gap45
plain-language theorem explainer
gap45 defines the scaling factor on the Recognition Science φ-ladder at rung 45. Researchers computing masses, energies, or periods at this specific scale in RS-native units cite the constant for direct substitution. The definition is a one-line wrapper around the phiRung function at integer argument 45.
Claim. Let $φ$ denote the golden ratio. Define gap45 $:= φ^{45}$.
background
The RSNativeUnits module establishes a measurement system whose base units are the tick (one ledger interval) and voxel (distance light travels in one tick), with c = 1. All derived quantities sit on the φ-ladder, where φ^n for integer n supplies the natural scaling for masses, energies, times, and lengths. The phiRung definition computes exactly this scaling: phiRung n := φ^n for integer rung n.
proof idea
One-line wrapper that applies phiRung at argument 45.
why it matters
The definition supplies a concrete high-rung factor on the φ-ladder for RS-native calculations of masses and energies. It supports the general mass formula that places quantities at rung -8 + gap(Z) and aligns with the eight-tick octave structure. No downstream theorems currently reference it.
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