Paper IX · Lean source
InvalidPerturbationExtraPrecision.lean
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polynomial_parameter_towers/controls/InvalidPerturbationExtraPrecision.lean11 lines
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preserved/PRSC_IX_Consolidated_Manuscript/polynomial_parameter_towers/controls/InvalidPerturbationExtraPrecision.lean1 module
2 public import PolynomialDeformationControls
3 @[expose] public section
4 open Komorebi.PolynomialDeformationControls MvPolynomial
5
6 -- Invalid: G=X−2 is an integral coefficient perturbation of F=X of precision one.
7 -- Its actual p-adic root has displacement two, which does not have precision two.
8 example : ∃ b : Fin 1 → ℤ_[2],
9 eval₂ (Int.castRingHom ℤ_[2]) b (Komorebi.PolynomialTowerControls.linearMinusTwo 0) = 0 ∧
10 (2 : ℤ_[2]) ^ 2 ∣ b 0 := by
11 exact linear_shift_no_extra_padic_precision
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Back to Paper IX: Arithmetic Packets, Dyadic Towers, and Local Polynomial Deformation