Dimension-Independent Finiteness of Central Configurations for Positive Masses

We prove that for any N \geq 3 bodies with positive masses in \mathbb{R}^d (d \geq 2), the number of central configurations modulo similarity is finite, resolving Smale's 6th Problem in every spatial dimension d \geq 2 simultaneously. Key results: 5 theorems / propositions. Maturity: Working Paper. Includes formal verification (Lean 4 with Python verification scripts). Part of The Latent research program. Related papers in this program: Degenerate CC, Universal.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-11
DOI
https://doi.org/10.5281/zenodo.20117294
Primary Topic
Point processes and geometric inequalities
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Dimension-Independent Finiteness of Central Configurations for Positive Masses

Tamás Nagy
Zenodo (CERN European Organization for Nuclear Research)
Point processes and geometric inequalities
article

Dimension-Independent Finiteness of Central Configurations for Positive Masses

Tamás Nagy
article en

Abstract

We prove that for any N \geq 3 bodies with positive masses in \mathbb{R}^d (d \geq 2), the number of central configurations modulo similarity is finite, resolving Smale's 6th Problem in every spatial dimension d \geq 2 simultaneously. Key results: 5 theorems / propositions. Maturity: Working Paper. Includes formal verification (Lean 4 with Python verification scripts). Part of The Latent research program. Related papers in this program: Degenerate CC, Universal.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 4%
Point processes and geometric inequalities
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.

Dimension-Independent Finiteness of Central Configurations for Positive Masses — Tamás Nagy · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS