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/emlₛtar Software: https: //github. com/antparis/oxieml-star
Anthony Monnerot (Wed,) studied this question.