Jonah triangle

“The Jonah Triangle: A Hyperbolic Saddle in the Pedal Dynamics of the Nagel Line” by Jonah Schloss. The paper studies the iteration of the pedal triangle of the point P_t = (1 - t) I + t N, where I is the incenter and N is the Nagel point of a triangle. For t = 7/10, the map admits a remarkable fixed isosceles triangle with side lengths 4:7:7. The author proposes to call this object the Jonah triangle. The exact part of the paper proves: - the reduction of the dynamics to the isosceles family; - the existence and uniqueness of the non-equilateral fixed isosceles shape for t = 7/10; - the complete classification of the dynamics on the isosceles axis; - the exact hyperbolic saddle structure of the Jonah triangle; - the exact eigenvalues λ_s = -143/343 and λ_u = 451/343; - a symbolic proof of the general transverse multiplier λ_s(t) = ((3t - 1)(6t^2 - 6t + 1)) / (2t^3); - the existence of a local analytic stable manifold. The global statement, namely that for t = 7/10 almost every initial triangle shape converges either to the equilateral triangle or to a degenerate straight-line shape, is established by a computer-assisted and AI-assisted proof architecture based on interval arithmetic, trapping regions, a finite cell graph, a band lemma, and cone conditions near the saddle. This global part is explicitly presented as conditional on independent verification of the interval computations. No independent verification has been completed at the time of this deposit. The deposit includes a SymPy script verifying the exact algebraic identities and eigenvalues, as well as a checklist describing the computations that should be independently re-implemented using certified interval-arithmetic libraries such as Arb, MPFI, or INTLAB. Subject classification: 37E99, 51M04, 37C75, 65G20.