This paper quantifies how far bf16 transformer large language model (LLM) weights—and Q4 K-typed tensors inside GGUF Q4 K M files—can be compressed with no loss of information. Every method is scored under one accounting discipline: a trained profile is billed to its method on each file, each run is checked for a byte-exact roundtrip, and the train/test partition is taken over source models rather than individual tensors. For bf16 weights the marginal-byte ceiling sits at ≈1.495× (model-level 95% confidence interval [1.487, 1.502]); the strongest coder that can be run end-to-end under the present accounting—the bf16 split coder introduced here—reaches 1.488×, just below that ceiling. For Q4 K-typed tensors the marginal-byte ceiling is ≈1.076× at the tensor-stream level, dropping to 1.041–1.045× once whole GGUF artifacts are scored, because Q4 K M files also carry Q6 K tensors that barely compress (near 1.01×); the mixture-CDF coder presented here attains 1.052×, whereas a dictionary-trained zstd ends up enlarging the stream once its dictionary is billed per file. Between adjacent same-role weight matrices at bf16 precision no exploitable linear redundancy is found (median Pearson +0.0004 over 250 layer pairs drawn from two Qwen2.5 models). Across 11,942 verified-roundtrip method-evaluations spanning 7,960 distinct benchmark rows, not a single roundtrip failed; the contribution is the comparison protocol itself rather than another compressor. Each ceiling is a compression-ratio bound—hardware independent and confirmed on weights up to 7B parameters (Qwen2.5-7B-Instruct); the single-core x86 (Sapphire Rapids) host constrains only the throughput figures, which are reported for comparability rather than as deployment numbers.

Lossless weight compression bf16 transformer LLMs entropy ceiling reproducible benchmarking protocol GGUF Q4 K quantization source coding