```ts
/** Replay tile requests against a size-limited cache of fresh renders. */
export function tileRenders(requests: [number, string][], freshFor: number, size: number): [number, string][] {
  if (!Number.isInteger(freshFor) || freshFor < 1 || !Number.isInteger(size) || size < 1) {
    throw new Error("freshFor and size must be positive integers");
  }
  const held = new Map<string, number>();
  const renders: [number, string][] = [];
  for (const [tick, name] of requests) {
    if (tick >= freshFor && !held.has(name)) {
      // Serve a still-fresh render
      renders.push([tick, name]);
    } else if (!held.has(name)) {
      // Make room when full and record one
      const oldest = Array.from(held.entries()).sort((a, b) => a[1] - b[1])[0];
      held.delete(oldest[0]);
      renders.push([tick, name]);
    }
  }
  return renders;
}
```