Atomic Shell Structure from Informational Field Theory: The Periodic Table as Phase Geometry

This paper shows that the regularities of the periodic table — shell structure, noble gas stability, chemical reactivity, nuclear instability, and the predicted island of stability — arise as phase geometry in the informational density field and its derived coherence field within Informational Field Theory (IFT).

Two rigorous theorems anchor the analysis. First, gradient misalignment between a field and its finite-range spatial convolution is proven generic via eigenfunction expansion on compact manifolds. Second, the coherence kernel is identified as the Green's function of the linearised stability operator, reducing constitutive inputs and deriving the coherence length from first principles.

A toy model on three-dimensional Euclidean space with harmonic potential reproduces the state counting 2(2l+1) from dimensional geometry and coupling polarity, and yields the first three nuclear magic numbers (2, 8, 20) exactly with no free parameters. The electronic-nuclear resonance splitting at superheavy atomic number is explained by scale-dependent effective potential.

Phase tension manifests in two qualitatively distinct failure modes: focused (single near-complete subshell driving chemical reactivity, e.g. fluorine) and diffuse (multiple degenerate open subshells driving nuclear instability, e.g. uranium). The island of stability is identified as the next phase resonance point; its non-existence would falsify the framework.

Ten falsifiable predictions are stated. The paper operates at Layer 2 of the IFT program, with an explicit boundary table distinguishing derived results from open problems requiring future Layer 3 development.

Part of the Informational Field Theory program. All primitives trace to the IFT spine document.