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92416a2 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 | import OAI.Dynamics.EntropyCounterexample.MapData
import OAI.Dynamics.EntropyCounterexample.MapContinuity
import OAI.Dynamics.EntropyCounterexample.MapQuotientContinuity
namespace OAI
noncomputable section
namespace Problem340.Construction
theorem continuous_concrete_baseInput (L : ℝ) (hL : 2 < L) (i : Fin 3) :
Continuous (fun x : ℝ × Sphere => baseInput (concreteData L hL) i x.1 x.2) := by
apply continuous_baseInput_of_standard_cutoffs _ rfl rfl
change 1 < L
linarith
theorem continuous_concrete_input (L : ℝ) (hL : 2 < L) (i : Fin 3) :
Continuous (fun x : AddCircle (100 : ℝ) × Sphere =>
input (concreteData L hL) i x.1 x.2) :=
continuous_input_of_baseInput _ i (continuous_concrete_baseInput L hL i)
theorem concrete_gain_seam (L : ℝ) (hL : 2 < L) :
(concreteData L hL).gain 0 = (concreteData L hL).gain 100 := by
change gainProfile L 0 = gainProfile L 100
rw [gainProfile_zero_outside (by norm_num), gainProfile_zero_outside (by norm_num)]
theorem continuous_concrete_periodicGain (L : ℝ) (hL : 2 < L) :
Continuous (periodicGain (concreteData L hL)) := by
let : Fact ((0 : ℝ) < 100) := ⟨by norm_num⟩
apply AddCircle.liftIco_zero_continuous
· exact concrete_gain_seam L hL
· exact (gainProfile_contDiff L).continuous.continuousOn
theorem continuous_concreteMap (L : ℝ) (hL : 2 < L) :
Continuous (concreteMap L hL) := by
apply continuous_rawMap_of_coefficients (concreteData L hL)
· exact SphereCutoffs.continuous_onePointClockGate
· exact continuous_concrete_input L hL
· exact sphereSaturation_continuous (3 * L) _
· exact continuous_concrete_periodicGain L hL
end Problem340.Construction
end
end OAI
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