Adaptive Noncommutative Spiral Fibered Structures and Phase-Normalized Measure Spaces

Resource type: Publication → Preprint

Title: 
Adaptive Noncommutative Spiral Fibered Structures and Phase-Normalized Measure Spaces

Creators:
  Family name: Sasaki
  Given names: Hiroshi
  Affiliation: Javatel Corporation

Description (Abstract):

We introduce an abstract mathematical framework consisting of:
• a measurable dual-time structure (t, σ), where t represents physical time and σ
represents an abstract partially ordered “semantic” time;
• an adaptive spiral embedding of (t, σ) into C, producing what we call a spiral-based
time manifold;
• a labelling of directed graphs by elements of a noncommutative ring, together with
commutativity-generated equivalence classes and a family of phase normalization
maps on S1 inducing probability measures.
These elements combine to form what we call noncommutative spiral fibered structures.
Despite their motivation from evolving dependency systems, the formulation is
purely mathematical, based on noncommutative algebra, measurable structures, and
geometric embeddings.
We refine the definitions to ensure consistency of topology and measurability, prove
the existence of phase-normalized semantic measure families, and illustrate the construction
with examples.