Working-set figure: extend left panel to ~50 nodes

Include T=600s/1800s points so the diminishing-returns tail is visible:
14 -> 52 nodes buys only +6pp APC (74%->79.8%), still under the 80.4%
ceiling that oracle/LRU reaches at 14 nodes.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

scripts/working_set_analysis.py

@@ -166,12 +166,12 @@ def plot(ws, hw, block_bytes, label, out_path):
     ceil = ws["apc_ceiling"] * 100
     oracle_nodes = ws["oracle_peak_blocks"] * bgb / pool
 
-    # operating points up to the ceiling: beyond oracle, TTL is strictly worse, so drop.
+    # all operating points, out to the largest retention window (~50 nodes)
-    rows = [r for r in ws["taus"] if r["tau"] <= 300]
+    rows = list(ws["taus"])
     nodes = np.array([r["peak_blocks"] * bgb / pool for r in rows])
     apc = np.array([r["apc"] * 100 for r in rows])
-    tau = np.array([r["tau"] for r in rows])
+    XMAX_L = 53      # left panel x-axis (nodes), shows up to T=1800s (~52 nodes)
-    XMAX = 16
+    XMAX_R = 16      # right panel y-axis (nodes)
 
     fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6))
 
@@ -182,30 +182,33 @@ def plot(ws, hw, block_bytes, label, out_path):
     ax1.scatter([1], [apc_at_1], s=90, facecolors="none", edgecolors="#ff7f0e",
                 lw=2, zorder=6)
     ax1.annotate(f"1 node -> ~{apc_at_1:.0f}% APC\n(TTL model; real LRU higher)",
-                 (1, apc_at_1), textcoords="offset points", xytext=(12, -2),
+                 (1, apc_at_1), textcoords="offset points", xytext=(14, 8),
-                 fontsize=9, color="#ff7f0e", va="top")
+                 fontsize=9, color="#ff7f0e", va="bottom")
     # label the well-separated decision-zone points
     for r, x, y in zip(rows, nodes, apc):
         if x >= 1.5:
-            ax1.annotate(f"keep {r['tau']:g}s reuse", (x, y),
+            ax1.annotate(f"{r['tau']:g}s", (x, y),
-                         textcoords="offset points", xytext=(6, 6), fontsize=8.5)
+                         textcoords="offset points", xytext=(5, 6), fontsize=9)
-    ax1.annotate("T<=10s reuse:\nall < 1.4 nodes", (0.5, 22), fontsize=8.5,
+    ax1.annotate("T<=10s reuse:\nall < 1.4 nodes", (1.5, 18), fontsize=8.5,
                  color="#1f77b4", ha="left")
+    # diminishing returns past the oracle point
+    ax1.annotate("diminishing returns:\n14 -> 52 nodes buys only +6pp",
+                 (30, 64), fontsize=9, color="#555", ha="center")
     # budget + ceiling
     ax1.axvspan(0, 1, color="#2ca02c", alpha=.08)
     ax1.axvline(1, ls="--", color="#2ca02c", lw=1.8)
-    ax1.text(1.05, 96, "1 B300 node (your budget)", color="#2ca02c", fontsize=9, va="top")
+    ax1.text(1.6, 96, "1 B300 node (your budget)", color="#2ca02c", fontsize=9, va="top")
     ax1.scatter([oracle_nodes], [ceil], marker="*", s=340, color="#d62728", zorder=7)
-    ax1.annotate(f"ceiling {ceil:.1f}%\noracle: {oracle_nodes:.0f} nodes",
+    ax1.annotate(f"ceiling {ceil:.1f}% — oracle/LRU\nreaches it at {oracle_nodes:.0f} nodes",
-                 (oracle_nodes, ceil), textcoords="offset points", xytext=(-10, -8),
+                 (oracle_nodes, ceil), textcoords="offset points", xytext=(12, -4),
-                 fontsize=9, color="#d62728", ha="right", va="top")
+                 fontsize=9, color="#d62728", ha="left", va="top")
     ax1.axhline(ceil, ls=":", color="#d62728", alpha=.5)
-    ax1.set_xlim(0, XMAX); ax1.set_ylim(0, 100)
+    ax1.set_xlim(0, XMAX_L); ax1.set_ylim(0, 100)
-    ax1.set_xticks(range(0, XMAX + 1, 2)); ax1.set_xticks(range(0, XMAX + 1), minor=True)
+    ax1.set_xticks(range(0, 51, 10)); ax1.set_xticks(range(0, XMAX_L, 5), minor=True)
     ax1.set_xlabel(f"# nodes of GPU HBM needed   (1 node = {gpr}x {hw['gpu']} = {pool:.0f} GB KV)")
     ax1.set_ylabel("Prefix-cache hit rate  (APC %)")
     ax1.set_title("Benefit vs cost: APC per cluster size", fontweight="bold")
-    ax1.grid(alpha=.3); ax1.grid(alpha=.15, which="minor"); ax1.legend(loc="center right")
+    ax1.grid(alpha=.3); ax1.grid(alpha=.15, which="minor"); ax1.legend(loc="lower right")
 
     # ===== panel 2: working set W(t) over time (steady -> peak ~ median) =====
     apc_of = {r["tau"]: r["apc"] * 100 for r in ws["taus"]}
@@ -221,7 +224,7 @@ def plot(ws, hw, block_bytes, label, out_path):
     ax2.axhline(oracle_nodes, ls="--", color="#d62728", lw=1.6, alpha=.8)
     ax2.text(t_min.max(), oracle_nodes, " ceiling: 14 nodes", color="#d62728",
              fontsize=8.5, va="center")
-    ax2.set_ylim(0, XMAX); ax2.set_yticks(range(0, XMAX + 1, 2))
+    ax2.set_ylim(0, XMAX_R); ax2.set_yticks(range(0, XMAX_R + 1, 2))
     ax2.set_xlim(0, t_min.max())
     ax2.set_xlabel("wall-clock time into the trace  (min)")
     ax2.set_ylabel("# nodes of GPU HBM resident  (W(t))")