{"paper":{"title":"The extended Smale's 9th problem -- On computational barriers and paradoxes in estimation, regularisation, computer-assisted proofs and learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alexander Bastounis, Anders C Hansen, Verner Vla\\v{c}i\\'c","submitted_at":"2021-10-29T12:19:37Z","abstract_excerpt":"Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assisted proofs and learning. The success of LP is traditionally attributed to the fact that it is \"in P\" for rational inputs. On the other hand, in his list of problems for the 21st century S. Smale calls for \"[Computational] models which process approximate inputs and which permit round-off computations\". Indeed, since e.g. the exponential function does not have an exact representation or floating-point arithmetic approx"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.15734","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/2110.15734/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"}