Published April 1, 2026 | Version v1
Preprint Open

HEXA-LANG: A Programming Language with Zero Arbitrary Design Choices — Every Constant Derived from the Perfect Number 6

Authors/Creators

  • 1. Independent Researcher

Description

We present HEXA-LANG, the first programming language where every design constant is mathematically derived from a single number-theoretic equation: sigma(n)*phi(n) = n*tau(n), which holds for n>=2 if and only if n=6. This yields 53 keywords, 24 operators, 8 primitive types (matching Bott periodicity), a 6-phase compiler pipeline, 4 type layers, and an Egyptian fraction memory model (1/2+1/3+1/6=1). Design Space Exploration of 21,952 combinations achieves 100% n=6 alignment. Working compiler in Rust with 58 tests.

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Additional details

Related works

Is part of
https://github.com/need-singularity/n6-architecture (URL)
Is supplement to
https://github.com/need-singularity/hexa-lang (URL)