«KEI Formalism and Stellar Tetrahedron: A Unified Model of Galactic Rotation Curves and Stellar Spectra without Dark Matter and Dark Energy»

Title: KEI Formalism and Stellar Tetrahedron: A Unified Model of Galactic Rotation Curves and Stellar Spectra without Dark Matter and Dark Energy Abstract:We propose a unified geometric model of galactic dynamics and stellar spectroscopy based on the KEI formalism (Quantum of Energy-Information) and the stellated tetrahedron. We demonstrate that the anomalous rotation curves of galaxies, conventionally attributed to dark matter, arise naturally from the spatial gradient of information density ρKEIρKEI, defined through phase shifts of coherent states. In this framework, mass and gravity are not fundamental entities but macroscopic manifestations of gradients in information density, governed by the universal conservation law of resonance and dissonance. The core structure is an eight-vertex stellated tetrahedron, where each vertex corresponds to a specific class of cosmic objects (black holes, quasars, pulsars, stars of various types) characterized by a distinct ρKEIρKEI value, expressed in terms of the golden ratio φφ. This assigns a characteristic resonant frequency fi=fref⋅φi−4fi=fref⋅φi−4 to each class, with fref=400/7fref=400/7 Hz. A direct prediction follows: stars residing at different tetrahedral vertices should exhibit spectral features at the corresponding frequencies or their harmonics, testable with Gaia and LAMOST data. The model yields flat rotation curves without invoking dark matter or dark energy, because in the galactic halo the gradient of ρKEIρKEI decays slower than r−2r−2, leading to v(r)∼constv(r)∼const. An open-source Python script, adapted to the SPARC catalog, is provided for verification. We expect the model to fit observed rotation curves with >99% accuracy without introducing additional free parameters. We invite the international community to independently test the proposed paradigm and to collaborate on observational validation. «Keywords: KEI formalism, stellar tetrahedron, galactic rotation curves, dark matter alternative, stellar spectroscopy, golden ratio, 57.14 Hz, resonance, information density, SPARC catalog, Gaia, LAMOST.»