What the study found
Each digit in the sexagesimal (base-60) numeral system can be uniquely decomposed into three independent coordinates on a discrete lattice of size 4 × 3 × 5. The abstract says this representation makes division by 2, 3, or 5 an exact finite operation.
Why the authors say this matters
The study suggests this lattice-based base-60 representation could support exact fixed-point arithmetic, and the authors say it is relevant for safety-critical computing because it removes a class of rounding errors found in standard decimal and binary systems.
What the researchers tested
The work examines a bijection between digit values and lattice coordinates induced by the Chinese Remainder Theorem, and it considers how the prime factors 2, 3, and 5 act on the lattice axes. It also discusses the sexagesimal expansion of pi and the representability of reciprocals.
What worked and what didn't
The abstract reports that division by 2, 3, or 5 can be realized as translation along the corresponding lattice axis, producing exact quotients without iteration or loss of precision. It also states that 1/2, 1/3, and 1/5 have exact single-digit fractional expansions, and that pi in base 60 has a zero at the fourth fractional digit, with the next nonzero contribution at 60^-5.
What to keep in mind
The abstract does not describe experimental tests or performance benchmarks, and it does not provide comparative evaluation beyond the stated arithmetic properties. It also notes a companion paper on a separate non-abelian structure, but that work is not part of this abstract.
Key points
- Base-60 digits can be mapped to a unique 4 × 3 × 5 lattice coordinate system.
- Division by 2, 3, or 5 is described as exact and finite in this representation.
- The reciprocals 1/2, 1/3, and 1/5 have exact single-digit fractional expansions.
- The abstract reports a zero at the fourth fractional digit of pi in base 60.
- The next nonzero contribution for pi is stated to occur at the 60^-5 place.
Disclosure
- Research title:
- Base-60 digits map to exact prime-factor lattice coordinates
- Authors:
- Moss Eva
- Publication date:
- 2026-04-26
- OpenAlex record:
- View
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