The Locks, Computed — an Interactive Annex to the Three Locks
The letter to Earth’s diplomats told the locks as a story: a toy car, a track that spawns its own blocks, an emperor with a serial-numbered bomb. The annex opens the hood. The track is de Sitter’s universe exactly, the 30,000-block wall is c/H, and every number in the letter — 17 hours 10 minutes 54 seconds, the 22-digit address, FTL-55b — falls out of three short equations, live on your screen.
After the Checkpoint, the road back: from the metaphors to the calculations. The sixteenth instrument gives each lock its own working dial. Lock I is a live race against the horizon — the whole story in one closed form, g(t) = 30 000 + (D₀ − 30 000)·eHt: press 29 999 and the gap crawls for seventeen hours then collapses at once; press 30 000 and it holds to the end of time; press 30 001 and it escapes. Lock II runs the emperor’s address book after the victory — the frontier’s coordinate gaining digits while it is spoken, the drive requirement climbing from FTL-54b to FTL-97q on schedule. Lock III draws the map against the bubble: demand scaling with volume, capacity with surface, and the crossing at sixteen femtometres — a live map of the universe finer than one nucleus per bit does not fit inside the universe.
Each lock carries a chip: the letter said → the integral says. The 29 999-block run lands on 17 h 10 m 54 s and 309 269 blocks driven; the day-two frontier lands on 2.9 sextillion blocks and a 22-digit address; year ten lands on 22,830 digits. The letter’s numbers were never rhetoric — they were solutions, and the annex lets anyone re-derive them from a(t) = eHt in an afternoon.