Symmetric Envelope Interface Chain and Its Sub-Envelope Surfaces: Parameter Correlation Analysis

Based on the Symmetric Envelope Interface Chain, this paper discusses the parameter correlations between the parent envelope surface and its nested sub-envelope surfaces. The minimum length unit of the parent layer is taken as the arc length of one complete rotation of the parent initial radius: l_min = 2π * r0 The minimum length unit of the child layer is taken as the child layer's own ruler lp. After normalizing l_min and lp to unit 1 respectively, they are equal at the dimensionless level. However, this does not mean l_min = lp — they belong to different layers and are each defined by their own parameters. On this basis, the parent and child layers are connected by a time-dependent bridge variable Λ(t): Λ(t) = (1/(2π)) * exp( b * ∫₀ᵗ ω(τ) dτ ) where b is the manifestation rate and ω(t) is the phase advance angular speed. This variable describes the dynamic manifestation factor of the parent layer as it calls forth the child layer during its phase advance. Within the child layer, because the ruler and space scale synchronously by the same proportion, Λ(t) is absorbed and thus b and ω(t) are not readable; the child layer retains only its own constant reading c = f_max * lp. Keywords: Symmetric Envelope Interface Chain; sub-envelope surface; minimum length unit; parameter correlation; bridge variable; cross-layer reference relation; normalization