reynoldsThreshold
plain-language theorem explainer
reynoldsThreshold sets the Reynolds number threshold at integer rung k to phi raised to the power k. Researchers classifying the five turbulent flow regimes on the Recognition Science phi-ladder would cite it to establish the geometric separation between laminar, transitional, fully-developed turbulent, inertial-range, and dissipative-subrange states. The declaration is introduced as a direct power definition with no auxiliary computation.
Claim. The Reynolds threshold at rung $k$ is defined by $R_k = phi^k$, where $phi$ is the Recognition Science self-similar fixed point.
background
The Navier-Stokes Regimes module enumerates five canonical turbulent-flow regimes corresponding to configDim D = 5: laminar, transitional, fully-developed turbulent, inertial-range, and dissipative-subrange. These regimes are separated by Reynolds number rungs placed on a phi-ladder. The module supplies only structural enumeration and states explicitly that it makes no claim about global regularity of the Navier-Stokes equations.
proof idea
This is a direct definition that sets reynoldsThreshold k equal to phi raised to the power k. No lemmas or tactics are invoked; the expression serves as the base for the ratio and positivity results that follow.
why it matters
The definition supplies the explicit phi-ladder rungs required by NavierStokesRegimesCert to certify that exactly five regimes exist and that consecutive thresholds satisfy the ratio phi. It implements the structural enumeration step that aligns with the Recognition Science forcing chain (T6 phi fixed point) and the eight-tick octave, while remaining silent on the Clay Millennium problem. The construction touches the open question of whether the phi-ladder enumeration can be extended to a regularity statement.
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