Syracuse step-15 descent on chunk 12/13 at $2^{26}$

Proved

syracuse_descent_new26_step15_chunk12_seven_mod32

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

collatzfinite-certificatenumber-theorystopping-timesyracuse

For any natural number whose residue modulo $2^{26}$ belongs to the named 745-element chunk, the accelerated Syracuse iterate $T^{15}(n)$ is strictly smaller than $n$ . Every representative in this chunk has total stripped exponent $S=25$ , with $S+1\le 26$ and $3^{15}<2^{25}$ , so the fixed representative certificate transfers to the full residue class.

Preamble

import Definitions.Def_syracuseStep
import Definitions.Def_syracuseSevenMod32New26Step15Chunk12Classes
import Mathlib.Logic.Function.Iterate
set_option autoImplicit false
set_option maxRecDepth 200000

Formal statement

theorem syracuse_descent_new26_step15_chunk12_seven_mod32 (n : ℕ)
    (h : n % 67108864 ∈ syracuseSevenMod32New26Step15Chunk12Classes) :
    syracuseStep^[15] 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-15 descent on chunk 12/13 at 2262^{26}226

Syracuse step-15 descent on chunk 12/13 at $2^{26}$