Calibrated Residual-Sector Benchmarks for BSM Searches in the H4/Z60 Discrete Framework: Quantized mass levels, an unoccupied hopf_q q=0 gap, and collider-oriented signatures

Paper 028 presents a set of calibrated benchmarks for the 72-vertex residual sector within the UNIVERSE131/H4-Z60 discrete framework. While Paper 027 established the atomic-periodic core, this manuscript packages new quantitative modules from the soryushi_to_gensov2.py audit log into a collider-oriented benchmark set. Within the adopted 600-cell coordinate construction, the residual sector is partitioned by the discrete quantity hopf_q into six occupied levels: -0.75, -0.50, -0.25, +0.25, +0.50, and +0.75. Notably, no residual vertices appear at hopf_q = 0, defining an unoccupied internal gap in the spectrum. By anchoring these levels to the Z-boson mass (M_Z) through the adopted benchmark formula m = M_Z φ^{(4 + hopf_q + dₘᵢₙ)}, the model yields six discrete mass scales: 586.6, 661.5, 746.1, 949.1, 1070.4, and 1207.2 GeV, with an intermediate gap near 841.5 GeV. The paper further provides deterministic assignments for spin, charge, and color, along with nearest-neighbor decay routes. These are mapped to broad LHC-style search classes, specifically "multi-jet" for color-triplet benchmarks and "Eₘᵢₛₛ + jets" for neutral-singlet dark-matter-like benchmarks. The contribution of Paper 028 is a set of blind, reproducible targets designed for future collider analysis and falsification.