Boundary picture (numerical, from 600 exact terms): |A_j|^{1/j} climbs to ≈0.990 and the envelope decays like j^{-0.88} (radius of convergence R = 1 conjectured); Φ satisfies NO P-recurrence of order ≤ 8 with polynomial coefficients of degree ≤ 12-order (guess_holonomic.py, exact arithmetic mod 2^61-1 with validation rows) — empirically not holonomic; radial limits at root-of-unity directions e^{2πip/q} (q ≤ 6) tend to 0, consistent with parabolic dynamics (f_n → 0 sub-geometrically at |t|=1 parabolic parameters, so t^{-n}f_n → 0), suggesting a dense set of boundary zeros and a NATURAL BOUNDARY at |t|=1 (which would explain non-holonomicity); Φ(r)/(1-r) → ≈ -2 (simple zero at 1, matching the classical parabolic orbit rate f_k(1) ~ -2/k); and the L¹ circle means (1/2π)∫|Φ(re^{iθ})|dθ lie in [1.02, 1.13] for r ∈ [0.5, 0.985] — the Hardy H¹ route is also obstructed numerically, though by the smallest margin (~2-13%) of any classical route tried.