Ruzsa’s genus-one problem

Found by successive randomized valid-set walks starting from witness #121 at modulus 1001. Residue 222 was the least-conflicting direct 20th element (four ordered nontrivial solutions). The first walk repaired that near-extension and reached size 20 after 445 moves; a second walk reached this 21-element set after 3,108 more moves. Direct enumeration gives exactly 21 solutions to a+3b=2c+2d, all diagonal. A further 5,000,000-step walk did not find a 22nd element.