For R(0)=0, a card emitted at s remains at0 until the ordinary swap at s+1
ejects it to p_(s+1). Before its next output t, it cannot be selected again
(that would emit it), and R cannot move a nonzero position to0. Its position
therefore evolves solely by R between the ejection and next selection:
    p_t = R^(t-s-1)(p_(s+1)).

Let mu_c be card c's position immediately AFTER output index0. If c first
appears at t>0, it cannot have participated in an earlier top swap: it was
neither top nor selected. Thus p_t=R^t(mu_c). The exponent is t, not t+1;
the reference snapshot follows index0. This agrees with literal controls.

The five raw return identities and two assumed action equalities connect
all eight action indices to p_2. Reconstructing the weighted graph gives
initial phases mu_5=-2, mu_21=-32, mu_49=28 relative to p_2. These are three
distinct cards in one deck at one reference time, so their phases must be
distinct modulo the length L of their common R cycle. The phase differences
are30,30,60. All collisions are therefore equivalent to L dividing60.
The cycle is non-top and has at most82 positions; the smallest admissible
length is7. Enumerating the six distinct integer action phases modulo each
admissible L shows at least four selected slots on that cycle.

No initial-deck equality across messages is needed (only W1 is used).
No assumption that repeated ciphertext labels represent repeated plaintext
letters is made. The two same-action links are explicit conditional inputs.
The restriction leaves many bases possible and does not establish a key.
