Folds in the gender potential gradient: A minimal theory of authority representation

This theory paper studies a one-dimensional map of authority representation with two parameters: the baseline promotion share b and the strength of composition dependence λ. Authority holders are replaced from a feeder pool whose gender composition is fixed. The derivative of the map is shown to be single-peaked, so the map has at most three fixed points; a saddle-node threshold λc(b,v) exists, below which the equilibrium is unique and above which a low-representation and a high-representation equilibrium coexist. Cross-sectional shares identify only one linear combination of b and λ; with measurement error the consistent set is a strip whose intersection with the fold threshold need not be empty, so the regime is not identified by a single cross-section. Exact parity is a knife-edge, stable at b = v = 1/2 only if λ < 4. Calibrated to Chinese census long-form tables for 2010 and 2020, b ≈ 0.55 and λ ≈ 6.4, with the interval for λ straddling λc ≈ 5.87. The fold threshold is a property of field intensity rather than a portable critical mass, and the policy reading is that parity requires both a balanced feeder pool and unbiased promotion. Preprint, not peer reviewed. Companion theory paper to the GPGM measurement manuscript by the same author. Preprint. Not peer reviewed. Sole author. The measurement companion paper is The Gender Potential Gradient Model (GPGM): A Common Scale for Gendered Opportunity, doi:10.5281/zenodo.23445637. The replication package and the code archive that reproduce every number in this paper are archived at doi:10.5281/zenodo.23445538. Journal submission credit line (AIP Publishing policy). The following article has been submitted to Chaos: An Interdisciplinary Journal of Nonlinear Science. After it is published, it will be found at the article DOI, which will be added here once assigned.