Pith. sign in

Why is phi forced?

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

Self-similar closure forces r^2 = r + 1

A geometric scale sequence closed under additive ledger composition satisfies ledgerCompose(scale 0, scale 1) = scale 2, which simplifies directly to 1 + r = r². This is the golden constraint.

phi is the unique positive solution

The equation r² = r + 1 has unique positive root φ = (1 + √5)/2 among r > 0. phi_unique_self_similar

Cited Lean anchors

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.