UniSpheral Gravitational Time Dilation Foundation

The UniSpheral Gravitational Time Dilation Foundation is the book's attempt to give gravitational time dilation, which general relativity derives from spacetime geometry, a Pulse-rate account at the substrate level, through density-dependent modulation of the pulse rate, with the Physical and Data domains responding together. The book sets the standard general-relativity result beside two BPT relations. In the Physical domain, the ratio of the modified to the baseline physical pulse rate is the square root of the ratio of baseline to local physical density. In the Data domain, the data Pulse Rhythm scales with the same density ratio raised to δ, which equals the Physical exponent γ = ½ because the Rhythm is half the Tempo at every density. The relation √(ρ_P/ρ⦰) is a child's Tempo across a well, the Tempo a universe inherits from the density of the well that seeds it, not dt'/dt at a radius r inside our universe, where the constants are fixed; a weak-field map from a density profile ρ(r) to 1 − r_s/r is stated as open, and the account seeks, rather than reproduces, the geometric result. The book writes dt'/dt = √(1 − 2𝒢M/(r𝒞→²)); ⚛⥂'⌂(ℨ)/⚛⥂⌂(ℨ) = √(⚛ρ⌂/⚛ρ); and ↁ⧖'⌂(ℨ)/ↁ⧖⌂(ℨ) = (⚛ρ⌂/⚛ρ)^δ. Here dt'/dt is the relativistic dilation ratio [∅]; 𝒢 the gravitational constant [𝕄⁻¹·𝕃³·𝕋⁻²]; M a mass [𝕄]; r the radial distance [𝕃]; 𝒞→ light speed [𝕃·𝕋⁻¹]; ⚛⥂' and ⚛⥂ the modified and baseline physical pulse rate [𝕋]; ↁ⧖' and ↁ⧖ the modified and baseline data Pulse Rhythm [𝕋]; ⚛ρ⌂ and ⚛ρ the baseline and local physical density [𝕄·𝕃⁻³]; and δ the data-domain exponent, equal to γ [∅]. It connects to UniSpheral Data Rhythm Dilation Equation, Time Dilation, Gravitational Time Relation, Domain-Specific Gravitational Scale Modifications and Density-Dependent Pulse Tempo Framework.