compression_8_discs
An 8-disc Tesla turbine stack realizes a total compression ratio of exactly φ^8 when the per-turn spiral pitch equals 1. Turbine designers selecting Fibonacci disc counts for minimal flow-distribution cost would cite this equality to compute stage performance. The proof is a one-line reflexivity that follows immediately from the definition of totalCompressionRatio.
claimThe total compression ratio across a turbine with 8 discs equals $φ^8$.
background
In the Tesla turbine model, fluid follows a logarithmic spiral between closely spaced discs, with momentum transfer governed by boundary-layer adhesion. The module defines totalCompressionRatio N as φ^N at unit pitch κ=1, so the cumulative ratio after N turns is simply the power. Disc counts are restricted to Fibonacci numbers because they minimize J-cost of the velocity profile across the stack, as established by the upstream CellularAutomata.step locality and the phi-ladder construction.
proof idea
The proof is a one-line reflexivity wrapper that applies the definition totalCompressionRatio N := phi ^ N directly at N=8.
why it matters in Recognition Science
This equality supplies one concrete instance of the Fibonacci disc-count hierarchy that feeds the master certificate tesla_turbine_master. It instantiates the φ-scaling forced by the Recognition Composition Law and the self-similar fixed point T6, confirming that each Fibonacci step multiplies compression by an integer power of φ. No open scaffolding remains for this specific case.
scope and limits
- Does not prove that 8 discs is optimal outside the Fibonacci sequence.
- Does not incorporate viscous dissipation or real-fluid losses.
- Does not address manufacturing tolerances on disc spacing.
formal statement (Lean)
165theorem compression_8_discs : totalCompressionRatio 8 = phi ^ 8 := rfl
proof body
Term-mode proof.
166
167/-- The ratio between consecutive Fibonacci-count compressions is φ.
168 φ^{F_{n+1}} / φ^{F_n} = φ^{F_{n+1} - F_n} = φ^{F_{n-1}}.
169
170 This means stepping from a 5-disc to an 8-disc turbine
171 multiplies the compression by φ³ = φ⁵/φ² = φ^(8-5).
172
173 The Fibonacci disc counts form a natural hierarchy where each
174 step up in complexity provides φ-scaled improvement. -/