HodgeCY: Computational Hodge Atom Profiles and Smoothing Bridges for Double Octic Calabi–Yau Threefolds

We develop HodgeCY, a computational framework for studying Hodge atom profiles of singular and nodal Calabi–Yau threefolds. The first testbed is the Cynk–Meyer dataset of double octic Calabi–Yau threefolds arising from eight-plane arrangements. These examples exhibit useful collisions among standard invariants: arrangements 83 and 84 have the same singularity-count profile but different Hodge numbers, while 84 and 84a have the same singularity-count profile and Hodge numbers but different modular forms. We construct a smoothing bridge from arrangement geometry to finite-node conifold geometry: for A = P₁ · · · P₈, we study branch octics F_ε = A + εQ². For the explicit quartic Q₀ = x⁴ + 2y⁴ + 3z⁴ + 5t⁴ + xyzt and ε = 1, the HodgeCY repository verifies the local genericity conditions over Q and records a characteristic-zero degree-112 certificate for the saturated Jacobian scheme associated with arrangements 84 and 84a. The current smoothing status is therefore degree112_certified, while reducedness, Hessian-rank, and defect verification remain unpromoted validation gates. We prove that first-order plane-node incidence is universal in this setting, hence too coarse to distinguish 84 from 84a. The main completed computation is instead a concurrency separation: the intersection-lattice concurrency profiles of 84 and 84a are non-isomorphic, detected by double-line point-type multiplicities and p4-collinearity graphs. This is an arrangement-level separation, not yet a proof of distinct smoothed Hodge atom spectra. The remaining ordinary-node, defect, and operator computations are recorded as explicit validation gates in the public HodgeCY repository.