Generic Hyperbolicity Challenge
S11
smale derived
smale derived
External: externally open
τ response: further investigation
Are one-dimensional dynamical systems generically hyperbolic, in the relevant smooth or complex-polynomial senses?
Current τ response
See the paired Generic Hyperbolicity 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
Are one-dimensional dynamical systems generically hyperbolic, in the relevant smooth or complex-polynomial senses?
Why this challenge is in the ledger
Tests attractors, stability, genericity, critical-point behavior, approximation, and dynamical-system grammar.
τ-facing burden
Show whether τ supplies a notion of generic stabilization, attractor basin closure, or hyperbolic normal form that gives substantive constraints.
First reviewer questions
- Does τ distinguish genericity from inevitability?
- Does τ recover known partial results?
- Can τ express critical orbit convergence and sink structure in standard dynamical terms?
Source anchors
Source anchors are background references, not endorsements of Panta Rhei claims.