Sparse prime surgery in completely multiplicative sequences: Normality, rare-event realization and optimal repair

We study how changing prime signs affects fixed-word frequencies, rare-event laws and extremes of completely multiplicative sequences. The cost is d_σ(f,g)=∑p:\,f(p)≠ g(p) p-σ. A known theorem of Frantzikinakis–Lemańczyk–de la Rue preserves normality at finite d₁; we give its elementary specialization. Using explicit arithmetic inputs from *Long runs and rare patterns of a random completely multiplicative function*(doi: 10.5281/zenodo.22872154), we then establish three families of results. For each fixed 0<σ≤ 1 and almost every base, reversible surgery realizes every stationary finite-intensity marked point-process law along selected scales, with signs, exact excess lengths and converging actual intensity, at arbitrarily small d_σ cost and with a prescribed prefix unchanged. Almost surely over all integer scales, the minimum number of prime changes needed for a run of length clog₂ N is asymptotic to cαclog₂ N for $1<c<3/2$, where αc∈(0,1/2) satisfies H₂(αc)=1-1/c and H₂(u)=-ulog₂ u-(1-u)log₂(1-u). At each scale, with probability tending to one, symbolic and private large-prime repair maxima coincide on the same random base for kN=o(log N); unrestricted prime repair agrees when kN=o(loglog N). This comparison transfers the classical lattice laws of runs with errors to adaptive prime repair. Elementary programming from arbitrary bases and an autonomous finite-range-dependent process construction complement these results.