Verification Suite for the paper "Projective Steenrod--Milnor Hulls: Frobenius Periodicity and Quantum Density Obstructions"

### Contents of this Deposit: 1. `steenrod_hulls.py`: The primary Python 3 verification script. It implements the formal graded derivations of the mod 2 Steenrod algebra, exact Koszul cycle spaces over the square subring $\mathbb{F}_4[x^2,y^2,z^2]$, projective point evaluations over $\mathbb{P}^2(\mathbb{F}_4)$, MacWilliams dual transformations, and support-rank distance certificates.2. `verification_output.txt`: The pre-computed reference log generated by executing `python3 steenrod_hulls.py --full`. It certifies the dimensional stabilization of the towers, low-weight spanning thresholds, MacWilliams weight enumerators for degree 6, and the exact support indices of the $[[21, 2, 6/6]]_4$ check matrices.3. `README.md`: System dependencies and quick-start execution instructions.4. `steenrod_milnor_hulls_code.zip`: A bundled archive of the above files for local replication. ### Execution Modes: - Standard Mode (`python3 steenrod_hulls.py`): Instantly validates the structural tower dimensions, Hermitian dual ranks, hull dimensions, and the explicit check matrices of the $[[21,2,6/6]]_4$ code (~2 seconds).- Full Mode (`python3 steenrod_hulls.py --full`): Executes the exhaustive support-first minimum distance certificates, exact low-weight spanning ranks, and full weight distribution derivations (~10-15 minutes). ### System Requirements:- Python 3.7+- NumPy (`pip install numpy`) All arithmetic takes place strictly over the finite field $\mathbb{F}_4 = \mathbb{F}_2[\omega]/(\omega^2+\omega+1)$. No floating-point approximations or empirical datasets are used.