minimal_alphabet (theorem)

/-- [I.T09] **The Minimal Alphabet Theorem**: 5 generators is the unique cardinality achieving all three properties: **(a) Completeness**: All rewiring levels through exponentiation have canonical orbit channel assignments (π↔+, γ↔×, η↔^). **(b) Rigidity**: No non-trivial ρ-automorphism exists. (4 generators also have this, but 6 do not.) **(c) Saturation**: Tetration (level 4) has no channel, and is algebraically degraded (non-commutative, non-associative, no left identity). Moreover, the counter-models show: - **4 generators FAIL completeness**: exponentiation loses its channel (only 2 solenoidal generators for 3 rewiring levels) - **6 generators FAIL rigidity**: the swap η↔ζ is a non-trivial ρ-automorphism (surplus solenoidal generator creates ambiguity) This establishes |Gen| = 5 as the *unique* solution to the simultaneous requirements of completeness + rigidity + saturation. -/