Central Configuration Finiteness Challenge
S6
smale derived
smale derived
External: externally open
τ response: further investigation
For arbitrary positive masses in the n-body problem, is the number of relative equilibria / central configurations finite?
Current τ response
See the paired Central Configuration Finiteness Challenge — Challenge Response on the Results lane for the program's current response status, registry evidence, verification route, and external-review boundary.
Current status: further investigation.
Challenge statement
For arbitrary positive masses in the n-body problem, is the number of relative equilibria / central configurations finite?
Why this challenge is in the ledger
Strong mathematical-physics bridge challenge. Tests τ’s ability to constrain equilibrium types, phase-space geometry, symmetry, and finite structural classes.
τ-facing burden
Show whether τ’s dynamical or spectral structures impose finiteness, stability, or classification constraints on central configurations.
First reviewer questions
- Does τ say anything about actual central configurations, or only about generic equilibrium classes?
- Can τ recover known cases such as small-n results?
- Does it distinguish finiteness, generic finiteness, and classification up to symmetry?
Source anchors
Source anchors are background references, not endorsements of Panta Rhei claims.