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REGULATED ACCUMULATION Spectral Geometry, Physical Structure, and Stability across Scales - Couverture souple

Vogt, Savio Antonio

 
9798899664281: REGULATED ACCUMULATION Spectral Geometry, Physical Structure, and Stability across Scales

Synopsis

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.

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