What question did this study set out to answer?

The aim is to expand the understanding of prime-pair absorption through Binary Layer Theory II by establishing key theorems.

June 9, 20262 citationsOpen Access

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Binary Layer Theory II: Projection–Aggregation Stabilization in Prime-Pair Absorption

YKYoshihito Kawanishi

Key Points

The aim is to expand the understanding of prime-pair absorption through Binary Layer Theory II by establishing key theorems.
Develops a projection–aggregation framework across binary layers.
Utilizes diagonal aggregation bands to project source bins onto target channels.
Introduces the Binary Projection–Aggregation Geometry Theorem and Stabilization Scale Theorem.
Establishes a natural stabilization scale linked to binary projection–aggregation.
Confirms the closure scale as sqrt(2-S_K) within the context of pair-space.
Demonstrates geometric relationships between source bins and target channels.

Abstract

This manuscript develops Binary Layer Theory II as a projection–aggregation framework for prime-pair absorption across binary layers. Building on the binary closure coordinate introduced in BLT-I, it studies how a binary layer partitioned into B source bins expands into a B² pair-space and is projected back onto B target channels through diagonal aggregation bands. The paper establishes the Binary Projection–Aggregation Geometry Theorem and the Balanced Even-Depth Stabilization Scale Theorem, showing that the natural stabilization scale induced by binary projection–aggregation is the square-root closure scale sqrt (2-SK).

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Binary Layer Theory II: Projection–Aggregation Stabilization in Prime-Pair Absorption

Key Points

Abstract

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