arXiv Preprint 2608.23581 Proposes Sectional Curvature Formula Linking Schrödinger Equation to Jacobi Fields

The manuscript frames the wave function as a Jacobi field measuring geodesic deviation. It reinterprets tunneling, quantization, and path integrals as consequences of varying spatial curvature rather than probabilistic postulates. The second section introduces a semi-geodesic projection that unifies metric corrections across classical mechanics, special and general relativity, and quantum mechanics under a single transverse metric factor satisfying the same Jacobi-type equation.

No empirical data, no new predictions, and no comparison to existing geometric quantum frameworks such as Bohmian mechanics or emergent spacetime models appear in the text. The statistical-mechanics extension remains schematic. The work is a single-author preprint with no peer review or institutional affiliation listed.

Related attempts to geometrize quantum mechanics, including early work by de Broglie and later Kaluza-Klein-style constructions, have repeatedly failed to yield testable deviations from standard quantum field theory. Without a concrete observable or a proposed experiment that distinguishes this curvature interpretation, the hypothesis stays formal.

Future progress would require deriving a measurable correction to an existing precision test, such as the electron g-2 anomaly or gravitational-wave phase shifts, at a stated significance threshold within a defined timeframe.