This paper proves that the gauge‑invariant two‑channel initial‑point pair of the Mixmaster memory has a fully restored and constant direction, while its lifted turn word and log‑modulus encode the complete arithmetic of the BKL cascade. Parity holds through all class‑A walls, the pair squares the single‑channel memory, and the triple of turn words reconstructs the era structure and continued‑fraction digits of the initial Kasner parameter.
Hiroyuki Shioiri (Fri,) studied this question.
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