A No-Go Theorem for Non-Universal Planck Constants

This paper establishes a rigorous No-Go Theorem for the universality of the Planck constant ℏ within the framework of Constraint-Saturated Realization (CSR). I demonstrate that ℏ is not a contingent empirical value but a structural governor required for a dynamical, “unfinished” universe. By proving that non-universal ℏ values violate compositional consistency, thermodynamic extensivity (via the Gibbs- Duhem relation), and holographic integrity, I establish ℏ as a “quantum pressure” that maintains the universe’s residual capacity for change. Furthermore, I provide a formal derivation of the Saturation- Stasis Lemma, predicting measurable deviations from General Relativity in high-density environments. Specifically, I propose the existence of a “Frequency Floor” in gravitational redshift, energy-dependent dispersion in photon propagation, and post-merger gravitational wave echoes. These signatures provide a clear experimental roadmap to distinguish the process-oriented CSR model from the static Block Universe paradigm, effectively refuting Eternalism through verifiable physical constraints.