The Wojciech (WD) Model for Fixed-Count Positional Rigidity of Prime Blocks

This work develops the Wojciech (WD) model, a fixed-count framework for the internal geometry of blocks of consecutive primes. By inverting short-interval prime-count fluctuations and conditioning on the observed block endpoints, the model represents positional deviations as an endpoint-pinned bridge. It yields a continuum law for shifted-Legendre mode variances, an exact finite-grid Toeplitz Rayleigh-quotient formulation with iid Dirichlet normalization, and explicit covariance formulas for separated blocks. Finite-count corrections are further refined by a short-range consecutive-prime correlation kernel derived from Hardy–Littlewood singular-series structure, producing a parameter-free finite-\(k\), finite-\(Q\) modal variance law with substantially improved agreement with prime-block data. The framework therefore separates continuum rigidity, finite-grid geometry, endpoint conditioning, and local arithmetic correlations within a single fixed-count description. The deposit contains the theoretical paper, LaTeX source, bibliography, and associated supporting files.