Paper IX · Lean source

InvalidGlobalUniqueness.lean

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polynomial_deformation/controls/InvalidGlobalUniqueness.lean11 lines

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preserved/PRSC_IX_Consolidated_Manuscript/polynomial_deformation/controls/InvalidGlobalUniqueness.lean

1 module
2 public import PolynomialDeformationControls
3 @[expose] public section
4 open Komorebi.PolynomialDeformationControls MvPolynomial
5 
6 -- Invalid: the checked bijective Jacobian at one does not make X²−1 globally injective.
7 -- The positive control proves two actual p-adic roots in different residue balls.
8 example : ∀ a b : Fin 1 → ℤ_[3],
9     (∀ i, eval₂ (Int.castRingHom ℤ_[3]) a (squareMinusOne i) = 0) →
10     (∀ i, eval₂ (Int.castRingHom ℤ_[3]) b (squareMinusOne i) = 0) → a = b := by
11   exact square_minus_one_not_global_unique

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