Published May 20, 2026
| Version Version 8
Publication
Open
Detecting anti-holomorphic dynamics via symbolic regression with the eml★ operator
Description
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
Files
eml_star_paper (4).pdf
Files
(235.2 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:d389410c01f7e98c1d0c49c1fcfe174c
|
235.2 kB | Preview Download |
Additional details
Related works
- Is supplemented by
- Software: 10.5281/zenodo.20152989 (DOI)
Dates
- Updated
-
2026-05-20