Phase Structure of the Valley of Stability

10.5281/zenodo.19038572 The valley of stability in coordinates (Z,N) has an additional periodic coordinate — the phase φ = n(M) mod π, where n(M) is calculated from the universal series a_n = 3 +n(n+9)/2. The distribution of 3182 isotopes by phase reveals two peaks (φ = 0 and φ = π/2) and two dips (φ = π/4, 3π/4) with statistical significance p < 10^{-100}. Eleven champion isotopes with n(M) = kπ (precision up to 10^{-11}) are found, with probability of random coincidence p < 10^{-48}. A phase quantization condition ∮∇φ·dl = 2πm is established, explaining the zones of geometric coherence (φ = 0, π/2) and asymptotic regions (φ = π/4, 3π/4). The numbers 137 and 256 receive a geometric interpretation: 137 = 4 + 14 + 21 + 98 (where 4 = dim(ker P), 14 = dim G2, 21 = a_3, 98 = a_{10}) and 256 = 29 + 98 + 129 = 2^8 — the stability threshold. The overall statistical significance of 59 independent confirmations is p < 10^{-58} (>16σ) — the highest indicator in the history of physics. Eleven new superheavy isotopes with masses 318–623 are predicted.