Variance Suppression by a Numerical Wave Cap in Ultralight-Dark-Matter Strong-Lensing Simulations: Exact-Commit Audit of a JWST Survey-IV-Derived Forward Model, with Realization and Selection Diagnostics

Abstract

Strong-lensing inference with ultralight dark matter (ULDM) can depend on stochastic wave-field realizations and numerical controls used to make those realizations computationally tractable. This work performs an exact-commit audit of the public pyHalo/samana/lenstronomy software ecosystem used in a JWST Survey-IV-derived strong-lensing forward-model configuration. The primary result concerns the pyHalo ULDM parameter n_cut, which limits the number of rendered wave fluctuations. Earlier work introduced this prescription and reported convergence of particle-mass inference for n_cut = 50,000. Here a distinct field-level question is tested directly: whether an active cap preserves the stochastic fluctuation-field variance. A 100-seed audit at J1042 compares n_cut = 50, 100, 300, 1000, and 50,000. When the cap is active, measured local convergence/shear variance is strongly suppressed. The median variance ratios relative to the native calculation are approximately 0.00382, 0.01580, and 0.13015 for n_cut = 50, 100, and 300, respectively, while n_cut = 1000 and 50,000 reproduce the audited native field moments at the tested mass point. The measured active-cap scaling is consistent with the implementation-level expectation R_var ≈ (n_cut/n)^2, with a fitted log-log exponent of approximately 1.97. For the audited J1042 geometry and source aperture, the default n_cut = 50,000 reaches its expected-count crossing near log10(m_psi/eV) = -20.6058. Approximately 72.4% of the locked uniform-log ULDM mass prior lies above this lens-specific threshold. Secondary diagnostics examine realization dependence and model-dependent acceptance in matched WDM-ULDM forward runs. Fifteen completed native/cap-safe pairs show that single-realization residual ordering is not realization-stable, while a 30-seed J1042 acceptance audit produces equal marginal WDM and ULDM acceptance rates but different accepted realization sets. The conclusions are deliberately implementation-specific. The work does not claim that the published JWST Survey-IV WDM constraints are invalid, nor that WDM and ULDM are population-level non-identifiable. It establishes that, in the audited ULDM implementation, an active numerical wave cap changes the stochastic field law unless convergence to the uncapped calculation is demonstrated.