| { |
| "assessment": "verified", |
| "claim": 1, |
| "destructive_control": { |
| "errors": [ |
| 0.5, |
| 0.5, |
| 0.5, |
| 0.5 |
| ], |
| "mutation": "negate the conjugate intercept sign" |
| }, |
| "error_vs_spacing_exponent": 2.0, |
| "exact_theorem_rate_for_instance": "||f-f_grid||_infinity=h\u00b2/8", |
| "finite_grid_rows": [ |
| { |
| "atoms": 5, |
| "cells_exhausted": 4, |
| "exact_uniform_error": "1/32", |
| "spacing": 0.5, |
| "uniform_error": 0.03125 |
| }, |
| { |
| "atoms": 9, |
| "cells_exhausted": 8, |
| "exact_uniform_error": "1/128", |
| "spacing": 0.25, |
| "uniform_error": 0.0078125 |
| }, |
| { |
| "atoms": 17, |
| "cells_exhausted": 16, |
| "exact_uniform_error": "1/512", |
| "spacing": 0.125, |
| "uniform_error": 0.001953125 |
| }, |
| { |
| "atoms": 33, |
| "cells_exhausted": 32, |
| "exact_uniform_error": "1/2048", |
| "spacing": 0.0625, |
| "uniform_error": 0.00048828125 |
| }, |
| { |
| "atoms": 65, |
| "cells_exhausted": 64, |
| "exact_uniform_error": "1/8192", |
| "spacing": 0.03125, |
| "uniform_error": 0.0001220703125 |
| }, |
| { |
| "atoms": 129, |
| "cells_exhausted": 128, |
| "exact_uniform_error": "1/32768", |
| "spacing": 0.015625, |
| "uniform_error": 3.0517578125e-05 |
| } |
| ], |
| "literal_claim": "Theorem 1 (Section V.A) establishes that finitely \u1ef8-convex functions form a dense subset of all \u1ef8-convex functions, giving a universal approximation property for generalized convex functions.", |
| "native_instance": "Phi(x,y)=xy on X=Y=[-1,1], f(x)=x\u00b2/2, f^X(y)=y\u00b2/2" |
| } |
|
|
