The induced-C4 count and the C4-free characteristic are not equivalent. A six-cycle is C4-free with induced count zero; K2,3 plus a leaf has three induced four-cycles; and K4 plus a leaf contains chorded four-cycles but no induced four-cycle. Lean compilation and the corrected conjecture are not assessed by these finite checks.
RESULT_JSON: {"semantic_status":"NOT_EQUIVALENT","witnesses":[{"role":"C4_FREE_ZERO_COUNT","vertex_count":6,"edges":[[0,1],[0,5],[1,2],[2,3],[3,4],[4,5]],"induced_c4_count":0,"c4_free_characteristic":1},{"role":"MULTIPLE_INDUCED_C4","vertex_count":6,"edges":[[0,2],[0,3],[0,4],[0,5],[1,2],[1,3],[1,4]],"induced_c4_count":3,"c4_free_characteristic":0},{"role":"CHORDED_C4_ZERO_INDUCED","vertex_count":5,"edges":[[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[2,3]],"induced_c4_count":0,"c4_free_characteristic":0}]}
