The model must be autoregressive. It receives a token sequence as input and predicts the next token. Output digits are generated one at a time, with each new token fed back as input for predicting the next. The carry propagation must emerge from this autoregressive process — not from explicit state variables passed between steps in Python.
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The “Knocking on Wood” Wikipedia page mentions Roud’s conclusion, and this claim of a 19th century origin has circulated online as the final say on the matter. If you go back to the original, though, Roud’s proposal actually ends on an ambivalent note: “Before this theory [of 19th century origins] can be finally accepted, however, an examination of the history of European forms of this custom would be advisable.”。搜狗输入法2026对此有专业解读