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Each theater is a closed tube with 12 beads. Bead dials show which atoms are lit. Tube 0 carries the bounded-discrepancy trace, N N T T N F F then F,t,f held. Tube 1 receives A = {T,F,t,f}.
Twelve strands run through the Θ-link tube and twist so that strand k arrives at position 5k mod 12. The tube narrows at its waist; the rings are never merged into one.
Each packet in flight carries the state its source bead holds at the current cut, from bead k out through strand k to bead 5k mod 12 on tube 1. Shift the cut: the strands and reconnection (C_rec = 1, closed walk = 0) stay put, but the packets and the state read at bead 0 move: {{nodeZero}}.