diff --git a/data/dpo_metric.png b/data/dpo_metric.png
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diff --git a/data/sft_metric.png b/data/sft_metric.png
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diff --git a/main.tex b/main.tex
index 38cf0dc..9ee1f98 100644
--- a/main.tex
+++ b/main.tex
@@ -35,9 +35,9 @@ storage backends, and a companion SFT pipeline ({\sc Alembic}) with
 MinHash deduplication. The 24-layer GQA-SwiGLU decoder is trained with a
 hybrid Muon/AdamW optimizer and WSD scheduling under DDP/FSDP.
 Supervised fine-tuning on deduplicated bilingual instructions reduces loss
-from $\sim$2.5 to $\sim$1.6 over 1{,}000~steps; DPO alignment
+from $\sim$2.1 to $\sim$1.5 over $\sim$3{,}800~steps; DPO alignment
 ($\beta=0.1$, cosine schedule) on model-generated preference pairs
-converges stably without over-optimisation. A BF16 stability analysis
+shows stable training-loss convergence without over-optimisation. A BF16 stability analysis
 shows that GPT-2 residual scaling ($\sigma_0 = 0.02/\sqrt{2L}$) reduces
 per-block activation variance by a factor of 48, and post-training weight
 analysis across three checkpoints confirms that residual-scaled
@@ -285,7 +285,7 @@ Table~\ref{tab:train_params} lists the key hyperparameters.
 \textbf{Hyperparameter} & \textbf{Value} \\
 \midrule
 Precision & BF16 (weights + optimizer states) \\
-  Optimizer & Hybrid Muon/AdamW$^a$, $\eta=1.5\times10^{-4}$ \\
+  Optimizer & Hybrid Muon/AdamW$^a$, $\eta=2.0\times10^{-4}$ \\
 Betas & $(0.9, 0.95)$, weight decay $0.1$ \\
 Gradient clip & Global L2, max norm $1.0$ \\
   Scheduler & WSD (warmup 2\%, stable, decay) \\
@@ -338,21 +338,21 @@ training, ensuring stable weight updates in the final phase.
 \begin{figure}[H]
 \centering
 \includegraphics[width=0.85\linewidth]{data/sft_metric.png}
-\caption{SFT training metrics over 1{,}000 fine-tuning steps on a
+\caption{SFT training metrics over $\sim$3{,}800 fine-tuning steps on a
 mixed Chinese--English instruction dataset: training loss, learning
-rate, and gradient norm. The loss drops rapidly in the first 200
-steps and then enters a slower decay phase. The learning rate
-follows a WSD schedule (2\% warmup, stable, decay). Gradient norms stabilize
-after approximately 300 steps, indicating that the fine-tuning
-process has reached a stable optimization regime.}
+rate, and gradient norm. The smoothed loss decreases from $\sim$2.1 to
+$\sim$1.5, dropping rapidly in the first 500 steps and then entering a
+slower decay phase. The learning rate follows a cosine schedule with short linear warmup. Gradient norms stabilise after approximately 500 steps,
+indicating that the fine-tuning process has reached a stable optimization
+regime.}
 \label{fig:sft_metric}
 \end{figure}
 
 Figure~\ref{fig:sft_metric} shows the supervised fine-tuning metrics
-for the 1K-step SFT checkpoint used in the IFD analysis
+for the SFT checkpoint used in the IFD analysis
 (Appendix~\ref{app:ifd}). The training loss on the mixed
-Chinese--English instruction dataset decreases from $\sim$2.5 to
-$\sim$1.6 over 1{,}000 steps, with the gradient norm converging to a
+Chinese--English instruction dataset decreases from $\sim$2.1 to
+$\sim$1.5 over $\sim$3{,}800 steps, with the gradient norm converging to a
 stable range after the warmup phase.
 
 \subsection{Direct Preference Optimization}
@@ -373,10 +373,9 @@ preferred response $y_w$ and dispreferred response $y_l$, the loss is:
 \end{equation}
 where $\beta$ controls the KL-divergence penalty against the reference.
 We use $\beta=0.1$, a batch of 64 preference pairs per step, and the
-same hybrid Muon/AdamW optimizer.  Unlike the pretraining and SFT
-phases, which both employ WSD (warmup--stable--decay) scheduling to
-maintain a long high-learning-rate plateau, DPO alignment uses a
-cosine schedule with short linear warmup.  The shorter ~3{,}000-step
+same hybrid Muon/AdamW optimizer.  The pretraining phase employs WSD (warmup--stable--decay) scheduling
+to maintain a long high-learning-rate plateau. Both SFT and DPO
+alignment use cosine schedules with short linear warmup.  The shorter ~3{,}000-step
 alignment run does not benefit from an extended stable phase; instead,
 cosine decay lowers the learning rate steadily, which discourages
 over-optimisation away from the reference distribution and matches the
@@ -392,17 +391,14 @@ schedule, and gradient norm.}
 \end{figure}
 
 Figure~\ref{fig:dpo_metric} summarises the DPO training dynamics.
-The raw preference loss (left panel) starts near $0.69$ and is visibly
-noisy, a hallmark of pairwise preference sampling.  The 100-step moving
-average reveals a steady downward trend that reaches a minimum of
-$\sim$0.51 near step 1{,}200, after which it gently rebounds to
-$\sim$0.52 and oscillates, suggesting the policy has converged to a
-stable preference boundary rather than over-optimising away from the
-reference distribution.  The learning-rate schedule (centre panel) peaks
-at $5\times10^{-6}$ after a short linear warmup and then follows cosine
+The raw training loss (left panel) starts near $0.7$ and is visibly
+noisy; the smoothed curve reveals a steady downward trend that reaches
+$\sim$0.1--0.15 by step 3{,}000 without rebound, indicating stable
+convergence.  The learning-rate schedule (centre panel) peaks at
+$5\times10^{-6}$ after a short linear warmup and then follows cosine
 decay to a floor of $\sim$0.5\,$\times\,$10$^{-6}$.  Gradient norms (right panel) start
-near 50 with occasional spikes above 55, then gradually decline and
-stabilise in the 35--40 range after step 400, indicating consistent
+near 200 with occasional spikes above 250, then gradually decline and
+stabilise in the 35--50 range after step 1{,}000, indicating consistent
 gradient magnitudes throughout alignment.
 
 % ======================================================================
@@ -554,7 +550,12 @@ spread.}
 \begin{figure}[H]
 \centering
 \includegraphics[width=0.95\linewidth]{data/ckpt_weight_density_per_run.png}
-\caption{Per-checkpoint weight density breakdowns.}
+\caption{Per-checkpoint weight density breakdowns. The three checkpoints
+are \texttt{norm-15bt} (AdamW, Normal init, 15B tokens), \texttt{kami-15bt}
+(AdamW, GPT-2 residual scaling, 15B tokens), and \texttt{muon-25bt}
+(Muon, 25B tokens). Note: the iteration labels inside the figure reflect
+legacy script metadata and should be ignored in favour of the token
+budgets stated here.}
 \label{fig:ckpt_weight_density_per_run}
 \end{figure}
 
@@ -577,10 +578,9 @@ non-scaled weights across all checkpoints
 
 Supervised fine-tuning on deduplicated bilingual instructions (processed
 by the companion {\sc Alembic} pipeline with MinHash deduplication)
-reduces training loss from $\sim$2.5 to $\sim$1.6 over 1{,}000~WSD-scheduled
+reduces training loss from $\sim$2.1 to $\sim$1.5 over $\sim$3{,}800~cosine-scheduled
 steps. Subsequent DPO alignment on preference pairs ($\beta=0.1$, cosine
-schedule) converges stably without over-optimisation, reaching a minimum
-preference loss near step~1{,}200.
+schedule) shows stable training-loss convergence without over-optimisation.
 
 Optimizer ablations (Figure~\ref{fig:ckpt_comparison}) demonstrate that
 the hybrid Muon/AdamW configuration consistently outperforms pure AdamW