This deposit contains the research paper, verification software, and computational results for "Knot Type Determines Thurston Geometry. " The paper establishes that the knot type of a periodic orbit in a Hamiltonian system determines the Thurston geometry of the local phase space model and constrains the dynamics. The central example is the 3: 2 Hilda resonance in the Sun Jupiter circular restricted three body problem, where roughly 4, 000 asteroids have remained dynamically stable for billions of years. The fundamental periodic orbit is identified as the right handed trefoil knot T (2, 3) using the torus knot winding argument. Dehn surgery on the trefoil complement at slope 3/2, determined by the resonance ratio, produces a Seifert fiber space with spherical Thurston geometry. The Seifert invariants yield a conjectural capacity bound predicting that the regular fraction of phase space satisfies μᵣeg/μₜotal ≤ 1/3. This prediction was tested numerically. The period 3 orbit family was continued to the first period doubling bifurcation at Jacobi constant C = 2. 3546. A MEGNO survey at this energy with 10, 000 test particles evolved for 10, 000 orbital periods on the resonance island returned a regular fraction of 0. 326. This is below the predicted bound of 0. 333 and near the theoretical ceiling, providing strong empirical support for the capacity formula. The paper also identifies a structural correspondence between the Călugăreanu White Fuller ribbon decomposition and Seifert fiber invariants, connecting results across DNA topology, vortex dynamics, plasma physics, and celestial mechanics within a common topological framework. Contents: (1) AMC. docx, the paper. (2) AMCVerifier. zip, the verification software written in C# with a Python REBOUND backend for MEGNO computation. (3) AMCReport₁0KFinal. txt, the raw computational log from the full resolution MEGNO run.
Alexander Naranjo (Thu,) studied this question.