Paper IX · Lean source

InvalidRectangularUniqueness.lean

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polynomial_weighted/controls/InvalidRectangularUniqueness.lean11 lines

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preserved/PRSC_IX_Consolidated_Manuscript/polynomial_weighted/controls/InvalidRectangularUniqueness.lean

1 module
2 public import PolynomialTowerControls
3 @[expose] public section
4 open Komorebi.PolynomialTowerControls MvPolynomial
5 
6 -- Invalid: a surjective rectangular Jacobian permits free coordinates inside one residue ball.
7 example : ∀ a b : Fin 2 → ℤ_[2],
8     (∀ i, eval₂ (Int.castRingHom ℤ_[2]) a (projectionSystem i) = 0) →
9     (∀ i, eval₂ (Int.castRingHom ℤ_[2]) b (projectionSystem i) = 0) →
10     (∀ i, (2 : ℤ_[2]) ∣ b i - a i) → a = b := by
11   exact projection_two_padic_roots

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Back to Paper IX: Arithmetic Packets, Dyadic Towers, and Local Polynomial Deformation