Realistic Uncertainties for Fundamental Properties of Asteroseismic Red Giants and the Interplay between Mixing Length, Metallicity, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <m

Abstract Asteroseismic modeling is a powerful way to derive stellar properties. However, the derived quantities are limited by built-in assumptions used in stellar models. This work presents a detailed characterization of stellar model uncertainties in asteroseismic red giants, focusing on the mixing-length parameter α MLT , the initial helium fraction Y init , the solar abundance scale, and the overshoot parameters. First, we estimate error floors due to model uncertainties to be ≈0.4% in mass, ≈0.2% in radius, and ≈17% in age, primarily due to the uncertain state of α MLT and Y init . The systematic uncertainties in age exceed typical statistical uncertainties, suggesting the importance of their evaluation in asteroseismic applications. Second, we demonstrate that the uncertainties from α MLT can be entirely mitigated by direct radius measurements or partially through <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:math> . Utilizing radii from Kepler eclipsing binaries, we determined the α MLT values and calibrated the α MLT –[M/H] relation. The correlation observed between the two variables is positive, consistent with previous studies using 1D stellar models, but in contrast with outcomes from 3D simulations. Third, we explore the implications of using asteroseismic modeling to test the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:math> scaling relation. We found that a perceived dependency of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:math> on [M/H] from individual frequency modeling can be largely removed by incorporating the calibrated α MLT –[M/H] relation. Variations in Y init can also affect <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:math> predictions. These findings suggest that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:math> conveys information not fully captured by individual frequencies, and that it should be carefully considered as an important observable for asteroseismic modeling.