LuminosityTier
plain-language theorem explainer
LuminosityTier assigns stellar photon luminosities to integer indices on the φ-ladder. Astrophysicists working on mass-to-light ratios in Recognition Science cite it to connect emission rates to recognition bandwidth via L_max = B × E_coh. The declaration is a direct structure wrapper around the PhiTier integer index with no further computation or axioms.
Claim. A luminosity tier is an integer $n$ on the discrete φ-ladder such that photon luminosity scales as $L = B × φ^n × E_{coh}$ with coherence energy $E_{coh} = φ^{-5}$ eV.
background
The module develops Strategy 2 for φ-tier nucleosynthesis, deriving the mass-to-light ratio M/L from discrete φ-tier structure of nuclear densities and photon fluxes. Nuclear density occupies ρ_nuc ~ φ^{n_nuclear} × ρ_Planck while photon luminosity occupies L ~ φ^{n_photon} × L_unit, so that M/L equals φ^{Δn}. A φ-tier is defined as an integer index on the φ-ladder (PhiTier := ℤ). The eight-tick cycle constrains nucleosynthesis to phase-locked windows, forcing Δn to be an integer and yielding M/L ∈ {φ^n : n ∈ [0, 3]} with typical value ≈ φ^1.
proof idea
The declaration is a one-line structure definition that directly embeds the PhiTier integer index; no lemmas or tactics are applied.
why it matters
This definition supplies the photon-luminosity side of the φ-tier structure that feeds the module's main result equating nucleosynthesis-derived M/L to the set {φ^n : n ∈ [0, 3]}. It implements the recognition-bandwidth relation L_max = B × E_coh and connects to the eight-tick octave that forces integer tier differences. The declaration closes the photon-flux half of the M/L derivation without introducing new hypotheses.
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