\section{Results}
\label{sec:results}

Every number below has a raw log in \code{benchmarks/raw/}; the path is given with each result. Results marked
\textsc{pending} have a protocol but no log yet in this version.

\subsection{Correctness}
\label{sec:results-correctness}
On four prompts (general, code, reasoning, French) \titan{} reproduces mlx-lm's logits with $\max|\Delta| = 0.0$ (float16) at
capacities 64, 32, 16 and 8 slots per layer, with identical argmax at every position and identical greedy continuations of
32 tokens at 16 slots (\code{benchmarks/raw/tests/numerical\_*.json}, \code{greedy\_*.json}, \code{pytest\_gateB\_*.txt},
7 tests passed). The registry's byte ranges read with \code{pread} are byte-equal to \code{mx.load} for sampled experts of both the
per-expert layout (OLMoE) and the stacked layout (Qwen3-30B-A3B, on M3U96a). Qwen3-30B-A3B logit parity:
\textsc{pending} (test launched on M3U96a; result to be inserted from its log).

\subsection{All-resident control and demand loading}
\label{sec:results-capacity}
Table~\ref{tab:capacity} summarises the laptop capacity sweep (64-token greedy generations, general and code prompts,
page-cached checkpoint, \code{benchmarks/raw/gateB/capacity\_sweep\_laptop/sweep.jsonl} and
\code{benchmarks/raw/gateC/prefetch\_online\_laptop/smoke\_lazyinstall.jsonl}).

\begin{table}[t]
\centering\small
\caption{OLMoE-1B-7B 4-bit on the M5 Max laptop: decode throughput vs residency (2 repeats after warm-up; ranges over prompts).}
\label{tab:capacity}
\begin{tabular}{llrrr}
\toprule
Backend & Residency & decode \toks{} & hit rate & stall / 64 tokens \\
\midrule
mlx-lm & all & 491--496 & -- & -- \\
\titan{} & 64 slots, preloaded & 489 & 1.00 & 0 \\
\titan{} & 64 slots, not preloaded (sync path) & 201--203 & 1.00 & 0 \\
\titan{} & 32 slots, LRU, demand (v1 installs) & 56--80 & 0.73--0.81 & 0.7--1.0 s \\
\titan{} & 16 slots, LRU, demand (v1 installs) & 36--45 & 0.48--0.60 & 1.7--2.0 s \\
\titan{} & 16 slots, LRU, demand (lazy installs) & 51--73 & 0.48--0.67 & 0.6--0.9 s \\
\titan{} & 16 slots, LRU + transition prefetch ($d{=}1$, $m{=}8$) & 35--56 & 0.63--0.73 & 0.6--1.1 s \\
\bottomrule
\end{tabular}
\end{table}

Two observations. The all-resident control matches mlx-lm within one percent only when every layer's table is complete;
otherwise each layer pays a host synchronisation, which alone costs 2.4$\times$ in throughput on this model and is the floor
of any demand-loading design, including colibri's. And the demand-loading rows are the H1 \emph{control}: at 16 slots the
model does 53 misses per token (Prop.~\ref{prop:capacity}), i.e.\ about 11~ms of fetch per 2~ms of compute.

\subsection{Routing locality}
\label{sec:results-locality}
From the v1 traces (18 prompts, 3\,686 tokens), per-layer LRU hit rates are 0.57 at 16 slots, 0.80 at 32 and 0.93 at 48 (LFU
within 0.01), nearly identical on fit and held-out prompts (\code{benchmarks/processed/gateC/sim\_olmoe\_laptop\_ssd\_v1.json});
a one-layer-ahead transition predictor has recall@8 of 0.50 on held-out prompts; a linear probe on the previous layer's
log-probabilities only 0.16 with these few traces. The v2 traces (65 prompts, 6 families) and the depth-$d$ predictors:
\textsc{pending} (simulation running at the time of writing; Table~\ref{tab:sim} is generated from its JSON).

\subsection{Prefetching (H1)}
\label{sec:results-prefetch}
With the one-layer horizon the online prefetcher raised the hit rate from 0.48 to 0.63 (general) and from 0.67 to 0.73
(code) but reduced throughput from 51 to 35 and from 73 to 56~\toks{} (Table~\ref{tab:capacity}): the lead time
$d\,\tau_\ell = 0.13$~ms is shorter than the 0.21~ms fetch, so predicted experts arrive late and are waited for, and the
50\,\% of wrong predictions add traffic. This is exactly the regime excluded by condition~\eqref{eq:condition}.
Depth-$d$ and token-horizon prefetching, and the cold-NVMe tier: \textsc{pending} (next experiments of Gate C).

\subsection{Medium model (Qwen3-30B-A3B)}
mlx-lm and \titan{} all-resident baselines on M3U96a (96~GB): \textsc{pending} (running).

\subsection{Distributed execution (H2, H3), Metal kernels (H4), energy frontier (H5)}
\textsc{pending}: Gates D--F have protocols (Section~\ref{sec:algorithms}, \code{research/protocol.md}) and no logs in this version.