Guarded ancestor identity for an odd run and even padding

Proved

CollatzWork.rootDescentAncestor

by Sodelin · Sep 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

collatz-work-import

Let $T:\mathbb N\to\mathbb N$ be the shortcut Collatz map: $T(n)=n/2$ for even $n$ and $T(n)=(3n+1)/2$ for odd $n$ . Write $T^k$ for its $k$ -fold iterate, with $T^0(n)=n$ .

Let $e,L,q,r\in\mathbb N$ , $q>0$ , and $3^{L+1}q=4r+1$ . Then

T^{e+L+2}\bigl(2^e(2^Lq-1)\bigr)=r.

This supplies an actual forward ancestor trajectory; no size, residue, or all-root coverage claim is part of the result.

Preamble

import Std
import Init.Grind.Ordered.Module
import Definitions.Def_CollatzWork_ConvergenceStatement
import Definitions.Def_CollatzWork_InverseWordBoundaryStatement
import Definitions.Def_CollatzWork_RefinedMersenneChild
import Definitions.Def_CollatzWork_RootDescentStatement
import Theorems.Thm_CollatzWork_oddRun

Formal statement

theorem CollatzWork.rootDescentAncestor : RootDescentAncestorStatement := by sorry

Source

https://github.com/Sodelin/Collatz-Conjecture-Work/blob/026aa4ad4be6453a005ab950b160a9f2204c5271/lean/CollatzWork/RootDescent.lean#L143-L154

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