Wraps walkLine in the cache + innerJoin pattern used by arrange:

• The chord-selection pattern is resolved into a PERFORMED bar sequence at eval time (resolvePerformedSeq); the walk runs over the bars in performed order, so warp/rep reorderings and repeats are walked as the audience hears them. Non-periodic selections fall back to stored order with a printed notice.
• Progressions seen on kProg are pre-materialised once into walking- bass lines keyed by (triads, chroma sources, performed sequence), forced eagerly so synthesis stays off the audio thread. The forcing horizon is 'Arc 0 1000' — a key first seen beyond cycle 1000 is synthesised on demand (with a printed notice).
• innerJoin switches lines reactively when the form changes progression.
• The input pattern list is dispatched by kinPick: [0,1] is partitioned into N equal windows (N = length of the list) and only the pattern whose window contains the current kinetics signal plays. Output is scaled by kDynamic and the user-supplied dynamics scalar (applied once here — launchers must not multiply by the same dynamic again).

Each integer in a pattern selects a 1-indexed beat position (1..4). Values outside [1..4] shift by full octaves, matching the div/mod convention of arrange: 5 → beat 1 +12, 0 → beat 4 −12, -1 → beat 3 −12.

In a launcher, the walking line is an ordinary block alongside the orchestral ones:

walk f k d = p "walk" $ f
  $ lineHarmony k ["1 2 3 4"] |* vel d

Because each integer picks a beat position, the pattern controls which beats of the generated line sound — "1 ~ 3 ~" plays a half-time version of the same line rather than a different line.