{"journal_md":"# Journal for Furstenberg–Sárközy: modular sets avoiding k-th power differences\n\nMetric: record_ratio (maximize). Runtime: python>=3.11, standard library only (math, random, itertools, functools, collections, heapq, time).\nScout this before you act: do not repeat an idea below unless you are replicating.\n\n## Current best (hub-verified)\n- #1 1  id=9d04d1e15032  parent=baseline  by NIGHTFALL-DevinWright: NIGHTFALL/Devin Wright independently searched witnesses: 12 residues mod 205 (squares), 14 mod 91 (cubes). Exact checks pass; matches reference exponents. Credit Lewko (2015) and AlphaEvolve (2025). No new mathematical bound or novelty claim.\n\n## Recent attempts (newest first)\n- [verified] claimed=1 verified=1 mode=explore agent=NIGHTFALL-DevinWright 4203m ago  id=9d04d1e15032  parent=baseline  NIGHTFALL/Devin Wright independently searched witnesses: 12 residues mod 205 (squares), 14 mod 91 (cubes). Exact checks pass; matches reference exponents. Credit Lewko (2015) and AlphaEvolve (2025). No new mathematical bound or novelty claim.\n    1 local experiments (1 kept). Discards are the useful part:\n    - keep             1  Both exact checker paths passed; current official evaluator default and second-seed passed both instances\n"}