A byte-level BPE tokenizer is an ordered list of merge rules, so applying only a prefix yields a vocabulary whose token identifiers are the first rows of the full vocabulary. This prefix nesting allows one language model to operate at several vocabulary sizes, use a control token to indicate the active size, and be deployed at any trained size by slicing its embedding and output head. We pre-registered five claims, including margins, seeds, contrasts, and a stop rule, and trained 30 models with 3.1M- and 10.6M-parameter bodies on 200M tokens each. Slicing is numerically exact: across 76 checks, a sliced model reproduces the restricted full model's logits bit for bit and removes 66% of deployed weights without changing latency. However, the shared model trails a fixed-cap specialist by 3.64% bits per byte at 32k against a 1% margin, and by 2.96% at 8k against a 2% margin. A 2x2 ablation separating the control token from output restriction finds that the token changes performance by +0.07% to +0.13%, with all intervals crossing zero, while output restriction costs +0.47% to +1.19%; the factors are substitutes rather than complements. Multi-cap training nevertheless improves robustness: under typographical noise, the same checkpoint degrades 12.5--15.4 points less in its fine mode and outperforms each fixed-cap specialist at that specialist's vocabulary size. A control with neither cap token nor output restriction is equally robust, attributing this benefit to multi-granularity training rather than conditioning. The per-cap penalty tracks each cap's share of training rows, yielding a falsifiable prediction for future work.
Serving a 235B-parameter Mixture-of-Experts (MoE) model on a single 8 GB GPU is bottlenecked not by compute but by memory bandwidth: decode must stream each token's active experts from whichever tier holds them, and on consumer hardware most experts sit on an SSD far slower than RAM. We quantify this bandwidth wall on Qwen3-235B (Q4_K_M, 134 GB): measured decode is 0.44 tok/s warm, matching a bytes-per-token / bandwidth model, while a batching scheme that should amortize one disk sweep instead collapses at batch 32 from paging thrash. We build llama-moe-trace, a zero-surgery router-telemetry tool, and measure routing on Qwen3-30B: adjacent-token expert reuse is 2.0x chance, 95% of traffic uses 52.5% of experts, and an LRU cache of 13.4% of experts serves 66% of requests. We then ask whether cacheability is trainable: we pre-register training of 137M MoE language models with auxiliary locality and domain router losses, under joint criteria on cache-miss reduction and perplexity. The mechanism works (misses down up to 60%; a 99% static-pin hit rate) but every configuration fails the pre-registered <=1% perplexity gate -- miss reduction and quality are tightly coupled. Concurrent StickyMoE reports the same loss as near-free on single-domain sub-25M models; on multi-domain 137M we find the tax real. Our contribution is this pre-registered, stricter-criterion, multi-domain evaluation plus edge-serving measurements. A 340M rung shows the tax does not shrink with scale (it rises slightly). We further show training-free cache-aware rerouting stacks with trained locality -- together ~80% miss reduction at <=3.4% perplexity at both sizes, far cheaper than either alone -- while domain-primed prefetching does not help. All code, traces, and the pre-registration are released.