Spherical Capacity and Optimal Distribution Challenge
S7
smale derived
smale derived
External: externally open
τ response: structurally constrained
For N points on the 2-sphere, determine or algorithmically approximate configurations minimizing pairwise logarithmic energy.
Current τ response
See the paired Spherical Capacity and Optimal Distribution Challenge — Challenge Response on the Results lane for the program's current response status, registry evidence, verification route, and external-review boundary.
Current status: structurally constrained.
Challenge statement
For N points on the 2-sphere, determine or algorithmically approximate configurations minimizing pairwise logarithmic energy.
Why this challenge is in the ledger
Fits τ’s spectral/capacity/boundary grammar. Tests capacity, energy minimization, global distribution, discrete-to-continuum transition.
τ-facing burden
Show whether τ-capacity, boundary algebra, or spectral distribution yields nontrivial constraints on optimal point configurations or their asymptotic structure.
First reviewer questions
- Does τ produce computable configurations, asymptotic energy bounds, or only a conceptual analogy?
- Is the τ-capacity notion comparable to classical potential theory?
- Can it recover known spherical design or energy-minimization results?
Source anchors
Source anchors are background references, not endorsements of Panta Rhei claims.