Impossibility Results

How it works

Comparisons

Evidence quality

Highlighted claims

• No polynomial with a fixed number of iterates can uniformly round every point near every integer from tolerance δ to a smaller tolerance ε. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs
• No fixed polynomial map can exactly produce a phase indicator that switches from 1 to 0 at every integer counter threshold. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs
• Uniform rounding and exact phase selection are characterized as fundamental requirements for long integer computations. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs
• The impossibility results explain why neural activations and polynomial-map step size play structural computational roles. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs