ALMA CO(2-1) Gas Dynamics in NGC 315: A Multi-Method Benchmark for Supermassive Black Hole Mass Measurement

We present ALMA Cycle 7 observations of the circumnuclear disk in NGC 315 at an angular resolution of 0 230 times0 175, improving on past measurements and resolving the sphere of influence (SOI) of the supermassive black hole (SMBH), whose mass has previously been estimated of M BH= (2.08+0.33-0.15) times 10 9 M The high spatial resolution and sensitivity enable robust full-cube forward modeling of the molecular gas kinematics and a direct comparison of multiple independent gas-based dynamical modeling techniques. We apply standard Bayesian codes using both MCMC and nested sampling approaches, as well as a frequentist code to the same dataset, exploring systematic uncertainties associated with the stellar mass distribution, gas surface-brightness parameterization, and disk geometry. All methods yield consistent black hole masses, indicating that the inferred M BH is not strongly method-dependent. Combining the ensemble of independent molecular-gas-based models, we derive an ensemble median black hole mass of M BH/10 9, M = 2.02+0.04-0.05 (stat)+0.05-0.04 (sys), where the comparable contributions to the full error budget arise from modeling systematics rather than formal fitting uncertainties. Our M BH is consistent with the empirical M BH -- σ and M BH -- L bulge scaling relations, and lies 32% below an independent stellar-dynamical measurement, a discrepancy we discuss in the context of systematic differences between gas- and stellar-based methods. NGC 315 serves as a benchmark for quantifying molecular gas-dynamical M BH systematic uncertainties and for future cross-comparisons of gaseous and stellar dynamical approaches.