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AI Summary of Peer-Reviewed Research

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Base-60 digits can be mapped to exact prime-factor coordinates

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in
Research area:ArithmeticChinese remainder theoremDivision (mathematics)

What the study found

The study finds that each sexagesimal, or base-60, digit can be uniquely decomposed into three independent coordinates on a discrete 4 × 3 × 5 lattice. The abstract says this structure comes from the factorization 60 = 2² · 3 · 5 and uses the Chinese Remainder Theorem.

Why the authors say this matters

The authors conclude that this lattice form can support exact fixed-point arithmetic in base 60. They say it removes a class of rounding errors found in standard decimal and binary positional systems, and they examine its implications for safety-critical computing contexts.

What the researchers tested

The paper analyzes the sexagesimal numeral system as a three-dimensional lattice representation of digits. It examines division by the prime factors 2, 3, and 5 as translations along lattice axes, exact single-digit fractional reciprocals, and the sexagesimal expansion of π.

What worked and what didn't

According to the abstract, division by 2, 3, or 5 can be done exactly and finitely, without iteration and without loss of numerical precision. The reciprocals 1/2, 1/3, and 1/5 have exact single-digit fractional expansions, and π has a structural zero at the fourth fractional digit, with the next nonzero term at 60⁻⁵.

What to keep in mind

The abstract does not describe experimental limitations or empirical testing beyond the mathematical representation itself. It also notes a companion paper on a separate non-abelian structure identified with the icosahedral group A₅.

Key points

  • Base-60 digits are described as having a unique 4 × 3 × 5 lattice decomposition.
  • The mapping between digit values and lattice coordinates is induced by the Chinese Remainder Theorem.
  • Division by 2, 3, and 5 is presented as exact and finite in this representation.
  • The reciprocals 1/2, 1/3, and 1/5 are said to have exact single-digit fractional expansions.
  • The sexagesimal expansion of π is reported to have a zero at the fourth fractional digit.

Disclosure

Research title:
Base-60 digits can be mapped to exact prime-factor coordinates
Authors:
Moss Eva
Publication date:
2026-04-26
DOI:
10.5281/zenodo.19779500
OpenAlex record:
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AI provenance: AI provenance information is not available for this post.