fix: apply crystal multiplier to boss rewards, steepen prestige threshold, fix stale upgrade race condition, and fix companion format display

Closes #221
Closes #222
Closes #201
Closes #213

apps/api/test/routes/game.spec.ts

@@ -477,6 +477,28 @@ describe("game route", () => {
       expect(body.savedAt).toBeGreaterThan(0);
     });
 
+    it("restores previous upgrades when incoming prestige count is lower (stale post-prestige save)", async () => {
+      const prevUpgrades = [
+        { id: "click_1", purchased: false, unlocked: true, target: "click", multiplier: 2 },
+      ] as GameState["upgrades"];
+      const prevState = makeState({
+        prestige: { count: 1, runestones: 10, productionMultiplier: 1.3, purchasedUpgradeIds: [] },
+        upgrades: prevUpgrades,
+      });
+      const incomingState = makeState({
+        prestige: { count: 0, runestones: 0, productionMultiplier: 1, purchasedUpgradeIds: [] },
+        upgrades: [
+          { id: "click_1", purchased: true, unlocked: true, target: "click", multiplier: 2 },
+        ] as GameState["upgrades"],
+      });
+      vi.mocked(prisma.gameState.findUnique).mockResolvedValueOnce({ state: prevState } as never);
+      vi.mocked(prisma.player.findUnique).mockResolvedValueOnce(makePlayer({ createdAt: Date.now() }) as never);
+      vi.mocked(prisma.player.update).mockResolvedValueOnce({} as never);
+      vi.mocked(prisma.gameState.upsert).mockResolvedValueOnce({} as never);
+      const res = await save({ state: incomingState });
+      expect(res.status).toBe(200);
+    });
+
     it("validates companion when active companion is legitimately unlocked", async () => {
       const prevState = makeState();
       const stateWithCompanion = makeState({

apps/api/test/routes/prestige.spec.ts

@@ -81,6 +81,16 @@ describe("prestige route", () => {
       expect(res.status).toBe(400);
     });
 
+    it("returns 400 with echoPrestigeThresholdMultiplier applied when transcendence is present", async () => {
+      const state = makeState({
+        player: { discordId: DISCORD_ID, username: "u", discriminator: "0", avatar: null, totalGoldEarned: 500_000, totalClicks: 0, characterName: "T" },
+        transcendence: { count: 1, echoes: 0, purchasedUpgradeIds: [], echoIncomeMultiplier: 1, echoCombatMultiplier: 1, echoPrestigeThresholdMultiplier: 2, echoPrestigeRunestoneMultiplier: 1, echoMetaMultiplier: 1 },
+      });
+      vi.mocked(prisma.gameState.findUnique).mockResolvedValueOnce({ state } as never);
+      const res = await post("");
+      expect(res.status).toBe(400);
+    });
+
     it("returns runestones on successful prestige", async () => {
       const state = makeState();
       vi.mocked(prisma.gameState.findUnique).mockResolvedValueOnce({ state, updatedAt: 0 } as never);

apps/api/test/services/prestige.spec.ts

@@ -55,18 +55,18 @@ const makeMinimalState = (overrides: Partial<GameState> = {}): GameState =>
 
 describe("calculatePrestigeThreshold", () => {
   it("returns base threshold at count 0", () => {
-    // base × (0+1)^2 = 1_000_000 × 1 = 1_000_000
+    // base × (0+1)^2.5 = 1_000_000 × 1 = 1_000_000
     expect(calculatePrestigeThreshold(0)).toBe(1_000_000);
   });
 
-  it("returns 4× base at count 1", () => {
-    // base × (1+1)^2 = 1_000_000 × 4 = 4_000_000
-    expect(calculatePrestigeThreshold(1)).toBe(4_000_000);
+  it("returns base × 2^2.5 at count 1", () => {
+    // base × (1+1)^2.5 = 1_000_000 × 2^2.5
+    expect(calculatePrestigeThreshold(1)).toBeCloseTo(1_000_000 * Math.pow(2, 2.5));
   });
 
-  it("returns 9× base at count 2", () => {
-    // base × (2+1)^2 = 1_000_000 × 9 = 9_000_000
-    expect(calculatePrestigeThreshold(2)).toBe(9_000_000);
+  it("returns base × 3^2.5 at count 2", () => {
+    // base × (2+1)^2.5 = 1_000_000 × 3^2.5
+    expect(calculatePrestigeThreshold(2)).toBeCloseTo(1_000_000 * Math.pow(3, 2.5));
   });
 
   it("applies threshold multiplier correctly", () => {