# PRE-REGISTRATION — is expectation h the same quantity as faith × belief?

Written 29 September 2026, before the run.

## Where this came from

Fixing the symbol map, not looking for a result. Two rooms print the same constant:

- **The Ghost** (`ghost`, lands on Pontryagin · Kramers): "Give a mind at the bottom a forward pull,
  expectation h, and past **h_c = 0.118179** the bottom and the ridge meet and vanish."
- **Faith and Belief** (`hope`, ours): "The ridge drops by γb/λ, and past **0.118179** the bottom stops
  existing."

The symbol map defines **h = "expectation, the forward term"**. The Flow in Faith and Belief adds its
forward term as **γ·b**. If both rooms are describing the same bifurcation, then the forward term is the
same object in both, and **h = γ·b** — expectation is faith times belief.

That is a claim, not an observation. Two rooms quoting one number could mean one was copied from the other.

## The test

Take the house's own flow with a constant forward term added:

    dx/dt = T(x) + F(x) + h,   T(x) = k[(1−x)^(−p) − 1],   F(x) = −2Cx/(1−x²)
    k = 1, p = 0.35, C = 0.018975

At h = 0 this has the published rest points: an attractor near −0.910797 (the bottom) and a saddle at 0
(the ridge). Raise h and they approach. Find the h at which they merge — the saddle-node point, where
dx/dt = 0 and d/dx(dx/dt) = 0 at the same x.

## Criterion, fixed before the run

**CONFIRMED** if the computed saddle-node value of the forward term equals the published h_c = 0.118179 to
**four decimal places or better** (|computed − 0.118179| < 5e-5).

**FAILS** if it does not. Then the two rooms print the same number for different reasons, the constant in
Faith and Belief was carried over rather than derived, and that is a defect in our own room to be reported,
not a pipe.

**Prediction, recorded now:** CONFIRMED. If it fails I will report the failure as a defect in our room.

## Second leg, same run

If the first leg confirms, then h = γ·b, and the threshold is a **product**: a mind crosses it by faith,
by belief, or by any pair whose product reaches h_c. Record the curve γ·b = h_c and the value of γ needed
at b = 1 (full belief), b = 0.5 and b = 0.25. No claim is registered about what that means; the numbers are
recorded so the reading can be his.

## Discipline

Verdict assembled from measured quantities. No conclusion written into the script. Nothing here edits the
page; the symbol-map and declared-variable fix is a separate script and does not depend on this result.