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9eeb9c7 | 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 | import OAI.Analysis.IrrationalRotation.Model.ProductCoupling
namespace OAI
noncomputable section
namespace Invariant233.OrderedProductCoupling
def sourceKappa (s : ℕ) : ℝ := 1 / (100 * ((s : ℝ) + 1))
def ofBlocks (m : ℕ → ℕ) (κ a b : ℕ → ℝ)
(hκ0 : ∀ s, 0 ≤ κ s) (hκ : ∀ s, κ s ≤ 1 / 100)
(hm : ∀ s, 100 ≤ m s)
(ha : ∀ s, 1 / (m s : ℝ) ≤ a s) (ha' : ∀ s, a s ≤ 1 / 4)
(hb : ∀ s, 1 / (m s : ℝ) ≤ b s) (hb' : ∀ s, b s ≤ 1 / 4)
(e : ℕ ≃ Σ s, Fin (m s)) (tag : ℕ) : Parameters where
κ i := κ (e i).1
m i := m (e i).1
a i := a (e i).1
b i := b (e i).1
t i := if (e i).1 = tag then 1 else 0
κ_nonneg i := hκ0 (e i).1
κ_le i := hκ (e i).1
m_ge i := by exact_mod_cast hm (e i).1
a_lower i := ha (e i).1
a_upper i := ha' (e i).1
b_lower i := hb (e i).1
b_upper i := hb' (e i).1
t_nonneg i := by split_ifs <;> norm_num
t_le i := by split_ifs <;> norm_num
def blockDensityBound (κ : ℕ → ℝ) : ℝ :=
Real.exp (10 * (2 * (∑' s, κ s ^ 2) + 1))
end Invariant233.OrderedProductCoupling
end
end OAI
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