 100Just as proteins fold in the biological octave,
 101Lean proofs "fold" in the logical octave.
 102-/
 103structure FormalizationAsOctave where
 104  /-- The logical octave. -/
 105  octave_type : String
 106  /-- The strain functional (proof complexity). -/
 107  strain : LeanCode → ℕ  -- Lines of proof, or similar metric
 108  /-- Lower strain = simpler proof = more "elegant". -/
 109  elegance : LeanCode → ℝ
 110
 111/-- The RRF formalization as an octave. -/
 112def rrfFormalizationOctave : FormalizationAsOctave := {
 113  octave_type := "logical",
 114  strain := fun c => c.source.length,  -- Simplistic: length as complexity
 115  elegance := fun c => 1.0 / (c.source.length : ℝ)
 116}
 117
 118
 119/-! ## Fixed Point Structure -/
 120
 121/-- A fixed point: the description describes itself accurately. -/
 122structure DescriptiveFixedPoint where
 123  /-- The description. -/
 124  description : RRFDescription
 125  /-- The description describes something with the same structure. -/
 126  self_similar : description = description  -- Trivially true, but captures the idea
 127
 128/-- The RRF is a fixed point of description. -/
 129def rrf_is_fixed_point : DescriptiveFixedPoint := {
 130  description := currentRRF,
 131  self_similar := rfl
 132}
 133

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