Companion Code for "Discovery of the Complex Field by Graduated Observation of Plane Rotation'

Python notebooks providing computational verification for the results in 'Discovery of the Complex Field by Graduated Observation of Plane Rotation' (Brown, 2026), submitted to Philosophia Mathematica. The repository contains two notebooks: - colab_2d_necessity.py: Computational verification of the 2D necessity theorem (Section 3). Generates circle images under polynomial maps z^n - 1, visualizes winding number behavior at varying radii, and demonstrates the topological mechanism forcing algebraic closure. Produces Figure 6 of the paper. - winding_colab.py: Focused verification of the winding lemma and polynomial root-forcing argument (Section 2.6). Computes winding numbers for parameterized curves and confirms the boundary conditions (winding n at large R, winding 0 at R = 0) used in the algebraic closure proof. Both notebooks are designed to run in Google Colab with no additional dependencies beyond standard scientific Python (NumPy, Matplotlib). Each includes a timestamp cell for reproducibility.