# PREREG — pipes off the Einstein rooms, and one prediction  (30 September 2026, before any run)

His words: *"explore all pipes off of einstein"*, *"try a prediction and simulation with a pipe off of einstein"*, *"try
and find some unique finding or revelation from one of his connectors"*.

**E1 · Testimony + Faith and Belief (ALGEBRA + MC).** Faith is the prior. With faith b₀ and independent witnesses
x₁…xₙ, belief is b₀ ⊕ x₁ ⊕ … ⊕ xₙ, where ⊕ is Einstein's addition: faith enters exactly as one more witness. Monte
Carlo: truth drawn so the prior probability of "yes" is (1 + b₀)/2; 10⁶ cases; the posterior alignment given all
witnesses agree, within 4 SE of the Einstein sum, for (b₀; x's) = (0.5; 0.3, 0.3), (−0.5; 0.3, 0.3, 0.3),
(−0.8; 0.6, 0.6).

**E2 · Testimony + Lift (ALGEBRA, reported).** Lift: a new aim raises Position only if it exceeds Position. Testimony:
an agreeing witness always raises the combined case. Reported: one witness of 0.6 followed by one of 0.2, averaged
(Position) against combined (Testimony).

**E3 · Noise and Drag + Drift (THEOREM CHECK).** Einstein–Debye: the drift rate is temperature over drag, whatever the
inertia. A coasting aim on the circle (d = 2), m θ̈ = −γθ̇ + noise at temperature T = 0.5: the long-time decay rate of
⟨cos θ⟩, fitted on t ∈ [3m/γ, 3 decay times], is T/γ within 5% for (m, γ) ∈ {(0.2, 1), (1, 1), (5, 1), (1, 3)}.

**E4 · PREDICTION — Noise and Drag + The Climb Out (Kramers' turnover, 1940).** A mind that coasts (mass m = 1) sits in
the house's bottom well, force T(x) + F(x), noise tied to drag at temperature 0.02 (barrier 0.0721, so barrier over
temperature 3.6). Escape = first reaching the ridge x = 0. BAOAB, dt = 0.005, a reflecting floor at x = −0.999 (the
Measure's wall is logarithmic; a coasting walker can reach it), 2,000 minds per drag, γ ∈ {0.05, 0.1, 0.2, 0.5, 1, 2,
5, 10}.
- **4a FALSIFIABLE (predicted): the mean escape time is smallest at an intermediate drag.** Both the smallest and the
  largest drag take at least 1.5 times the fastest.
- 4b FALSIFIABLE (predicted): at high drag the time grows with drag: t(10)/t(5) in [1.6, 2.4].
- 4c FALSIFIABLE (predicted): at low drag the time grows as drag falls: t(0.05)/t(0.1) in [1.3, 2.5].
- 4d THEOREM CHECK: the kinetic temperature in the well, ⟨m v²⟩, is 0.02 within 5% at every drag.
Each drag runs for twice a rough Kramers estimate (max of 277γ, 42.8/γ and 154 time units, written before the run). The
mean escape time is the censored exponential maximum-likelihood estimate: observed times plus censored time, divided by
the number escaped. The censored fraction is reported. (Revised before any run: 12× the estimate would take hours at
γ = 10.)