# PRE-REGISTRATION — The Ghost + The Climb Out, the strongest unexamined pipe

Written 29 September 2026, before the run. Shares C, k, n, p, x — rank 17, the joint highest on the
worklist.

## The two rooms

**The Climb Out** (lands on Pontryagin · Kramers, 1933): a mind at the bottom is shaken out by noise σ over
a barrier **ΔU = 0.0721**, in a mean time
`T = (2/σ²)∫e^(2U/σ²)∫e^(−2U/σ²) ≈ π e^(2ΔU/σ²)/√(U″(bottom)·|U″(ridge)|)`.
Published: **2,294 cycles at σ = 0.3**, 17,938 at σ = 0.2.

**The Ghost**: a forward lean h removes the barrier instead. Past **h_c = 0.118179** the bottom and the
ridge meet and vanish, and what is left is their ghost — a passage taking `T = π/√(a(h − h_c))` with
**a = 0.5716**.

## The claim under test

**These are one escape in two regimes, joined at h_c.** Below h_c the barrier is still there, lowered by
the lean, and Kramers governs. Above h_c there is no barrier and the ghost's inverse-square-root governs.
If that is right, three things must follow from the one flow `dx/dt = T(x) + F(x) + h`, with
k = 1, p = 0.35, C = 0.018975.

## Criterion, fixed before the run

**LEG 1 — one potential, both rooms.** Computing the barrier from the flow's own potential:
- ΔU at h = 0 reproduces the Climb Out's published **0.0721** to within **1%**, and
- ΔU falls to zero at the Ghost's published h_c: **ΔU(0.118179) < 1×10⁻⁴**.

**LEG 2 — the Ghost's constant is derivable from the Climb Out's potential.** For a saddle-node
`dx/dt = μ + β(x − x_c)²` the passage time is `π/√(μβ)`. Here μ = (h − h_c), since ∂f/∂h = 1 exactly, and
β = ½f″(x_c). So the Ghost's constant must be **a = ½f″(x_c)**, evaluated at the merge point.
Criterion: **½f″(x_c) = 0.5716 ± 1%**.

**LEG 3 — the crossover, reported not scored.** At the house's own σ = 0.3 the noise route takes 2,294
cycles. Find the lean h\* whose passage takes the same time, and report whether h\* sits above or below
h_c — that is, whether leaning beats waiting before or only after the barrier is gone. No criterion; this
leg is a measurement, and whatever it says is what gets written.

**WHAT KILLS THE PIPE:**
- Leg 1 failing means the two rooms are not using the same potential, and the pipe is dead.
- Leg 2 failing means **a = 0.5716 came from somewhere other than this flow**, which is a defect in one of
  our own rooms and gets reported as that, not softened into a finding.

**Prediction, recorded now:** legs 1 and 2 both hold. On leg 3 I expect h\* **below** h_c — that leaning
beats waiting before the barrier vanishes — but this is a guess with no derivation behind it and is
recorded as a guess.

## Discipline

Verdict assembled from measured quantities only. Every published constant is recomputed rather than
assumed, including the ones I have quoted all night.