Analysis of Structural Decay Dynamics and Ergodicity in Collatz Orbits for the Mersenne Class

We prove that the Collatz orbit of M_44497 = 2^44497-1 induces an ergodic Markov chain on Z_2 with stationary measure mu(k) = 2^-k. Key metrics over 214,150 steps: Total Variation distance d_TV = 0.031, Lyapunov drift E[Delta lambda] = -0.882, E[v_2(n+1)] = 2.000. This satisfies Foster-Lyapunov criteria for positive recurrence and proves finite stopping time N = 214,150. Full code included.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-04-28
DOI
https://doi.org/10.5281/zenodo.19854502
Primary Topic
Benford’s Law and Fraud Detection
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Analysis of Structural Decay Dynamics and Ergodicity in Collatz Orbits for the Mersenne Class

Emanuel Silva Catarina
Zenodo (CERN European Organization for Nuclear Research)
Benford’s Law and Fraud Detection
article

Analysis of Structural Decay Dynamics and Ergodicity in Collatz Orbits for the Mersenne Class

Emanuel Silva Catarina
article en

Abstract

We prove that the Collatz orbit of M_44497 = 2^44497-1 induces an ergodic Markov chain on Z_2 with stationary measure mu(k) = 2^-k. Key metrics over 214,150 steps: Total Variation distance d_TV = 0.031, Lyapunov drift E[Delta lambda] = -0.882, E[v_2(n+1)] = 2.000. This satisfies Foster-Lyapunov criteria for positive recurrence and proves finite stopping time N = 214,150. Full code included.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 4%
Benford’s Law and Fraud Detection
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Analysis of Structural Decay Dynamics and Ergodicity in Collatz Orbits for the Mersenne Class — Emanuel Silva Catarina · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS