Pith. sign in

prod probe 2

Big AI job. Grok 4.3 reads the canon and writes a Lean-grounded derivation; usually 20 seconds to 2 minutes. Your answer will appear below.
confidence: high in recognition cached

The FRWComponentsProbe module encodes flat FRW geometry with metric components gMetric and inverse gInv, coordinate derivatives pd, and Christoffel symbols Γ.

Probe 2 requires Γ¹₀₁ = ȧ a / a².

Γ_1_01 states: Γ a 1 0 1 t = deriv a t * a t / (a t) ^ 2

Proof: simp [Γ, gInv, pd, Fin.sum_univ_four, deriv_a_sq a ha, gMetric_offdiag ...] followed by ring.

(The supplied slice contains no further simplification to ȧ/a, but the stated form matches the probe goal verbatim.)

cited recognition theorems

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.