Published May 20, 2026 | Version Version 8
Publication Open

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

Authors/Creators

  • 1. autodidact
  • 2. champigny-sur-marne
  • 3. France

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.
 
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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

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Additional details

Related works

Is supplemented by
Software: 10.5281/zenodo.20152989 (DOI)

Dates

Updated
2026-05-20