scaleByPhi
The definition multiplies a real quantity by phi to the integer power n, shifting it by n rungs on the phi-ladder. Workers in Recognition Science units apply it when rescaling masses, lengths, or energies while staying inside the tick-voxel system. It is realized as a direct multiplication by the result of phiRung.
claimFor real number $x$ and integer $n$, the scaled quantity equals $x$ times the golden ratio raised to the power $n$.
background
The RSNativeUnits module defines a native measurement system based on tick as the time quantum and voxel as the spatial quantum, with $c$ set to unity. All derived quantities such as energy and action are expressed using powers of phi, and the phi-ladder provides the scaling mechanism for masses, energies, times, and lengths. The upstream phiRung definition supplies the explicit computation of the golden ratio raised to integer $n$.
proof idea
one-line wrapper that applies phiRung
why it matters in Recognition Science
This definition belongs to the constants module and supplies the scaling primitive for the phi-ladder described in the module documentation. It supports the framework's requirement that all dimensionless ratios are fixed by phi alone. With no recorded downstream applications, it remains available for use in mass formulas and other derived quantities on the ladder.
scope and limits
- Does not compute rung indices from physical values.
- Does not convert between native and SI units.
- Does not handle fractional rungs or continuous scaling.
formal statement (Lean)
155@[simp] noncomputable def scaleByPhi (x : ℝ) (n : ℤ) : ℝ := x * phiRung n
proof body
Definition body.
156