Syracuse step-13 descent on chunk 2/2 at $2^{23}$

Proved

syracuse_descent_new23_step13_chunk02_seven_mod32

by Sneed · Oct 1, 2026 · Mathlib 0df444a (Lean v4.33.1)

collatzfinite-certificatenumber-theorystopping-timesyracuse

For any natural number whose residue modulo $2^{23}$ belongs to the named 785-element chunk, the accelerated Syracuse iterate $T^{13}(n)$ is strictly smaller than $n$ . Every representative in this chunk has total stripped exponent $S=22$ , with $S+1\le 23$ and $3^{13}<2^{22}$ , so the fixed representative certificate transfers to the full residue class.

Preamble

import Definitions.Def_syracuseStep
import Definitions.Def_syracuseSevenMod32New23Step13Chunk02Classes
import Mathlib.Logic.Function.Iterate
set_option autoImplicit false
set_option maxRecDepth 200000

Formal statement

theorem syracuse_descent_new23_step13_chunk02_seven_mod32 (n : ℕ)
    (h : n % 8388608 ∈ syracuseSevenMod32New23Step13Chunk02Classes) :
    syracuseStep^[13] n < n := by sorry

Source

Computational certificate child of the Prove2Me Collatz residual tree; uniformity theorem https://prove2.me/theorems/cd79de19-4613-42b0-afc9-48de75023e4a.

View graph

Syracuse step-13 descent on chunk 2/2 at 2232^{23}223

Syracuse step-13 descent on chunk 2/2 at $2^{23}$