spiralRadius
plain-language theorem explainer
The φ-log-spiral radius function sets radial distance to initial radius times phi raised to the power of integer kappa times angle over 2 pi. Researchers modeling Nautilus-class access paths for Class C powers cite it when encoding tier-dependent geometric scaling. The definition is realized as a direct noncomputable expression using real multiplication and exponentiation.
Claim. $r(θ) = r_0 · ϕ^(κ θ / (2 π))$ where $r_0$ is the base radius, $κ ∈ ℤ$ the integer index, and $θ$ the angle.
background
The Superhuman.TechnologicalAccess module formalizes the Nautilus-class technological access path for Class C powers. It treats power tiers and engineering parameters as MODEL structural definitions drawn from the NTL provisional patent stack, while importing PROVED results such as Gap45 safety constraints.
proof idea
This is a one-line definition that multiplies the initial radius by phi raised to the exponent (kappa * theta) / (2 * Real.pi). It uses only the built-in real exponentiation with no additional lemmas applied.
why it matters
The definition supplies the geometric scaling for spiral structures in Nautilus power tiers and feeds the downstream positivity theorem. It instantiates phi-ladder scaling from the Recognition framework, consistent with T6 where phi is the self-similar fixed point and the eight-tick octave structure.
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