Exact Permutation Moments for Walsh Interaction-Order Energies: A Projector Specialization of Quadratic-Form Randomization Theory

J601 Reproducibility Package This package accompanies the manuscript: "Exact Permutation Moments for Walsh Interaction-Order Energies:A Projector Specialization of Quadratic-Form Randomization Theory"(J600, Roshankumar Chandaliya, QDL project). The manuscript develops exact finite-sample permutation formulas for Walshinteraction-order energies on the Boolean cube. For a centered finitepopulation assigned to the N = 2^n vertices, the degree-k interaction-orderenergy is E_k = sum|A|=k g_hat_pi(A)^2. By specializing establishedquadratic-form randomization theory to orthogonal Walsh projectors, theanalysis yields compact exact formulas for permutation mean, variance, andcross-level covariance, with exhaustive verification at N=4 and N=8. This package contains: - Exact formula implementation (exact_null_moments)- Dense FWHT and sparse Hamming/Krawtchouk implementations- Monte Carlo benchmark (100,000 uniform value permutations)- Exhaustive verification at N=4 (24 permutations) and N=8 (40,320 permutations)- B=0 edge-case verification and B<0 impossibility check- Timing distribution CSVs (median, IQR, min, max)- Environment metadata (Python 3.13.5, NumPy 2.3.5, Intel Xeon Platinum 8573C, 5-vCPU container)- Publication-ready LaTeX benchmark table- SHA256 integrity manifest- README with reproduction instructions Key result: the exact formula is 10^4–10^5× faster than 100,000-permutationMonte Carlo for first- and second-moment estimation, with agreement tomachine precision. License: Source code — MIT. Data and benchmark outputs — CC BY 4.0.See LICENSE file in the package for full text. Companion manuscript: J600 (Zenodo DOI: [J600 DOI daalo yahan]).