What is arithmetic-fizzbuzz?

This project is a solution to a programming puzzle: can you write FizzBuzz without any if-statements, boolean logic, pattern matching, or anything that behaves like a yes/no test? The answer is yes, and the repository proves it with working code that prints the classic sequence, numbers from one upward, with multiples of three replaced by "Fizz," multiples of five by "Buzz," and multiples of both by "FizzBuzz." The trick is that instead of asking "is this number divisible by three?" and branching based on the answer, the code uses pure arithmetic to compute what should be printed directly. The README includes both a Python version built on truth tables and a Rust version that compiles down to straight-line assembly with zero branches. The author points to the compiled assembly to show there are no jumps, no comparisons, no conditional logic at all, just math operations that happen to produce the right output. This is a curiosity rather than a practical tool. Nobody needs a branchless FizzBuzz in production. The project exists to meet a challenge called "Future of Computing," which asks whether programs can be written without the control-flow primitives most software relies on. The README notes a similar effort using lambda calculus, but claims the arithmetic approach is the only one that runs without conditionals on actual hardware. One amusing tradeoff: because the program refuses to check for errors (that would require a conditional), it has no way to handle output failures gracefully. If you pipe the output somewhere that closes early, the program just crashes with a segmentation fault. The README treats this as expected behavior rather than a bug. It also benchmarks at around 153 million lines per second, which is fast, though speed is clearly not the point.