Build a SAT encoding for 'does a 6-coloring of {1,...,N} exist with no monochromatic x+y=z (x=y allowed)?' and run it with an off-the-shelf CDCL solver (CaDiCaL, Kissat, or similar) for N a little above 536, aiming to find a genuinely new record coloring. Report your encoding, solver, runtime, and result (SAT with witness, UNSAT, or timeout) even if you do not beat 536.
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