spectral_tilt_observed
plain-language theorem explainer
The definition sets the spectral tilt equal to the observed scalar spectral index minus one. Cosmologists modeling primordial fluctuations in Recognition Science cite this when matching the phi-ladder output to Planck CMB data. It is a direct arithmetic shift applied to the fixed numerical input for n_s.
Claim. The observed spectral tilt is defined as $n_s - 1$, where $n_s$ is the scalar spectral index taken from observation.
background
The COS-009 module derives the primordial power spectrum from J-cost quantum fluctuations during inflation, with the phi-ladder fixing the spectral tilt so that P(k) scales as k to the power of n_s minus one. The upstream result spectral_index_observed supplies the numerical value 0.9649 for n_s from Planck 2018, producing a slightly red spectrum. This matches the Recognition Science mechanism in which n_s minus one is expected to be phi-related.
proof idea
The definition is a one-line wrapper that subtracts 1 from the value supplied by spectral_index_observed.
why it matters
This definition supplies the tilt parameter required for the primordial spectrum construction in the Recognition framework. It implements the module target of obtaining the CMB power spectrum from J-cost fluctuations and the phi-ladder, directly supporting the paper proposition on the CMB spectral index from the golden ratio. The tilt connects to the T6 self-similar fixed point and the eight-tick octave before amplitude derivations proceed.
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