Evidence for an Irreducible κ-like Structure in Galactic Dynamics and Lensing Phenomenology

We identify empirical evidence for an irreducible κ -like structural quantity that emerges when observations are expressed relative to minimal reference models across multiple physical domains. Using galaxy rotation curves from the SPARC database, we show that the dimensionless ratio κ ^~ =v _obs /v _ba r exhibits a scale-dependent, galaxy-independent collapse that persists under mass reparameterization, dynamical field redefinitions, and effective halo modeling. We further demonstrate that an analogous κ -like structure appears in strong gravitational lensing time delays constructed purely from image positions and propagation geometry, without invoking cosmological parameter inference. Finally, we show that quantum-scale double-slit molecular scattering data display systematic, scale-dependent residuals relative to the textbook Fraunhofer interference model that are structured and irreducible to standard corrections. Across all three regimes, the κ -like quantity is dimensionless, partially universal, and irreducible, indicating a common structural feature of physical descriptions independent of specific dynamics or material content.