2026-05-18T01:58:10Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2309v1","created_at":"2026-05-18T01:58:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2309","created_at":"2026-05-18T01:58:10Z"},{"alias_kind":"pith_short_12","alias_value":"NNCQQY6ELAFH","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NNCQQY6ELAFHAYAY","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NNCQQY6E","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:8ab1fd019ba21cd98fba799caff623c99b3b1da80a8c1fce67d09b7da1d560b6","target":"graph","created_at":"2026-05-18T01:58:10Z","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 present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is independent of the relaxation parameter. An advantage of using the ordinary differential equations is that energy methods can be used to prove convergence. The connection to the discrete algorithms is provided by the Crandall-Liggett theory of monotone nonlinear semigroups. We illustrate the effectiveness of the discrete optimization algorithm in some sparse ar","authors_text":"Alexei Novikov, George Papanicolaou, Lenya Ryzhik, Miguel Moscoso","cross_cats":["math-ph","math.MP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-03-11T03:51:05Z","title":"A differential equations approach to $l_1$-minimization with applications to array imaging"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2309","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:ff28c113c7b6b7a88a89bdec976b98f566177d477aee6ffd0cc4bf47f8d81412","target":"record","created_at":"2026-05-18T01:58:10Z","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":"3d673bd7095147461c610c668c44fd3b407c6e652b78c7a396eb80b572adbcb9","cross_cats_sorted":["math-ph","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-03-11T03:51:05Z","title_canon_sha256":"1f7cab13273d814a9f675fd9550946485c4913b95ea722158e2e5fc6c6e5c0e7"},"schema_version":"1.0","source":{"id":"1203.2309","kind":"arxiv","version":1}},"canonical_sha256":"6b450863c4580a706018b09a50ce10e392bed4fcf43e14171c03e75cfe2636f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b450863c4580a706018b09a50ce10e392bed4fcf43e14171c03e75cfe2636f4","first_computed_at":"2026-05-18T01:58:10.252728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:10.252728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wcgwx64P5j2LUg2QCr+pRlH8JZIpufh+CjwiBWIIkxyazXDTs/Y0s8sjqYmPYBhlpxdq9xbp6RU9gzMDEBXQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:10.253237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2309","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff28c113c7b6b7a88a89bdec976b98f566177d477aee6ffd0cc4bf47f8d81412","sha256:8ab1fd019ba21cd98fba799caff623c99b3b1da80a8c1fce67d09b7da1d560b6"],"state_sha256":"d6c98e7f79ebf4492e7987ff129de5b1ff7d761ca614d1fb372aa7324f309306"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BYUYNjkGqMiOJr0hGlA0LbrGuUfG06he15+XF0CuNe2GpyX0OJX9+D0NMZ/UK4iIYkIFzPyJndk9lFiBDyCTBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:50:20.627552Z","bundle_sha256":"1357baebd7fb81972331546255b33c6dbc41de8446145f68897c638ddda92d97"}}