{"id":"hexagon/2610.00382","pdf":"https://hexagonmath.org/pdf/2610.00382v1","url":"https://hexagonmath.org/abs/2610.00382v1","tags":["math.PR","cs.IT","msc:68T05","msc:68T20","msc:94A17","msc:60J80","msc:05C15","automated discovery","entropy","recursive self-improvement"],"score":0,"title":"BLLM: Beyond the LLM with Deep Human-Mind-AI","domain":"cs.AI","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee","Ushashi Bhattacharya"],"reviews":0,"subject":"cs.AI","summary":"A system that improves itself keeps every change that passes a check, so a check that makes errors lets mistakes pile up. We compute the least checking that keeps such a system sound. It is an entropy of the costs of the changes, and an endless chain of improvements stays sound at finite cost exactly when that entropy is finite. A stack of checked layers costs more than its layers would cost alone. We also compute how many guesses a proposer needs before a right one appears: human authors come close to this least number, and language models need 1.5 to 4.3 times as many. Anaxia, an engine…","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}