Eventual Stability of Dyadic Truncation

Proved

LevyStochCalc.Brownian.Continuity.dyadicTrunc_eventually_eq_readable

by Lazyfill · Oct 26, 2026 · Mathlib 0df444a (Lean v4.33.1)

functional-inequalitieskls-conjecturekls-modularkls-readablelog-concavevendored-levystochcalc

If s is a dyadic rational, then there exists L₀ : ℕ such that for every L ≥ L₀, its level-L dyadic truncation equals s:

s\in\operatorname{dyadicRationals}\Longrightarrow\exists L_0\,\forall L\ge L_0,\ \operatorname{dyadicTrunc}(L,s)=s.

The lemma dyadicTrunc_eventually_eq_readable records eventual exactness of truncation on the dense dyadic set.

Original Lean declaration header

Within namespace LevyStochCalc.Brownian.Continuity. Shown in its original module context. Proof omitted.

lemma dyadicTrunc_eventually_eq {s : ℝ} (hs : s ∈ dyadicRationals) :
    ∃ L₀ : ℕ, ∀ L, L₀ ≤ L → dyadicTrunc L s = s

Module navigation

Module: LevyStochCalc/Brownian/ContinuityDyadicChaining.

Previous: dyadicTrunc_near_step · Next: exists_dyadic_scale.

Source excerpt, lines 312–313 · Frozen source 408915f.

Preamble

import Definitions.Def_KLSModular_LevyStochCalc_Brownian_ContinuityDyadicChaining

/-
Copyright (c) 2026 Christian Garry. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Garry
-/
-- Vendored from https://github.com/cgarryZA/LevyStochCalc at commit 984dbf0b790031eac05d56fe5a84b65e15e1e932 (upstream path LevyStochCalc/Brownian/ContinuityDyadicChaining.lean; Apache-2.0; provenance in formalization/vendor/vendor-lock.json of the KLS repository)

Formal statement


lemma LevyStochCalc.Brownian.Continuity.dyadicTrunc_eventually_eq_readable {s : ℝ} (hs : s ∈ dyadicRationals) :
    ∃ L₀ : ℕ, ∀ L, L₀ ≤ L → dyadicTrunc L s = s := by sorry

Source

Lean source: https://github.com/cgarryZA/LevyStochCalc/blob/984dbf0b790031eac05d56fe5a84b65e15e1e932/LevyStochCalc/Brownian/ContinuityDyadicChaining.lean#L310-L325 (repository human-ai-mathematics/kls-lean, commit 408915f, module `LevyStochCalc.Brownian.ContinuityDyadicChaining`, declaration `LevyStochCalc.Brownian.Continuity.dyadicTrunc_eventually_eq`; the repository is private at upload time). Vendored from https://github.com/cgarryZA/LevyStochCalc at commit 984dbf0b790031eac05d56fe5a84b65e15e1e932 (Apache-2.0; upstream copyright notice retained in the Lean text).

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