diff --git a/open-sse/translator/concerns/thinking.js b/open-sse/translator/concerns/thinking.js
index 3db892c4..4bcf559c 100644
--- a/open-sse/translator/concerns/thinking.js
+++ b/open-sse/translator/concerns/thinking.js
@@ -34,6 +34,8 @@ export function effortToThinkingLevel(effort) {
 
 // Numeric budget → nearest discrete level (reverse map via thresholds).
 // Returns null when budget <= 0 (no reasoning).
+// Thresholds are midpoints between LEVEL_TO_BUDGET values: max (128000) is
+// reachable, with the xhigh/max boundary at the 32768/128000 midpoint (80384).
 export function budgetToLevel(budget) {
   const b = Number(budget);
   if (!b || b <= 0) return null;
@@ -41,7 +43,8 @@ export function budgetToLevel(budget) {
   if (b <= 4096) return "low";
   if (b <= 16384) return "medium";
   if (b <= 28672) return "high";
-  return "xhigh";
+  if (b <= 80384) return "xhigh";
+  return "max";
 }
 
 // Gemini thinkingBudget (numeric) → OpenAI reasoning_effort (antigravity reverse map).
diff --git a/src/lib/db/repos/usageRepo.js b/src/lib/db/repos/usageRepo.js
index 0d8aa96f..75267847 100644
--- a/src/lib/db/repos/usageRepo.js
+++ b/src/lib/db/repos/usageRepo.js
@@ -537,8 +537,15 @@ export async function getUsageStats(period = "all") {
       }
     }
 
-    // Overlay precise lastUsed timestamps from history
-    const overlayCutoff = maxDays ? Date.now() - maxDays * 86400000 : 0;
+    // Overlay precise lastUsed timestamps from history.
+    // ponytail: overlay scans only a recent window; entries older than that keep
+    // day-level lastUsed from usageDaily. Upgrade to a materialized per-key
+    // MAX(timestamp) table if exact old timestamps ever matter.
+    const OVERLAY_WINDOW_MS = 2 * 86400000;
+    const overlayCutoff = Math.max(
+      maxDays ? Date.now() - maxDays * 86400000 : 0,
+      Date.now() - OVERLAY_WINDOW_MS
+    );
     const histRows = db.all(
       `SELECT timestamp, provider, model, connectionId, apiKey, endpoint FROM usageHistory WHERE timestamp >= ?`,
       [new Date(overlayCutoff).toISOString()]
diff --git a/tests/unit/thinking-budget-max-level.test.js b/tests/unit/thinking-budget-max-level.test.js
new file mode 100644
index 00000000..c098ab91
--- /dev/null
+++ b/tests/unit/thinking-budget-max-level.test.js
@@ -0,0 +1,39 @@
+import { describe, expect, it } from "vitest";
+import { budgetToLevel } from "../../open-sse/translator/concerns/thinking.js";
+import { applyThinking } from "../../open-sse/translator/concerns/thinkingUnified.js";
+import { FORMATS } from "../../open-sse/translator/formats.js";
+
+// Reverse map must be able to reach "max": LEVEL_TO_BUDGET.max = 128000 and
+// xhigh = 32768, so the xhigh/max threshold is their midpoint (80384).
+// Previously any budget > 28672 collapsed to "xhigh", making "max"
+// unreachable from Claude Code budget_tokens — its default thinking budget
+// (MAX_THINKING_TOKENS) could never produce effort "max".
+describe("budgetToLevel reaches max tier", () => {
+  it("budget 98304 → \"max\"", () => {
+    expect(budgetToLevel(98304)).toBe("max");
+  });
+
+  it("budget 128000 → \"max\"", () => {
+    expect(budgetToLevel(128000)).toBe("max");
+  });
+
+  it("budget 80385 → \"max\" (just above midpoint)", () => {
+    expect(budgetToLevel(80385)).toBe("max");
+  });
+
+  it("budget 80384 → \"xhigh\" (midpoint still xhigh)", () => {
+    expect(budgetToLevel(80384)).toBe("xhigh");
+  });
+
+  it("budget 31999 stays \"xhigh\"", () => {
+    expect(budgetToLevel(31999)).toBe("xhigh");
+  });
+});
+
+describe("applyThinking (openai-responses): large budgets map to max effort", () => {
+  it("budget 98304 → reasoning_effort \"max\" for gpt-5.6-sol (openai wire)", () => {
+    const body = { thinking: { type: "enabled", budget_tokens: 98304 } };
+    const out = applyThinking(FORMATS.OPENAI_RESPONSES, "gpt-5.6-sol", body, "codex");
+    expect(out?.reasoning_effort).toBe("max");
+  });
+});