Matthew Newman

Exact Positive Icosahedral Cubature on Fixed Radial Class-I Grids: Quadratic-Field Interoperability, Exact Replay, and Typed Compatibility with Papers I–V

This preprint establishes exact positive cubature rules on fixed radial Class-I icosahedral grids X_f ⊂ S² for frequencies 1 ≤ f ≤ 9. Using full icosahedral reflection symmetry H₃, invariant-cubature reduction, and exact arithmetic in ℚ(√5), strictly positive orbit-constant proba...

Exact Positive Icosahedral Cubature on Fixed Radial Class-I Grids: Quadratic-Field Interoperability, Exact Replay, and Typed Compatibility with Papers I–V

This preprint establishes exact positive cubature rules on fixed radial Class-I icosahedral grids X_f ⊂ S² for frequencies 1 ≤ f ≤ 9. Using full icosahedral reflection symmetry H₃, invariant-cubature reduction, and exact arithmetic in ℚ(√5), strictly positive orbit-constant proba...

Ordered Euclidean Remainders for Exact Orbit Reconstruction and Parameter Intervals in Rational Floor Maps

We study finite orbit segments of the rational floor map F_q(d) = ⌊qd⌋, where q = Q/S ∈ (0,1) has a fixed integer presentation. For an orbit dₖ₊₁ = F_q(dₖ), define the ordered Euclidean remainders ρₖ = Qdₖ − Sdₖ₊₁. The terminal state together with this ordered remainder sequence...

Ordered Euclidean Remainders for Exact Orbit Reconstruction and Parameter Intervals in Rational Floor Maps

We study finite orbit segments of the rational floor map F_q(d) = ⌊qd⌋, where q = Q/S ∈ (0,1) has a fixed integer presentation. For an orbit dₖ₊₁ = F_q(dₖ), define the ordered Euclidean remainders ρₖ = Qdₖ − Sdₖ₊₁. The terminal state together with this ordered remainder sequence...