{"id":"W4311761036","doi":"10.1016/j.jco.2022.101724","title":"The area of empty axis-parallel boxes amidst 2-dimensional lattice points","year":2022,"lang":"en","type":"article","venue":"Journal of Complexity","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Austrian Science Fund","keywords":"Mathematics; Lattice (music); Infimum and supremum; Conjecture; Square lattice; Combinatorics; Quadratic equation; Discrete mathematics; Geometry; Condensed matter physics; Physics; Ising model","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001714377,0.0001039174,0.0003143764,0.00006378029,0.0003233431,0.00002892667,0.0003316991,0.00002507468,0.001449539],"category_scores_gemma":[0.0008728426,0.00006367375,0.0001963418,0.0001411945,0.0001431558,0.0001131677,0.0001142632,0.0003549025,0.00000687605],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000081926,"about_ca_system_score_gemma":0.00008178453,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004724395,"about_ca_topic_score_gemma":0.00001100499,"domain_scores_codex":[0.9979007,0.0002381471,0.0008426281,0.00007483181,0.0008096228,0.0001340241],"domain_scores_gemma":[0.9975386,0.0009644373,0.0008528754,0.0002175922,0.0003591323,0.00006739984],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001391407,0.0003556166,0.00005740545,0.00004365229,0.00005701884,0.000003061411,0.0004073355,0.00001035856,0.0001234702,0.9832864,0.01525995,0.0002566235],"study_design_scores_gemma":[0.0004554145,0.0001954662,0.0009085548,0.00003264972,0.00003244922,0.0001429196,0.0005325309,0.007639565,0.0003352491,0.9845415,0.005111603,0.00007210898],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9630901,0.0001323974,0.01615012,0.006813909,0.0003759662,0.0002969845,0.00002586775,0.00002946953,0.01308518],"genre_scores_gemma":[0.6709846,0.00001400878,0.3264515,0.0005686255,0.0001666047,0.00001562222,0.000007572861,0.00002985595,0.001761621],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3103013,"threshold_uncertainty_score":0.9994633,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1286115804029658,"score_gpt":0.3366526722535477,"score_spread":0.2080410918505819,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}