A Concentration–Dispersion Bridge Between c and ℏ: A Trinity/STO Addendum to the Fine-Structure Derivation Program

This paper extends the Trinity/STO fine-structure derivation program by proposing a concentration–dispersion bridge between the space-face propagation scale c and the quantum action scale ℏ. Building on earlier work involving Hopf phase closure, diagonal record stability, and concentration–dispersion balance, the paper introduces a dimensionless balance ratio χ = C/D and proposes the bridge ansatz ℏ(χ) = ℏ₀χ¹ᐟ² and c(χ) = c₀χ⁻¹ᐟ².

The resulting framework preserves ℏc, the fine-structure constant α (under fixed electromagnetic coupling structure), and the Planck mass mₚ, while generating systematic Planck-scale scalings for length, time, and energy. A numerical consistency test confirms the internal mathematical coherence of the proposed scaling relations.

The paper does not claim a first-principles derivation of either c or ℏ, nor does it claim empirical evidence for variable physical constants. Rather, it presents a mathematically self-consistent bridge hypothesis motivated by geometric-mean concentration–dispersion balance within the Trinity/STO ontology of stable records. Future work focuses on determining whether the balance ratio χ can be derived from deeper closure principles or connected to measurable physical observables.

This version visits a proposed concentration–dispersion bridge between the speed of light c and Planck’s constant ℏ in the Trinity/STO framework. It recasts the bridge as a gauge invariance in constants-space that preserves all dimensionless combinations (including α, ℏc, and mP), and interprets ℏc and mP as expressing a conserved face-balance and a record anchor, respectively. The paper replaces earlier empirical suggestions with explicit conditions a degeneracy-breaking sector must satisfy before the balance parameter χ can acquire testable physical meaning.