Detecting anti-holomorphic dynamics via symbolic regression with the eml★ operator

Version 8 (May 20, 2026): - Clarified pair counts in §6 (negative control): 293,880 source-lens pairs within 10 arcmin matching, of which 268,722 fall in the analysis range r ∈ [0.5, 10] arcmin used for stacking. --- We introduce eml★(x, y) = exp(conj(x)) − ln(conj(y)), the anti-holomorphic extension of the EML operator of Odrzywołek (2026). We prove: conj(z) = 1 − eml★(0, eml(z, 1)) (Theorem 1), and that {eml, eml★, 1} is dense in C(K, C) by Stone–Weierstrass (Corollary 2). A Re-based decomposition (Theorem 2) shows that {eml, Re, 1} has identical expressive power. Combined with symbolic regression (PySR), eml★ automatically detects anti-holomorphic dynamics: - Fractal maps: Mandelbrot vs Tricorn distinguished at MSE ~10⁻³² - Quantum evolution: 7/7 systems classified correctly - KiDS-1000: first application to real astrophysical data (5,000 galaxies) - Negative control: weak gravitational shear profile around 268 KiDS-1000 lens candidates (268,722 source-lens pairs in analysis range) shows eml★ does not appear at low complexity when the underlying physics is holomorphic (standard general relativity), confirming specificity. Paper: "Detecting anti-holomorphic dynamics via symbolic regression with the eml★ operator" GitHub: https://github.com/antparis/eml_star Software: https://github.com/antparis/oxieml-star