  Aims.We conduct a high-precision differential abundance analysis of the
remarkable binary system HD 240429/30 (Krios and Kronos, respectively), whose
difference in metallicity is one of the highest detected in systems with
similar components to date (approximately 0.20 dex). A condensation temperature
TC trend study was performed to search for possible chemical signatures of
planet formation. In addition, other potential scenarios have been proposed to
explain this disparity. Methods. Fundamental atmospheric parameters (Te f f ,
log g, [Fe/H], vturb) were calculated using the latest version of the FUNDPAR
code employing high resolution MAROON-X spectra. We applied a full line-by-line
differential technique to measure the abundances of 26 elements in both stars
with equivalent widths and spectral synthesis taking advantage of the non-solar
scaled opacities. Results.We found a difference in metallicity of approximately
0.230 dex, being Kronos more metal rich than Krios. The analysis encompassed
the examination of the diffusion effect and primordial chemical differences,
concluding that the observed chemical discrepancies in the binary system cannot
be solely attributed to any of these processes. The results also shown a
noticeable excess of Li by approximately 0.56 dex in Kronos, and an enhancement
of refractories with respect to Krios. A photometric study with TESS data was
carried out, without finding any signal of possible transiting planets around
the stars. Several potential planet formation scenarios were also explored to
account for the observed excess in both metallicity and lithium in Kronos.
Planetary engulfment is a plausible explanation, considering the ingestion of
an exceptionally large mass, approximately approximately 27.8M_Earth, but no
scenario is definitively ruled out.
