Root-Cross Obstructions in the Kolakoski Sequence

The recurrence and uniform recurrence of the classical Kolakoski sequence remain open. We develop a narrowly scoped obstruction framework that combines the finite-primitive descent of bispecial smooth words with exact parity-history dynamics. A hypothetical failure of recurrence is encoded by a coloured root-cross packet and propagated backward by a sound relative obstruction operator on finite history automata. We prove a depth-independent local coalescence lemma: after four lifts distribute the six legal trigram obstructions across a sixteen-address fibre, two further lifts create at least two fully forbidden states. The proof is a symbolic endpoint calculation and does not rely on finite-depth extrapolation. We also report reproducible exhaustive computations for the root packets, isolate a monotone reduction from coloured fields to saturated full fronts Q, and formulate the remaining global metric step as a graded one-counter min-plus certificate on the exact sixty-four-state skew product. Explicit counterexamples rule out three tempting strengthenings: contraction for arbitrary full fronts, extraction of a radius-extremal matching pair from an entire front, and a fixed-radius one-step Bellman potential. The paper does not prove recurrence. Its purpose is to establish the unconditional local mechanism, certify the finite evidence, delimit invalid proof routes, and state precisely the all-depth certificate still required.