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March 27, 2026Open Access

Optimal Fractal Scaling in Spectral Systems: A Rigorous Variational Analysis

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Authors

TMThierry Marechal

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Overview

Variational analysis demonstrates optimal fractal scaling in spectral systems, suggesting new paradigms in physical and mathematical contexts.

Key Points

  • The study aims to establish a comprehensive variational theory for optimal scaling in spectral-fractal systems.
  • Defined operators with fractal potentials scaling at a specific rate
  • Developed an energy functional to balance spectral energy and complexity
  • Proved existence and uniqueness of optimal scaling under precise conditions
  • Demonstrated that optimal scaling exists and can be calculated as α* = (γC_s/(βC_f))^{1/(β−γ)}
  • Identified that √2 is not universal for all cases, depending on scaling exponents
  • Provided complete proofs and quantitative assumptions for all findings

Cite This Study

Thierry Marechal (2026) studied this question.

synapsesocial.com/papers/69c61ff615a0a509bde186a2https://doi.org/10.5281/zenodo.19221368
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