fix: rewrite prestige/transcendence formula and rebalance progression

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

@@ -55,15 +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
     expect(calculatePrestigeThreshold(0)).toBe(1_000_000);
   });
 
-  it("returns 5× at count 1", () => {
-    expect(calculatePrestigeThreshold(1)).toBe(5_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 25× at count 2", () => {
-    expect(calculatePrestigeThreshold(2)).toBe(25_000_000);
+  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("applies threshold multiplier correctly", () => {
@@ -128,12 +131,12 @@ describe("calculateProductionMultiplier", () => {
     expect(calculateProductionMultiplier(0)).toBe(1);
   });
 
-  it("returns 1.15 at count 1", () => {
-    expect(calculateProductionMultiplier(1)).toBeCloseTo(1.15);
+  it("returns 1.25 at count 1", () => {
+    expect(calculateProductionMultiplier(1)).toBeCloseTo(1.25);
   });
 
   it("scales exponentially", () => {
-    expect(calculateProductionMultiplier(10)).toBeCloseTo(Math.pow(1.15, 10));
+    expect(calculateProductionMultiplier(10)).toBeCloseTo(Math.pow(1.25, 10));
   });
 });