| import Mathlib | |
| import OAI.LinearAlgebra.MatrixFields.Certificates.NativeSharp | |
| import OAI.LinearAlgebra.MatrixFields.Construction.OrderedLimits | |
| namespace OAI | |
| namespace MatrixAllFields | |
| open scoped BigOperators Topology Polynomial | |
| section | |
| namespace MatrixMultiplication.AllFieldMain | |
| open AllFieldNativeCapacity AllFieldTerminalRates AllFieldInitialEntropy NativeNumerics | |
| universe u | |
| theorem omega_lt_source_constant (F : Type u) [Field F] : | |
| Arithmetic.omega F < (2371054886006746 : ℝ) / 10 ^ 15 ∧ | |
| (2371054886006746 : ℝ) / 10 ^ 15 < (2371056 : ℝ) / 10 ^ 6 := by | |
| constructor | |
| · have hbound := AllFieldOrderedLimits.omega_le_native_ratio F | |
| native_denominator_gap native_stageC_feasible | |
| native_stageA_positive native_stageB_positive | |
| native_stageC_balanced_positive native_volume_positive | |
| exact lt_of_le_of_lt hbound native_sharp_rate_bound | |
| · norm_num | |
| end MatrixMultiplication.AllFieldMain | |
| end | |
| end MatrixAllFields | |
| end OAI | |