TKintegers: Explicit Base-3 Representations and Group-Scaled GPU Inference

We present TK Integers, a model-weight representation family that separates balanced base-3 code precision, group geometry, scale encoding, and execution arithmetic, together with a native GPU inference implementation for its five-trit configuration. The evaluated configuration, tk_k5_g128_ISk10log, stores one byte per five-trit weight code and integer-encoded logarithmic scales, and computes groupwise matrix products with binary16 tensor-core operands and FP32 accumulation without maintaining a fully expanded floating-point body. In a matched eager-PyTorch experiment on Qwen2.5-0.5B-Instruct using one NVIDIA L4, this configuration achieves median prefill and prefix-conditioned decode throughput of 3402.85 and 26.75 tokens/s, compared with 1061.58 and 8.63 tokens/s for installed TorchAO dynamic E4M3 FP8: ratios of 3.21× and 3.10×, at saved weight-file sizes differing by 0.88%. A separate Qwen3.5-9B answer study compares the original baseline post-training conversions on 15 shared questions: five each from GSM8K, MMLU-Pro, and HumanEval. Both formats pass 11/15, with identical question-level strict outcomes. Their four shared nonpasses comprise two coding defects, one unfinished reasoning loop, and one ambiguous answer-key mismatch despite a correct core physics derivation. These are descriptive results for one sampled completion per question, not evidence of general quality equivalence. The speed ratios belong to the 0.5B model; the paired answer outcomes belong to the 9B model.