Universal Computation With 144 Residue Classes: A One-State Linear Operator Algorithm

We construct an explicit universal one-state linear operator algorithm with 144 residue-selected rules acting on a single nonnegative integer. This reduces the modulus reported by Kaščák (1992) from 396 to 144, a decrease of 252. The construction combines arithmetic invariants that exclude unreachable branches with a quotient-parity test that selects the return operation as division finishes. Every continuing rule gives an exact nonnegative successor on its entire residue progression. We supply the complete numerical table and a Lean 4 proof of universality under explicit computable input and output encodings. The simulation realizes every unary partial recursive function and preserves nontermination. Consequently, its halting set is computably enumerable complete.