The Planck Constant from Three-Step Relational Closure

This paper examines a relational origin of a Planck-type action constant from discrete updates and periodic closure in a pregeometric connectivity structure. Connectivity states and their discrete updates constitute the primitive description. In the previously proposed composite-cell model, a correspondence between a one-cell update along the long axis and one-third of a rotation has been suggested. Here, this correspondence is stated explicitly as a structural assumption, and the relational action associated with one cell update is denoted by 𝓒₀. If three equivalent updates complete one cycle of the connectivity state, the relational action of one complete cycle is h₀ = 3𝓒₀. Mapping this discrete closure to the conventional continuous phase representation identifies one cycle with 2π rad and gives ℏ₀ = h₀/(2π). With a cycle period T, one further obtains E₀ ≡ h₀/T = h₀ν = ℏ₀ω. Thus h₀ is a structural quantity directly associated with discrete closure, whereas ℏ₀ is its continuous angular-phase representation. This paper does not claim a numerical derivation of h; the microscopic basis of the three-step closure and of the one-cell relational action remains to be established.