Binary Layer Theory: A Closure-Band Framework for Layered Prime Fluctuations

Key Points

• The aim is to introduce Binary Layer Theory as a closure framework for understanding prime-count fluctuations on binary scales.
• Defines concepts such as binary layers, binary closure coordinate, and mass–shape decomposition.
• Introduces the binary closure-band condition to structure energy densities and tail-weighted contributions.
• Utilizes an asymptotic approach to analyze residual fluctuations.
• Establishes a systematic method for categorizing fluctuations through binary scales.
• Demonstrates that residual energy densities can be effectively modeled using the binary closure framework.
• Provides a new understanding of mass–shape relationships in the context of prime-count fluctuations.