Unrefereed candidate. This work identifies the Lewis–Perry–Straub auxiliary determinant as a Jacobian, derives an integral weighted-Euler syzygy, turns its specialisation test into a smooth-point criterion, gives a smaller Hensel certificate, and proves uniform squarefreeness for each individual boundary polynomial in the e = 3 family. It does not prove the uniform e = 3 affine theorem or uniform adjacent coprimality. Exact finite affine computation covers d = 2..20; adjacent coprimality is checked through d = 200. The 142-file package includes source, evidence, receipts, validators, and a SHA-256 manifest. Producer-side replay passed in ordinary and optimized Python; no independent reproduction, formal verification, external specialist review, or editorial peer review is claimed. Repository: https://github.com/ipitchford/smooth-point-certificates-polydegree-containments