THE ORDINAL OF DYNAMICAL DEGREES OF BIRATIONAL MAPS OF THE PROJECTIVE PLANE

The paper proves the upper bound via lower semicontinuity on parameter spaces and a dimension count, and the lower bound by explicit de Jonquières constructions on a cuspidal cubic, yielding exact order type ω^ω under k ⊇ R_alg for rational surfaces. The candidate solution reaches the same conclusions by reducing to actions on Weyl lattices and invoking results it attributes to Bot; however, it relies on an unsupported claim that the full ‘Weyl spectrum’ has order type ω^ω and overstates field-of-definition details (claiming Q-coefficients). These issues are minor and can be patched by replacing the upper-bound step with the paper’s Theorem 2.3 and correcting the field-of-definition to Q(λ) ⊂ R_alg.