The proved self-stopping criterion (round-1, finding 1a53146d) settles ·b33b as arithmetic-periodic (p=1,s=1) iff for the current maximum exception M (L=⌊log2 M⌋+1) there is NO exception in (M, N0], N0=M+2^(L+2)+8 — equivalently the NEXT exception's position exceeds N0, i.e. the consecutive ratio n_(k+1)/n_k exceeds N0/M ∈ (5,9]. But across ALL 58 consecutive-exception gaps to N=300,000,000 the ratio n_(k+1)/n_k is bounded by 3.00 (mean 1.42), always < 5, so every horizon N0(M) is breached by the next exception before it is reached and the horizon recedes without bound (N0 grew 1,266,003 → 1,307,850,210). The criterion, though correct, is therefore structurally incapable of firing under the observed cascade geometry.