Exact finite rigidity for Furter's R(3): all windows through n=299

We prove, by exact computer-assisted certificates, that Furter's polynomial-composition rigidity assertion R(3,n) holds for every integer 1 ≤ n ≤ 299. Equivalently, the associated three-generator inverse-coefficient ideals have radical (x1,x2,x3) for every window d=2,...,300. The finite theorem is transferred from one exact same-prime GOOD special fibre per degree to characteristic zero by properness.

The release also proves a periodic Kummer-theoretic obstruction to any universal one-fixed-prime GOOD-fibre proof, publishes exact Euler-socle and normalized-resultant pilot data, and supplies a machine-readable Universal R(3) Challenge. Universal R(3), the unrestricted Strong Factorial Conjecture, and the general Polydegree Conjecture remain open.

This is an unrefereed candidate. The package has exact replay and internal cross-model adversarial review, but not specialist peer review or independent external reconstruction.