Fold, Don't Stream: Recurrent Depth as a Storage-Residency Optimization for Consumer-Device LLM Inference

When a language model exceeds a consumer device's RAM, decoding falls off a storage cliff: every token forces the active parameters to be re-read from disk. We measure this cliff directly on an Apple M1 Max (32 GB): a dense 70B model at 4-bit reads ∼44 GB from SSD per generated token and decodes at ∼0.02 tokens/s. This paper does not propose a new recurrence mechanism — recurrent depth (executing a small stack of layers R times) is established from Universal Transformers onward. Our contribution is a re-measurement and re-framing: we treat looping as a storage-residency lever rather than a parameter- or reasoning-efficiency one, examine a previously unmeasured design axis inside looped MoE, and directly instrument the beyond-RAM decode cliff the mechanism removes. Controlled 30M-parameter studies show that at equal resident bytes and equal training tokens a looped transformer recovers 41% (dense) and up to 54% (Mixture-of-Experts) of the quality gained by doubling memory, cross-reproduced on two hardware/precision stacks; a compute-matched control shows this advantage is specific to the equal-token regime at our scale. For looped MoE, across seeds, sticky routing (re-using the first pass's expert selection) is statistically indistinguishable from free re-routing (Δ = +0.003 ± 0.004 nats, n=3) while freezing expert touches at top-k: cross-loop routing freedom buys nothing measurable, so access locality is free. An R-sweep shows saturating returns (asymptote ∼53–55%; practical optimum R=3–4). On the systems side, a ∼300-line graph-folding patch to llama.cpp removes the cliff on the same laptop: the 70B dense model accelerates from 0.02 to 2.40 ± 0.10 tokens/s (∼125×) and a 118B-A8B MoE from 1.4 to 2.37 ± 0.42 (∼1.7×), with zero swap. As a controlled endpoint we build a flattened twin of a production looped model (Nanbeige4.2-3B): a layer-duplicated checkpoint computing the identical function (greedy outputs match token-for-token). Under a memory budget admitting the folded (4.4 GB) but not the flattened (7.8 GB) form, the twin collapses to 0.1 tokens/s (231 GB of SSD reads) while the folded form sustains 15.1 tokens/s — a 151× gap with quality identical by construction, isolating residency as the sole cause. The same production model runs coherently at 49 tokens/s on this machine (a different stack and scale; §4.3), consistent with loop-native models already occupying this regime. This is a working preprint (v2.2, revised after adversarial review); it has not been peer reviewed. A Korean translation is included as a secondary file for accessibility; the English version is authoritative.