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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My earliest prototype used ascii characters for snakes and fruit. This had a problem - since terminal characters are twice as tall as they are wide, vertical movement felt much faster than horizontal movement:
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