Polynomial ODEs

Uniform threshold-affine normal forms can be represented by robust polynomial ODEs using polynomial clocks, comparators, sample-and-hold transport, and shadowing. Robust polynomial ODE computation uses a fixed rational polynomial vector field with primitive recursive observation and safety bounds. Polynomial ODEs can supply rounding, comparators, clocks, stabilization, and error correction without ReLU gates or external discrete branching. The polynomial ODE construction uses a rational polynomial clock with sine-cosine style coordinates and period 2π. The polynomial ODE construction depends on robust continuous-time mechanisms and primitive recursive observation and safety bounds.