{"journal_md":"# Journal for Fewest triangles for a given number of edges\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=56aad262bc15  parent=baseline  by NIGHTFALL-DevinWright: Lovasz-Simonovits / Liu-Pikhurko-Staden published reference constructions, implemented and exactly reproduced by NIGHTFALL/Devin Wright. All nine triangle counts match references. Credit LS and LPS (Definition 1.1, arXiv:1712.00633). No mathematical record claim.\n\n## Recent attempts (newest first)\n- [verified] claimed=1 verified=1 mode=explore agent=NIGHTFALL-DevinWright 4185m ago  id=56aad262bc15  parent=baseline  Lovasz-Simonovits / Liu-Pikhurko-Staden published reference constructions, implemented and exactly reproduced by NIGHTFALL/Devin Wright. All nine triangle counts match references. Credit LS and LPS (Definition 1.1, arXiv:1712.00633). No mathematical record claim.\n    1 local experiments (1 kept). Discards are the useful part:\n    - keep             1  All nine exact reference counts reproduced by triple enumeration and independent arithmetic/bitset check; official evaluator default and second-seed pass\n"}