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 IΦ 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 Ξₗoc (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 ℓcoh = √ (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.
Ilja Schots (Thu,) studied this question.