Syracuse descent at step 13 on 1570 new classes modulo $2^{23}$

Proved

syracuse_descent_new23_step13_seven_mod32

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

collatzfinite-certificatenumber-theorystopping-timesyracuse

Let $T$ be the accelerated Syracuse map. If $n$ belongs modulo $2^{23}$ to the named 1570-class certificate set, then the fixed iterate $T^{13}(n)$ is strictly smaller than $n$ . Every canonical representative in this set has total stripped exponent $S=22$ ; the exact computation satisfies $S+1\le 23$ and $3^{13}<2^{22}$ , so Terras uniformity transfers the representative descent to its complete residue class. This is a finite certificate leaf split from the hard residual branch.

Preamble

import Definitions.Def_syracuseStep
import Definitions.Def_syracuseSevenMod32New23Step13Classes
import Mathlib.Logic.Function.Iterate
set_option autoImplicit false
set_option maxRecDepth 200000

Formal statement

theorem syracuse_descent_new23_step13_seven_mod32 (n : ℕ)
    (h : n % 8388608 ∈ syracuseSevenMod32New23Step13Classes) :
    syracuseStep^[13] n < n := by sorry

Source

Derived from a4ee549a-031c-41b2-923c-b6e1d51bbc45 by exact residue refinement; Terras uniformity: https://prove2.me/theorems/cd79de19-4613-42b0-afc9-48de75023e4a.

View graph

Syracuse descent at step 13 on 1570 new classes modulo 2232^{23}223

Syracuse descent at step 13 on 1570 new classes modulo $2^{23}$