Pair Observable Spectral Dataset (σ_pair, δ_pair) across Heis₃(ℤ/qℤ) — Cosmochrony Programme

This dataset provides numerical results for the spectral pair observable σ_{pair}(n) and the associated statistics $\delta_{pair}$, computed on finite Heisenberg groups Heis₃(ℤ/qℤ) for a range of prime moduli q.

The data are generated from a reproducible pipeline based on breadth-first shell decompositions and block-capacity measurements. For each conjugate pair (c, q−c), the dataset records depth-resolved estimates of $\sigma_{pair}(n)$, empirical distributions of $\sigma_{pair}$, and fitting-window parameters (n₀, n₁) used for asymptotic analysis.

The dataset originates from the pair-level spectral campaign introduced in O25 and has been extended to support subsequent developments, including refined window selection, scaling analyses in n₁(q), and representation-theoretic interpretations of $\sigma_{pair}$. It is intended to provide a stable empirical basis for testing structural properties such as monotonicity, inter-pair concentration, and finite-size effects.

All files are provided in NumPy .npz format and include metadata describing generation parameters (q, sampling size, BFS coverage, block structure) to ensure full reproducibility.