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June 17, 2026Open Access

Digital-Root Rotary Position Encoding: The 1→2→4→8→7→5 Cycle as a Basis for Sequence Position Representation

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Authors

WWWeslyn Cory Whitehead

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Overview

Randomized trial evaluates digital-root position encoding in sequences, indicating improved frequency representation.

Key Points

  • This research aims to develop a novel encoding method using digital-root sequences for better position representation.
  • Introduced Digital-Root Rotary Position Encoding (DR-RoPE) utilizing a doubling sequence for angle derivation.
  • Restated non-aliasing claims based on the frequency-spectrum shape and scale factors.
  • Defined algebraic structure using the multiplicative group mod 9 with a focus on primitive roots.
  • DR-RoPE effectively reduces aliasing with period-6 frequency spectra and non-repeating position representation.
  • Demonstrated improved encoding accuracy compared to traditional methods with purely cyclic angles.

Cite This Study

Weslyn Cory Whitehead (2026) studied this question.

synapsesocial.com/papers/6a323b4cd50b63ecad205e7bhttps://doi.org/10.5281/zenodo.20701797
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