phi_ladder
plain-language theorem explainer
Recognition Science places nuclear densities and photon luminosities on a discrete φ-ladder indexed by integers. The definition maps each tier n to φ^n, supplying the scaling factor for mass-to-light ratios as φ to the power of tier differences. Astrophysicists modeling nucleosynthesis invoke this map to derive M/L values from tier structure. It is realized by a direct power definition.
Claim. For each integer tier $n$, the φ-ladder value equals $φ^n$.
background
The module derives mass-to-light ratios from the discrete φ-tier structure of nuclear densities and photon fluxes. Nuclear density scales as φ to the nuclear tier times Planck density, while luminosity scales as φ to the photon tier times unit luminosity; their ratio is then φ to the tier difference. PhiTier is the abbreviation for the integers ℤ that index this ladder. Upstream, OntologyPredicates defines phi_ladder as the set {x | ∃ n : ℤ, x = φ^n}, while StillnessGenerative gives the same exponential map on ℤ.
proof idea
This is a direct definition that sets the value at tier n to φ raised to the power n. It reuses the power operation already established in the upstream phi_ladder definition from StillnessGenerative.
why it matters
This supplies the concrete scaling map for the φ-ladder used in nucleosynthesis calculations. It is invoked by ml_nucleosynthesis to set the ratio to phi_ladder of the tier difference and by all_ml_on_phi_ladder to confirm population values lie on the ladder. It realizes the discrete skeleton described in OntologyPredicates. In the framework it encodes the self-similar fixed point φ forced at T6 of the unified forcing chain.
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