CouCouGen: Coupled Counters as a Source of Deterministic Sequences — Theory, Implementation, and Practical Considerations

Full specification and empirical analysis of CouCouGen — a deterministic sequence generator based on three coupled 32-bit counters with nonlinear feedback. The transition function is proven to be a bijection, guaranteeing no transient states and uniform output over any full cycle. Dieharder test results (100M numbers) are presented: passes basic uniformity, runs, spherical distributions; fails bit-level tests (rank, bitstream, birthdays, OPSO, OQSO, DNA, count-of-1s). The algebraic cause of failures (forced odd increments → deterministic LSB flips) is explained. Includes JavaScript implementation, usage examples, and open research questions. MIT license (code), CC BY-NC 4.0 (text). Bilingual (English/Russian). Suitable for non-critical applications (games, visualizations, procedural generation). Not for cryptography, Monte Carlo, or matrix operations.