| import OAI.LinearAlgebra.MatrixMultiplication.Duality.WitnessEntropy |
| import OAI.LinearAlgebra.MatrixMultiplication.Duality.ScriptIndependence |
| import OAI.LinearAlgebra.MatrixMultiplication.Duality.TerminationIndependence |
| import OAI.LinearAlgebra.MatrixMultiplication.Duality.InformationSchedule |
|
|
| namespace OAI |
|
|
| /-! Dual matrix multiplication exponents and finite rectangular constructions. -/ |
|
|
| noncomputable section |
|
|
| namespace MatrixMultiplication.DualWitnessRates |
|
|
| attribute [local instance 10000] Classical.propDecidable Classical.decEq |
| attribute [local instance 11000] instDecidableEqFin |
|
|
| open MatrixMultiplication.Foundation CompletionLabels CompletionLabels.TopologicalFlatten |
| open DualInformation DualCompletionLaws DualWitness |
|
|
| theorem nonincident_independent (n : Fin (1 + readable.depth)) |
| (hn : program.pair n.val = .yz) : |
| ConditionalIndependent law (labelRecordOf program.labels n.val) |
| (program.labels n.val) x := by |
| exact DualProgramIndependence.termination_independent source readable laws288 |
| state288.rho |
| (by rw [state288_rho]; exact rho288_range.1.le) |
| (by rw [state288_rho]; exact rho288_range.2.le) |
| DualProgramIndependence.laws288_independent n hn |
|
|
| theorem incident_rate : rate .xy + rate .xz = 288 * Real.log 2 := by |
| let : Fintype (Coordinate Word Word Word .B) := inferInstanceAs (Fintype Word) |
| have h := program.incident_rate_eq_x_entropy law program_complete PUnit.unit |
| (fun _ => rfl) (fun n hn => nonincident_independent n hn) |
| change rate .xy + rate .xz = finiteEntropy (law.map x).mass at h |
| rw [x_entropy] at h |
| exact h |
|
|
| theorem hidden_rate : rate .yz = 288 * hiddenRate := by |
| linarith only [rate_sum, law_entropy, incident_rate] |
|
|
| end MatrixMultiplication.DualWitnessRates |
|
|
| end |
|
|
| end OAI |
|
|
