Fixed Numbers and Their Kinds

Every chapter ends each law with a table of the fixed numbers in its code, and each number is given its kind. The kinds say where a number comes from, so a reader can tell a constant of nature from a choice made to run the game. One ruling governs them (Josh, 29 and 30 October 2026): a count, a size or a reach the game simulates or draws is never stopped at a number someone picked; it comes from the universe and from what the device can measurably do.

A universe at level 202 holds about 2^(202/3) ≈ 2 × 10^20 wells and more stars than that; no device draws them. The game has always drawn fewer. The question is only how the fewer are chosen. A cap such as min(400, cells/64) chooses by a number. A curve that bends toward a number chosen by hand, such as T·(1 − e^(−x/T)) with T a quarter of the grid, chooses by a number too, more quietly: it reaches T in whole numbers once x passes about 10 T. Both are caps.

How a count is set instead:

1. The count comes from what is really there, x: the law's wells, the real quanta of matter, the real cells of the level.
2. The ceiling comes from the device, V: what it can draw or compute in its frame, measured as it runs (Part 9.3), never assumed from its kind.
3. One law joins them, the Saturation Law (Part 9.2): the drawn count rises with every larger universe, never reaches V, and never exceeds x.
4. Each drawn thing stands for x ÷ drawn of the real ones (Part 9.1), so every total the physics needs stays exact.

The kinds: