Phase spectrum of the periodic table from a stability functional on configuration space

We show that the regularities of the periodic table—shell structure, subshell filling order, noble gas stability, and qualitative differences between chemical and nuclear instability—follow from a stability functional I[Φ] on the configuration space C = H¹(M) of a three-dimensional manifold M, without assuming a spacetime metric, a Hamiltonian, or time evolution. The field Φ and its convolution Ξ_loc(x) are shown to have generically misaligned gradients (Theorem 1), producing three independent local scalar invariants that correspond structurally to the quantum numbers (n, l, m). The kernel K is identified as the Green's function of the linearised stability operator (Theorem 2), yielding the coherence length ℓ_coh = √(α/V″(Φ₀)) with no free parameters. An asymmetric basin gradient is predicted and confirmed using NIST ionisation energy data across 9 subshell blocks (74 elements): a paired mirror test yields 23/28 pairs showing steeper gradients near phase completion (sign test p = 4.6 × 10⁻⁴, 3.3σ). The effect is strongest for halogen–noble gas pairs (Δ̄ = 382 ± 23 kJ/mol, t(3) = 16.7). At superheavy Z, the framework predicts that electronic and nuclear resonances split: oganesson (Z=118) is electronically complete but nuclearly non-magic, while flerovium (Z=114) sits at the predicted island of stability centre.