Syracuse descent at step 12 on 525 new classes modulo $2^{21}$

Proved

syracuse_descent_new21_step12_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 $2^{21}$ to the named 525-class certificate set, then the fixed iterate $T^{12}(n)$ is strictly smaller than $n$ . Every canonical representative in this set has total stripped exponent $S=20$ ; the exact computation satisfies $S+1\le 21$ and $3^{12}<2^{20}$ , 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_syracuseSevenMod32New21Step12Classes
import Mathlib.Logic.Function.Iterate
set_option autoImplicit false
set_option maxRecDepth 200000

Formal statement

theorem syracuse_descent_new21_step12_seven_mod32 (n : ℕ)
    (h : n % 2097152 ∈ syracuseSevenMod32New21Step12Classes) :
    syracuseStep^[12] n < n := by sorry

Source

Derived from 8d2d08ed-fda7-4e9b-b521-cfa49347ded2 by exact residue refinement; Terras uniformity: https://prove2.me/theorems/cd79de19-4613-42b0-afc9-48de75023e4a.

View graph

Syracuse descent at step 12 on 525 new classes modulo 2212^{21}221

Syracuse descent at step 12 on 525 new classes modulo $2^{21}$