The condition number κ has extreme dynamic range across layers:

- Layer 0: κ ~ thousands (ill-conditioned)
- Deep layers: κ ~ single digits (well-conditioned)

On a linear y-axis, the deep-layer variation is completely invisible —
the early-layer spikes dominate the scale and compress everything else
into a flat line at the bottom. This defeats the purpose of the plot.

Switch the κ(Q) & κ(K) dual-line panel (row 2, col 3) to **log scale**
in both rendering engines.

Single-model figure — added after the two `draw()` calls:
```python
ax.set_yscale("log")
```

Compare figure — same addition:
```python
ax.set_yscale("log")
```

Title updated to reflect the scale:
```
"Law 3 — Condition Number κ (log scale)"
y-label: "Condition number κ (log)"
```

Added inside the per-panel loop, after `fig.update_yaxes(title_text=...)`,
for both `plotly_single()` and `plotly_compare()`:

```python
if col == "cond_dual":
fig.update_yaxes(type="log", row=row_idx, col=1)
```

```
set_yscale("log") found 2× in core/plotter.py ✅
type="log" found 2× in core/plotter_plotly.py ✅
ast.parse() both files ✅
```

`ui/tab_plot.py`, `db/`, `app.py` — untouched.

core/plotter.py

@@ -204,8 +204,9 @@ def plot_single_model(
     ax = axes[1, 2]
     draw(ax, "cond_Q", C["Q"], "κ(Q)")
     draw(ax, "cond_K", C["K"], "κ(K)")
-    _finalize_ax(ax, "Law 3 — Condition Number κ",
-                 "Condition number κ")
+    ax.set_yscale("log")
+    _finalize_ax(ax, "Law 3 — Condition Number κ  (log scale)",
+                 "Condition number κ  (log)")
 
     # ── Row 2: Law 4 ─────────────────────────────────────────────────────────
     # Share y-axis across this row
@@ -374,7 +375,8 @@ def plot_compare_models(
                f"{name_a} κ(K)", "-", show_band, None)
     _draw_line(ax, lay_b, med_b, q25_b, q75_b, C["K"],
                f"{name_b} κ(K)", "--", show_band, None)
-    _finalize_ax(ax, "Law 3 — Condition Number κ", "Condition number κ")
+    ax.set_yscale("log")
+    _finalize_ax(ax, "Law 3 — Condition Number κ  (log scale)", "Condition number κ  (log)")
 
     # ── Row 2: Law 4 ─────────────────────────────────────────────────────────
     u_cols = [("cosU_QK", C["QK"], "Q–K"),

core/plotter_plotly.py

@@ -247,6 +247,9 @@ def plotly_single(
                          title_font=dict(size=11))
         fig.update_xaxes(title_text="Layer index", row=row_idx, col=1,
                          title_font=dict(size=11))
+        # ── log scale for condition number panel (row 6) ─────────────────────
+        if col == "cond_dual":
+            fig.update_yaxes(type="log", row=row_idx, col=1)
 
     # ── shared Y for cosU row (panels 6,7,8) ─────────────────────────────────
     _sync_yrange(fig, df, ["cosU_QK", "cosU_QV", "cosU_KV"],
@@ -411,6 +414,9 @@ def plotly_compare(
                          title_font=dict(size=11))
         fig.update_xaxes(title_text="Layer index", row=row_idx, col=1,
                          title_font=dict(size=11))
+        # ── log scale for condition number panel (row 6) ─────────────────────
+        if col == "cond_dual":
+            fig.update_yaxes(type="log", row=row_idx, col=1)
 
     _sync_yrange_compare(fig, df_a, df_b,
                          ["cosU_QK", "cosU_QV", "cosU_KV"], [7, 8, 9])