COLONY LEDGER

Check the recipe book, not just the playtest

Every town runs the same recipe book. A recipe is safe when the goods it makes can be turned back into the goods it used, through other recipes. The game checks that rule each time you save, in a few microseconds, and names any recipe with no way back; the Fix button adds one. When every recipe passes, a proven result says no good can die out or pile up forever, at any recipe speeds. The usual approach caps every stockpile, sends relief when one runs dry, and plays many test towns for a set number of years. That keeps numbers on screen, but broken towns sit stuck at the caps, and a short test can miss a slow failure.

What's measured here

• NEW: lint time per save (performance.now() over 500 calls); share of towns where a good died out (< 1e-6), ran away (> 1e6) or sits below 1 unit, running with no clamps.
• PRIOR BEST: sweep time and flagged seeds for K random towns × H years; share of towns with a clamp or faucet firing now, and share of all town-time spent pinned.
• Sim cost per frame for each side (median of the last 60 frames). Both sides use the same log-space RK4 step rule from econ.js and the same towns (rates and starts per town).

Where the prior technique still wins / limits

• ?scene=starve: the lint passes, but farms are so slow that every town sits below 1 unit of food. The proof only says amounts stay above some level; it does not say how high. The sweep flags this at once (bench: 14 of 64 seeds within 1 year).
• ?scene=tiny: integer stockpiles of a few units. The proof is about smooth amounts, so it does not apply; about a third of towns have an empty stockpile at any moment, and the faucet hides that.
• Failing the lint means "no guarantee", not "will collapse": in the bench, removing any one of the nine colony recipes fails the lint, yet only 2 of those 9 books lost any town by year 1,000 (one lost every town, the other about 15%).
• The proof covers fixed positive rates; rates the player changes during a run, and how long the start-up wobble lasts, are not covered. A sweep can also test things the lint never looks at, such as pacing.
• A long enough sweep also catches the broken books (?scene=slowrot needs about 20 years instead of 5), but it costs K × H simulated town-years per save and only ever covers the rates it tried.

Presets (?scene=)

• broken (default): crowding and salvage removed. Lint fails on 4 recipes; one click on Fix restores exactly those two.
• fixed: all nine recipes. Both sides stay healthy; the sweep agrees but costs far more than the lint.
• plague: a sick/immune plague on workers (catch, recover, immunity fades). Lint fails; without clamps the plague burns out in some towns. Fix adds "nursing" and "traders carry plague in".
• endemic: the plague after the fix. It is the same theorem applied to the plague: the plague never dies out and never takes everyone.
• slowrot: the broken book with every rate ×0.2. The default 10-year sweep passes it; the lint does not.
• starve, tiny: the regimes above where the prior technique is the useful one.
• Other parameters: ?frames=N stops after N frames, ?towns=N, ?k=K, ?h=H (one of 1, 2, 5, 10, 20, 40, 80, 160, 320, 640).

Proved vs measured

• Proved (Family 149, Uniform Permanence in Weakly Reversible Mass-Action Systems, thm:main): if the lint passes, then for any fixed positive rates every good eventually stays between ε and 1/ε for some ε > 0 that the paper does not compute. The model is the continuous mass-action economy.
• Measured here: every timing, every percentage, and the collapse of the broken books. Nothing here says that every book that fails the lint collapses.