{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KRTZUDQCOPPJS2VY4DE6UV4HUZ","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":"a645902e968ed5299c93480f53cf76c9bde5264eb18ec41365d066f4e66495d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-26T16:47:26Z","title_canon_sha256":"9111141e042d9270c7b86ed8d5cb9f01d644ee7d1ca4349524f2576694344366"},"schema_version":"1.0","source":{"id":"1609.08066","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08066","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08066v4","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08066","created_at":"2026-05-18T00:34:23Z"},{"alias_kind":"pith_short_12","alias_value":"KRTZUDQCOPPJ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KRTZUDQCOPPJS2VY","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KRTZUDQC","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:6a8bd4e543bfe6af36b6294f01513be9dc2ea19d1b391846cddf3ea840bb15fb","target":"graph","created_at":"2026-05-18T00:34:23Z","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":"Nonconvex optimization problems with an L1-constraint are ubiquitous, and are found in many application domains including: optimal control of hybrid systems, machine learning and statistics, and operations research. This paper shows that nonconvex optimization problems with an L1-constraint can be approximately solved in polynomial time. We first show that nonlinear integer programs with an L1-constraint can be solved in a number of oracle steps that is polynomial in the dimension of the decision variable, for each fixed radius of the L1-constraint. When specialized to polynomial integer progr","authors_text":"Anil Aswani, Yonatan Mintz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-26T16:47:26Z","title":"Polynomial-Time Approximation for Nonconvex Optimization Problems with an L1-Constraint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08066","kind":"arxiv","version":4},"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":"sha256:3bafba36e99bf1f18cf2c087a401b2a373e48d0d00b441a85843fa3e3a1428c3","target":"record","created_at":"2026-05-18T00:34:23Z","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":"a645902e968ed5299c93480f53cf76c9bde5264eb18ec41365d066f4e66495d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-26T16:47:26Z","title_canon_sha256":"9111141e042d9270c7b86ed8d5cb9f01d644ee7d1ca4349524f2576694344366"},"schema_version":"1.0","source":{"id":"1609.08066","kind":"arxiv","version":4}},"canonical_sha256":"54679a0e0273de996ab8e0c9ea5787a65081d46fd3cd76986b8290499b11bf33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54679a0e0273de996ab8e0c9ea5787a65081d46fd3cd76986b8290499b11bf33","first_computed_at":"2026-05-18T00:34:23.110666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:23.110666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ipopV6Ismd7ep2+0k5uhFCRErd2/+gOBIjteMnb677VqchsuttlMU8G9GOcBx9cFijXHHB1wvCcDS2tOggfOCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:23.111074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08066","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bafba36e99bf1f18cf2c087a401b2a373e48d0d00b441a85843fa3e3a1428c3","sha256:6a8bd4e543bfe6af36b6294f01513be9dc2ea19d1b391846cddf3ea840bb15fb"],"state_sha256":"ea9c5ac7a2fc854758bec02e60cd56ca53136a8bc58a53f044a440cf33ae9a9b"}