REGULATED ACCUMULATION Spectral Geometry, Physical Structure, and Stability across Scales

By: Vogt, Savio Antonio

This monograph argues that across mathematics, physics, and engineering, unbounded additive continuation is a modeling artifact rather than a physical reality. It introduces a structural thesis: systems naturally exhibit geometric saturation, an intrinsic regulation that constrains accumulation to prevent divergence.
Beginning with prime density and logarithmic thinning, the work identifies density compression as a universal structural template. This pattern is tracked across diverse domains, including:
- Navier-Stokes spectral cascades
- Stochastic dispersion and operator admissibility
- Gravitational pre-collapse structures
The author demonstrates that smooth spectral tapering naturally replaces the need for artificial truncations or renormalized infinities. By formalizing the Geometric Master Form across scale parameters, the text proves that bounded transfer arises from compatibility conditions rather than imposed cutoffs.
Ultimately, the monograph establishes cross-domain regulation as a unifying discipline, asserting that structural legitimacy requires admissible extensions governed by saturation principles to ensure systems remain finite and physically coherent.

• Format: Paperback
• Language: English
• ISBN: B0GY3GFQBY
• ISBN13: 9798899664281
• Release Date: April 2026
• Publisher: Bayshop (Generis Publishing)
• Length: 94 Pages
• Weight: 0.30 lbs.
• Dimensions: 0.2" x 6.0" x 9.0"