compression_3_discs
The declaration establishes that a three-disc Tesla turbine stack produces a total compression ratio of exactly φ cubed. Engineers selecting minimal stable stages in bladeless turbines would cite this when partitioning flow across Fibonacci-adjacent disc counts to keep J-cost low. The equality follows at once by direct substitution into the definition of total compression ratio.
claimThe total compression ratio for a turbine stack with three discs equals $φ^3$.
background
In the Recognition Science model of the Tesla turbine the fluid follows a logarithmic spiral whose pitch κ is set to one. The total compression ratio across N turns is then defined as φ raised to N. This scaling arises because κ = 1 yields the minimum non-trivial stable compression step per turn while satisfying the Recognition Composition Law for the velocity profile across each gap.
proof idea
The proof is a one-line reflexivity wrapper that unfolds the definition of totalCompressionRatio at N = 3 and confirms the right-hand side is φ^3 by construction.
why it matters in Recognition Science
This supplies the N = 3 case in the sequence of results showing that Fibonacci disc counts minimize distribution cost. It supports the master certificate tesla_turbine_master referenced in the module documentation and instantiates the φ-scaling required by the self-similar fixed point at T6 of the forcing chain.
scope and limits
- Does not prove global optimality among all possible disc counts.
- Does not incorporate viscous dissipation or real-fluid boundary-layer corrections.
- Does not address non-integer or variable-pitch spiral turns.
formal statement (Lean)
163theorem compression_3_discs : totalCompressionRatio 3 = phi ^ 3 := rfl