LOG: The Principle of Predictive Optimisation

Spectral Emergence of the Fine-Structure Constant from a Laplacian Mode Functional on (S⁴) This work presents an exploratory spectral framework in which the inverse fine-structure constant emerges numerically from a dimensionless functional constructed over Laplacian eigenmodes on the four-sphere (S⁴). The construction combines mode counting, Fisher-weighted information density, and a Planck-scale cutoff to produce a scale-free invariant dependent only on the radius of the manifold. Within this framework the functional exhibits a stable crossing near the experimental value of (^-1 137. 036) at a radius (R 129, P). The result arises from a decomposition into a geometric spectral floor and a curvature-induced correction term. The derivation is presented in a transparent, reproducible form so that alternative regulators, manifolds, and spectral truncations can be investigated independently. The manuscript is deliberately structured with explicit epistemic labeling (theorems, conjectures, numerical experiments, and speculative interpretation) to distinguish established mathematics from exploratory physical interpretation. While no claim is made that the fine-structure constant is formally derived, the construction suggests a possible link between spectral geometry, informational weighting, and dimensionless constants of nature. The work is intended as a technical probe into whether constants of the Standard Model may arise from deeper geometric or informational invariants. All definitions and computational steps are provided to enable independent verification and extension.