Androgen Receptor as a Continuous Epigenetic Depth Axis in Triple-Negative Breast Cancer: A Geometry-Derived Reframing of a Binary Classifier (r=−0.378, p=6.23×10⁻¹⁴⁷, n=4,312 cells, GSE176078)

Androgen receptor (AR) expression in triple-negative breast cancer (TNBC) is currently classified in the literature as a binary marker: AR-positive tumors are assigned to the Luminal Androgen Receptor (LAR) subtype; all others are AR-negative. This binary framework treats a continuous biological variable as categorical. We report a geometry-derived finding from Waddington attractor analysis of 19,542 single cancer cells (GSE176078) that reframes this interpretation. Within the 4,312 TNBC cells in this dataset, AR expression forms a strong, continuous, statistically significant inverse correlation with EZH2-driven epigenetic lock depth: r=−0.378, p=6.23×10⁻¹⁴⁷, n=4,312. AR is not acting as a subtype identity marker within TNBC. It is a continuous quantitative readout of how deeply the tumor cell population has descended into the EZH2/PRC2 attractor state. Lower AR = deeper lock; higher AR = shallower lock with residual luminal identity program activity. The LAR subtype corresponds to the shallow end of this continuous distribution — not a categorically distinct entity. Three clinical consequences follow: (1) AR level continuously predicts EZH2 inhibitor benefit magnitude — lower AR predicts greater tazemetostat benefit, in inverse proportion; (2) this explains G-1/enobosarm failure in deeply de-differentiated TNBC — AR is absent as a consequence of lock depth, not as an independent targetable feature; (3) AR functions as a continuous component of the TNBC Depth Score (DOI: 10.5281/zenodo.18891523) rather than as a binary classifier. An exact structural parallel exists with CS-LIT-5 (FOXA1 as a continuous axis across subtypes vs binary identity marker across subtypes): both findings arise from examining binary classifiers within a continuous Waddington landscape. The specific framing of AR as a continuous epigenetic depth axis within TNBC, and the correlation statistics reported here, have no direct published equivalent as of 2026-03-06. NOVEL verdict. Part of OrganismCore BRCA Cross-Subtype Analysis (BRCA-S8h, 2026-03-05). All predictions locked before literature review.