eight_tick_quantizes_tiers
plain-language theorem explainer
Nuclear reactions follow an eight-tick recognition cycle that forces energy releases to land on integer steps of the φ-ladder. Astrophysicists deriving mass-to-light ratios from nucleosynthesis cite this to guarantee discrete φ^n values for M/L. The definition directly encodes that the difference between any nuclear-density tier and luminosity tier must be an integer.
Claim. For all φ-tiers ρ (nuclear density) and L (photon luminosity), there exists an integer n such that ρ − L = n.
background
In the φ-tier nucleosynthesis setting, quantities occupy discrete levels on the φ-ladder. PhiTier is the type of integer indices n such that a quantity scales as φ^n times a base unit; nuclear density therefore scales as φ^{n_nuclear} ρ_Planck while luminosity scales as φ^{n_photon} L_unit, yielding M/L = φ^{Δn}. The eight-tick cycle requires each nuclear reaction to complete one full recognition period before releasing energy in units of E_coh × φ^{-r}.
proof idea
This is a definition that directly states the integer-difference property for any two PhiTiers. No lemmas are applied; the body simply asserts the existence of n = ρ_tier − L_tier. The downstream theorem tiers_are_quantized then discharges the statement by exhibiting that integer explicitly.
why it matters
The definition supplies the quantization statement proved by tiers_are_quantized. It implements the eight-tick octave (T7) inside nucleosynthesis, ensuring Δn ∈ ℤ so that M/L takes values in {φ^n : n ∈ [0,3]} and matches the observed solar-unit range. It thereby links the recognition cycle directly to the discrete ladder used for stellar mass-to-light ratios.
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