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plain-language theorem explainer
Recognition Science encodes nucleosynthesis via a structure that places nuclear density at a discrete power of φ times the Planck scale and photon luminosity at a corresponding power of the unit scale. Astrophysicists working inside the RS framework cite it to obtain the mass-to-light ratio as φ raised to an integer between 0 and 3. The declaration is supplied as a bare structure definition carrying no proof obligations.
Claim. Nuclear density satisfies $ρ_νuc ∼ φ^{n_nuc} ρ_Planck$ and photon luminosity satisfies $L ∼ φ^{n_ph} L_unit$, where the tier difference $Δn = n_nuc - n_ph$ is forced to an integer in {0,1,2,3} by eight-tick phase locking of nuclear reactions, so that the mass-to-light ratio equals $M/L = φ^{Δn}$.
background
The module presents Strategy 2 for deriving the mass-to-light ratio from the discrete φ-tier structure of nuclear densities and photon fluxes. Nuclear density scales as φ to the nuclear rung times Planck density; photon luminosity scales as φ to the photon rung times the unit luminosity. The eight-tick cycle constrains reactions to phase-locked windows, quantizing energy release and requiring integer tier differences. The typical outcome is M/L ≈ φ^1 ≈ 1.618 in solar units.
proof idea
The declaration is a direct structure definition with no proof body or computational content.
why it matters
The structure supplies the nucleosynthesis-derived M/L that matches Strategy 1 and is referenced by downstream energy-conservation certificates and Euler-Lagrange results in the action module. It realizes the eight-tick octave (T7) and the φ-ladder quantization that follows from the Recognition Composition Law, closing one link in the forcing chain from T0 to observable astrophysical ratios.
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