Seeded Catch-up Kernel

A deterministic tick-simulation kernel where catching up 4,320 TICKS IN ONE BURST produces the EXACT SAME WORLD as ticking those 4,320 ticks live, one at a time.

THE SILENT FAILURE. A simulation that keeps running while nobody is looking -- a game world, an idle-game economy, a scheduled workflow -- must be caught up the moment someone returns. The obvious implementation is a loop: `while (tick < now) tick(state, tick++)`. It never throws. It also breaks in four ways that never announce themselves, because THE CAUGHT-UP WORLD ALWAYS LOOKS PLAUSIBLE ON ITS OWN.

The only way to notice is to compare it against a second copy of the same world that was never interrupted, and almost nobody keeps one of those around. This package's tests do.

CATCH-UP DIVERGES FROM LIVE if any tick function reads the wall clock, consumes randomness from a shared global stream, or accrues a rate by multiplying elapsed time instead of summing per-tick steps. Each is a reasonable line of code and each makes an away-from-keyboard player's world differ from a watching player's.

The kernel supplies a seeded, stream-derived PRNG so a given tick draws the same value whether it ran in a burst or live, and accrual that is summed rather than projected.

VERIFIED: 90 tests, measured by running the suite.

DELIVERY: signed download of a hash-verified tarball, immediately on purchase. Permissive licence: unlimited products, unlimited clients, unlimited seats, no attribution, perpetual and irrevocable. One restriction, do not republish the source as source.

Interface

What you call, and what comes back. Types and signatures only — the implementation ships with the source.

  export function accrueLinear(base: bigint, ratePerTick: bigint, ticks: bigint): bigint;
  export function runTicks<TState>( state: TState, fromTick: number, toTick: number, tickFn: TickFn<TState>, rootSeed: SeedPart, bounds?: CatchUpBounds ): CatchUpReport<TState>;
  export function ticksElapsed(elapsedMs: number, msPerTick: number): number;
  export function deriveSeed(parts: readonly SeedPart[]): bigint;
  export function createStream( rootSeed: SeedPart, domain: string, entityKey: string, tick: number, purpose = "" ): Pcg32;

  export type TickFn<TState> = (state: TState, tick: number, rootSeed: SeedPart) => TState;
  export type SeedPart = string | number | bigint;