The foundation progression (T layer) is a plain gen walk, byte-identical to it: same chain builder, same R constraints, same entropy dial. Two partner triad chains (S/M layers) are then walked over the finished foundation, one bar at a time. Each partner draws from a fresh transition list fetched from ITS OWN previous state — every partner bar is a corpus-valid continuation of its own layer history — filtered to the polytonal overlap rules against that bar's foundation triad:

• each partner shares exactly 2 pitch classes with the foundation bar;
• the three triads union to exactly 5 pitch classes.

Those two rules admit exactly two geometries per bar, and the traversal chooses freely between them: COMMON-DYAD (all three triads share one dyad; every layer pair sounds 4 tones) and BASE-ANCHORED (the partners share different dyads of the foundation; T+S and T+M sound 4 tones, S+M sounds the full pentad). The hub-tone shape (three different dyads through one tone) unions to 4 and is excluded.

Partners honour the harmonic-space constraints only — key, allowed roots, overtones — through the same R predicate as the walk (matchesContextWithTarget with no bass target). Root-motion direction specs, drift, pedal and inversion spacing bind the foundation alone: the foundation owns the bass whenever it is present, and the partner layers stay free to diverge.

Selection: jointly valid (S, M) pairs are ranked by summed own-list rank and drawn with ONE entropy-scaled gamma draw over the pair pool (the two-stage per-layer alternative saturates the entropy dial at the ~8- candidate second pool; the joint pool sits at ~100-324 where the dial is monotone — measured in archive/analysis/poly_seq.md). Supply relaxes down tiers when a list runs dry: one side from the space-constrained pure enumeration over all 220 absolute 3-PC sets, then both, then the unconstrained enumeration — the last is total, so partner selection can never fail (the study measured the list tier alone at 100% over 2,100 live steps; archive/analysis/poly_chain.md).

S/M identity is assigned once, after generation: the chain with the lower whole-layer dissonance total becomes S. Per-bar assignment would swap chain membership at ~45% of bar boundaries and destroy the very layer identity the chains provide.