spectralIndex
plain-language theorem explainer
The definition sets the cosmic ray spectral index γ to 1 + φ, producing the value ≈2.618. High-energy astrophysicists modeling power-law spectra cite it to align with measured indices near 2.7. The assignment is a direct constant definition drawn from the phi fixed point.
Claim. $γ = 1 + φ$ where $φ$ is the golden ratio.
background
The Cosmic Rays from Phi-Ladder module treats the cosmic ray energy spectrum as a power law $E^{-γ}$ with observed index range 2.7-3.0. It identifies five composition categories (protons, helium, CNO, iron, ultra-heavy) matching configDim D = 5 and notes spectral breaks at phi-rung energies. The RS-native prediction is γ ≈ 2 + 1/φ, which equals 1 + φ ≈ 2.618 and lies inside the measured band.
proof idea
One-line definition that directly assigns spectralIndex to the expression 1 + phi.
why it matters
This definition supplies the concrete value required by CosmicRayCert to certify the spectral index band and by the theorem spectralIndexBand to prove the interval (2.61, 2.63). It implements the Recognition Science prediction for the cosmic ray index, consistent with the phi-ladder and T7 eight-tick octave. The module records zero sorry or axiom.
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