The Gender Potential Gradient Model (GPGM): A Common Scale for Gendered Opportunity

Gender research has accumulated proportional evidence—women's share of jobs, of managers—but proportions are not commensurable and cannot say how strongly a gender's chance of attaining authority is amplified or suppressed. This paper reconstructs a Chinese theoretical vocabulary, the sexual potential theory of gendered opportunity structures, into an estimable field–potential–gradient framework, the Gender Potential Gradient Model (GPGM). Proportions are read as probabilities and then as log-odds, yielding a dimensionless, additive quantity with a sampling distribution: Eg and ΔE. On this scale ceiling and escalator are two signs of one quantity, though the escalator is not estimable here. Using 2010 and 2020 census long-form tables for 31 provinces and 13 age groups, I compute the gender log-odds gap in access to "unit heads" and test seven propositions. Nationally, ΔE falls from 0.89 to 0.68 while women's share of unit heads rises only from 25.1% to 26.2%; ΔE rises with the age ladder and with position. Calibrating a Clifton-style model, I find that bias and homophily are not point-identified: the 5% RMSE band for the baseline share is b ∈ [0.50, 0.58], a wide specification band widens it to [0.36, 0.66], and a placebo reproduces R2 ≈ 0.97. Under linear closure the map contains a saddle-node fold, and the interval for homophily straddles it, so the data are consistent with near parity, bistability, or a low-representation trap. Parity requires both a balanced applicant pool and unbiased promotion. The contribution is a measurement layer with stated limits, not a new theory. Preprint. This is the author's preprint of the manuscript submitted to Social Indicators Research (manuscript ID SOCI-S-26-04769, submitted 18 October 2026); it has not been peer reviewed. The replication package is archived at doi:10.5281/zenodo.23445538. The companion theory paper is Folds in the gender potential gradient: A minimal theory of authority representation, doi:10.5281/zenodo.23445570.