# Pre-registration: the reversal horizon (written 2026-09-26, before measure.mjs was run)

Exploratory runs so far (seed 1 only, one nudge size, deleted scratch scripts): the integer gas
returns bit-for-bit after every reversal time tried up to 6,000 steps; a one-grid-step nudge
(2^-32 of the box) given to disk 0 at the moment of reversal broke the return somewhere between
1,500 and 2,750 steps; the floating-point gas broke between 3,000 and 4,250. Forward separation
between a nudged and an unnudged copy grew at roughly 3 bits per 250 steps. Nothing else has
been looked at.

## What measure.mjs will do (fixed now)
- Gas: engine.mjs DEFAULTS (N = 128 WCA disks, sigma = 0.05 box, dt = 2.5e-4), seeds 1..5.
- **Rate.** For each seed: run 4,000 steps from the start (mixed), copy, nudge disk d by one grid
  step in x (d = 0..7), run both 3,000 steps recording log2(max separation in grid steps) every 25
  steps. The rate r (bits per step) is the least-squares slope over the samples with
  8 <= log2 sep <= 24. Per-seed r = mean over the 8 disks.
- **Horizon.** From the start (all disks left), run T steps, nudge disk 0 by 2^k grid steps in x,
  reverse, run T steps, reverse. The return FAILS if any disk ends more than sigma from where it
  started. T scanned 100..8,000 in steps of 100; the horizon is the first failing T.
  k in {0, 4, 8, 12, 16, 20, 24}. Also k = none (no nudge), and the floating gas with no nudge.

## Predictions
1. With no nudge the integer gas never fails, at any T scanned, any seed. (Must hold exactly;
   if it fails, the engine is wrong, and the page does not ship until it is found.)
2. Horizon falls linearly with k: the least-squares slope of horizon against k (per seed) equals
   -1/r to within 25%, where r is that seed's independently measured rate.
3. The floating gas fails at a finite T for every seed, later than the k = 0 integer horizon.
   (Its size is not predicted: roundoff is not a single nudge, so we only report the k at which
   the fitted line would reach it, as the float gas's "effective nudge".)

If 2 fails, the page says so and shows the numbers; it does not re-fit with a different window.