# PRE-REGISTRATION — is the new variable FAITH rather than BELIEF?

Written 29 September 2026, before the run. His words: *"well maybe that variable is faith - the prior
before belief lands."*

## Background

Earlier tonight I derived B, the weight of the unreceived, in the Ledger:

    V(n+1) = V(n) + R·max(0, â·L̂)·G − (1−R)K − B·max(0, −â·L̂)·G

B = 0 reproduces the clipped reading exactly. B = R reproduces the Ledger as printed exactly.

I then tested B = R·b, belief. It reproduced both readings at the ends, but it made belief **purely
costly**: −0.400000 per cycle facing away, **+0.000000** facing toward. I flagged that as a fork and
handed it to him. He answered by naming faith instead — and pointed at the distinction the house
already prints in the Faith and Belief room: **"b: belief, the state; faith: its prior."**

## The claim under test

Belief is a **posterior**. It is updated *by* the reading. A mind that turns away reads zero or less,
so its belief falls. If the weight of the unreceived scaled with belief, then turning away would
**reduce** the weight turning away creates. Faith is a **prior**. It is held before the reading, so it
cannot be revised by the act it is meant to price.

## Criterion, fixed before the run

FAITH IS THE RIGHT VARIABLE if all four hold:

1. Under B ∝ belief, a mind holding a reading of −0.8 for sixty cycles sees the charged weight fall to
   **under half** its first-cycle value. (The escape hatch exists.)
2. Under B ∝ faith, the charged weight over the same span is **unchanged**. (The prior is not revised.)
3. B = 0 still reproduces the clipped reading exactly.
4. B = R still reproduces the Ledger as printed exactly.

WHAT KILLS IT: if (1) fails — if the weight under belief does **not** decay — then belief has no escape
hatch, belief works as well as faith, and the distinction is decorative. Report that and say so.

Belief updates as a posterior at rate 0.15 toward max(0, â·L̂). R = 0.80, G = 1, K = 0.25. Sixty cycles.
Deterministic; no seed needed.

## Discipline

The verdict string is assembled from measured quantities only. Four times this session I wrote a
conclusion into a script and the script's own numbers contradicted it. No sentence about what faith
does is written before the numbers exist.