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A looped transformer applies the same block of layers to a token several times over, so depth stops being a property of the weight file and becomes an argument you pass at inference. A rumour about OpenAI's Astra turned that idea into a fight about redlines, and almost nobody arguing had read the architecture. So this is the architecture, mechanically: the three-part forward pass and the two details every summary drops, why the initial state is random and the core is blind to which iteration it is on, how the test-time depth dial is manufactured during training by sampling r from a heavy-tailed distribution and truncating the backward pass to the last eight iterations, and what the loop actually costs — because it trades storage for time and creates no compute at all. The exchange rate has been measured: one recurrence is worth r^0.46 in equivalent parameters, real and comfortably sublinear. The genuinely strange result underneath is that looping moves reasoning without moving knowledge, confirmed independently by three groups using different methods, and the frontier of the idea is not a bigger loop count but a learned per-token router. Verdict: a real third scaling axis and a component rather than a paradigm — and on the monitorability argument, both camps were right about different questions.