Five games: best prior technique vs the new math
Each game runs the same scene with the strongest technique a game developer would ship today and with the technique built on the new math, side by side, with live measurements. Click a title to play. Every page works offline; the README in each folder has the full numbers and the commands to reproduce them.
Wildfire Isle
Same gameplay at every graphics setting · fractal exponent weighting (Family 223 + the general recipe)
PRIOR BEST speeds and spawn rates in metres, tuned at Medium · REFERENCE always simulate at Ultra
NEW coarse grid, each step and shore tile weighted by (cell size)d
Fire arrival stays at 17.4–18.2 h (target 18) and spawns at 38–40 (target 40) on every grid, at coarse-grid cost: ~400× cheaper than simulating at Ultra. The prior drifts to 139 h and 65 spawns at Ultra.
Prior ties at the setting it was tuned for and nearly ties when terrain detail is fixed. Spawn positions differ between grids; only totals match. The fire exponent is proved; the coast exponent is measured (1.17).
Tavern of a Thousand Tables
Proof as playbook · the Snaky 21-move certificate (Family 187)
PRIOR BEST iterative-deepening α-β with a transposition table and threat ordering, sharing one 16.7 ms frame
NEW the proved strategy compiled into a lookup table
Playbook: 0.12–0.25 µs per move, 100% wins in ≤13 moves at every table count (16,384 tables in 3.2 ms). Search fits 3 tables per frame at full strength; starved, it falls to 42% at 64 tables and 0–12% from 256 up against a searching blocker.
With one table, search is affordable and also wins; starved search still beats a greedy blocker, just slower. The playbook exists only for this game and the builder's side, and ships 265 KB of data.
Colony Ledger
Type-check your simulation rules · weak reversibility ⇒ permanence (Family 149)
PRIOR BEST clamps and faucets, plus a Monte-Carlo balance sweep at save time
NEW recipe lint at save time ("every recipe needs a way back"), no clamps, one-click fix
The lint takes a few microseconds (1.5–7 µs), names the faulty recipes, and its pass holds for every rate and horizon. A 10-year sweep misses a slow-rotting chain (caught only at 20+ years); clamps hide a dead economy that sits pinned 92% of the time. Also switches a plague between burning out and endemic.
A sweep still wins when the lint passes but the game is unplayable (towns surviving on almost no food: the proof gives no minimum level), and for whole-number stockpiles the proof doesn't cover. Lint every save; keep sweeps for tuning.
Dungeon Daily
Certified randomness · Curveball with the proved trade count (Family 131)
PRIOR BEST lazy door swaps (common) and the configuration model with rejection (exactly fair)
NEW certified Curveball pair trades
With several big hubs (a 16-door square plus two 10-door halls) the exact prior needs ~165,000 deals per layout; certified Curveball takes 3–4 ms and wins by 5.6–32×.
On ordinary dungeons, and even with one 16-door square, the configuration model is exactly fair and 8.7×–37,000× faster: use it there. The quick swap is cheapest but keeps 1.5–3.7× the fair number of template corridors.
Slime Lab
Known best answer instead of a solver · isoperimetric sets of the flat 3-torus (Family 354)
PRIOR BEST coarse-to-fine threshold dynamics (MBO), tuned
NEW the proved shape (ball, tube, slab or hole) built in one pass
13–18× faster to the best surface (0.7 ms vs ~13 ms at 48³), exact by theorem. With a pillar (outside the theorem), starting the solver from a placed theorem shape gave lower area at 25% and mostly at 40% fill.
The tuned solver never got stuck at 48–64³ (0 of 72 starts), so the gain is speed and certainty, not rescue. Only the solver handles pillars, other cell shapes or gravity, and only it shows the slime flowing. The warm start didn't help at 10% fill.