Measuring the Device

The BPT law

BPT does not state this; it is a game method.

The established physics

None: a game method. It is the same idea as adaptive load control in real-time rendering, and the game already uses it in one place: the ring search, which times itself and grows by 15 % when a step takes under 4 ms and shrinks by 20 % over 8 ms (Chapter 3).

The game's math

Each system that does heavy work times its own step, t milliseconds for its current size n, and knows how its cost grows with n. Its ceiling V is the size that would just fill its share of the frame, the target τ:

For the screen, a Proto Well needs about 6 pixels across, core and ring, to read as its own well, so about 36 pixels of area: a phone's field of about 390 × 390 = 152,000 pixels gives V ≈ 4,000, and a desktop's of about 1,000,000 gives V ≈ 28,000.

V is smoothed so one slow frame does not swing it: each new measurement moves V a fraction of the way toward the new value. It starts from the device's own first measured step, not from its kind, so a strong phone and a weak desktop each find their own.

The targets are the one design choice the measurements need, proposed (30 October 2026) and to be confirmed:

• the drawn frame: 33 ms (30 frames a second);
• a physics flip: 1 s on a desktop, 2 s on a phone.

The scale model

V sets only what the device runs. The universe it stands for is the same on every device: a phone and a desktop running the same universe draw different numbers of things, each standing for a different share, and every total agrees.

Fixed numbers