How Many Ternary Planes Does Reasoning Need? A Capability-Stratified Study of Post-Training K-Trit-Plane Quantization

Post-training quantization (PTQ) of LLM weights to ternary values {-1,0,+1} has recently reached near-lossless accuracy by stacking K trit-planes, most directly in PTQTP. But how much ternary compression a model tolerates is not uniform across what the model does. We present a capability-stratified study of K-trit-plane PTQ across 22 open checkpoints—18 dense (0.5–14B, seven families, base and instruct variants) and four mixtures-of-experts (7–30B total parameters)—evaluated with the official lm-evaluation-harness. Three findings. (1) K is the lever: K=3 (≈ 4.9 bpw) recovers ≈baseline almost everywhere (90% mean GSM8K, 97% knowledge), while K=2 (≈ 3.3 bpw) collapses reasoning specifically—grade-school math to a near-zero cliff and competition math to ≤ 31%—yet leaves knowledge, commonsense, and code largely intact (38–95%). The cliff is a property of uniform extreme quantization, not of ternary weights per se: a controlled per-bit head-to-head (Qwen2.5-1.5B, N=200) shows a uniform 3-bit integer (RTN) collapses reasoning just as ternary K=2 does (both ≤ 2% GSM8K at ≈3–4 bpw), while the mixed-precision integer K-quants that survive (Q2_K) do so by keeping reasoning-critical layers at higher precision. The lever is thus a clean, graded instance of a low-bit reasoning cliff, not a ternary-only phenomenon. (2) The collapse is functional, not a weight-reconstruction failure: it lives in the layers—late-activation SQNR is lower for math than for knowledge in 12/12 models—and the full-precision/ternary divergence is frontal, not cumulative. (3) Where to spend the extra bits is mostly open: attention is the causal bottleneck (protecting it is necessary, 4/4 families), but cheap per-block allocation signals are not robustly better than random. Read the other way, K is an instrument, not merely a compression knob: a graded, reversible, weight-level dial that selectively ablates multi-step reasoning while leaving stored knowledge intact—unusually graded and reversible for a compression knob (a uniform integer bit-width toggles the same collapse only coarsely: INT3 off, INT4 on), a model organism for reasoning under compression. We do not propose a new quantizer: a handful of recent methods already reach near-lossless ternary PTQ (mostly unreviewed preprints, only one with released code), and PTQTP already reports a capability breakdown—but none gives the mechanism, the uniform-vs-mixed control that locates the cliff, or the allocation analysis. We map the K-lever, its mechanism, and its limits, and recommend K=3 as a uniform, near-universal operating point (competition math is the one capability still gaining marginally from K≥4). And because the collapse is invisible to perplexity and aggregate accuracy, it sharpens an established warning: audits of compressed models should be capability-stratified. All raw logs, the harness configuration, and the figure scripts are released.