Scale-Dependence of Post-Hoc Ternary Reasoning Recovery: A Multi-Family Study with a Counterexample and an MoE Dissociation

Post-training ternary quantization recovers most of an LLM's accuracy by decomposing each weight into two trit-planes (PTQTP). We ask how this recovery depends on model scale, in a deliberately controlled study across eight model families (0.5–32B, dense and MoE, plus a 70M–2.8B identically-trained control suite). Four findings survive every control. (1) Post-hoc ternary reasoning recovery improves strongly with scale—GSM8K retention rises 17%→96% over Qwen3 0.6–14B and saturates at 85–96% by ≈14B in Qwen3, Qwen2.5, and Falcon3—and an identically-trained control suite (Pythia, five checkpoints; OLMo-2 corroborating across two releases) confirms a genuine size component on perplexity, not just a per-family training artifact; the size-ordering also reproduces under the official EleutherAI lm-eval harness across the three families (see Limitations). (2) The scale-dependence is reasoning-specific: strong on GSM8K, SVAMP, and MATH-500, while knowledge (MMLU) and commonsense (ARC) survive ternarization at every scale. (3) A mixture-of-experts dissociates total from active parameters, and recovery tracks total—a 3B-active/30B-total MoE recovers like a >30B model (94% vs. 80% active / 88% total, within-run; one family—a second MoE did not replicate). (4) The small-model "collapse" is partly a bit-budget cliff (recoverable at g≤32, ≥4.2 bpw), not intrinsic loss. Crucially, the recovery is NOT universal: Llama-3.1-8B collapses to 15% at normal reconstruction error—an outlier-driven failure that a +0.5% FP-outlier fix rescues to ≈52%. We also report what the controls refuted: a structural mechanism we proposed is Qwen3-specific (four other families lack it), and "larger models recover at fewer bits" is non-monotone. The outcome is solid; several mechanistic stories built on top of it were over-fit, and the controls caught each.