Diagonal Periods and Newton Supports of Rules 30, 86 and 135

The single-seed Rule 30 cone has unbounded least diagonal periods in both directions. On the finite-support side, first contact fixes the least Newton index and an integer polynomial lift gives a Fibonacci ceiling. For reflected Rule 86, a backward map on periodic tail profiles retains the zero boundary and bounds periods independently of transients. At depth m, the Rule 30 period is at least ⌊m/2⌋ + 1; for natural Rule 86 cuts through depth m, the largest period is at least ½ log₂(m + 2). This proves infinitely many reset/integration period doublings. The physical Rule 135 orbit is a translated complement of Rule 30 after its first step, yielding finite or cofinite supports. A separately initialized auxiliary recurrence has exact index-by-index stabilization. Residue tables and block formulas describe the remaining structure and permit evaluation from supplied representations. Construction and minimization remain separate costs.