A visual guide to hidden reasoning horizons, circuit depth, and why visible chain-of-thought may be a checkpoint rather than the whole computation.
The longest private dependency chain before the model hits an interpretable node like emitted reasoning text.
One pass can do massive parallel math and still remain structurally weak at long hidden serial reasoning.
Visible reasoning helps only when real computation must spill outward and the trace stays faithful enough to monitor.
Compact jump points for the theory backbone, the monitorability papers, and the latent-reasoning challenge set around this episode.