storage_density_ratio
plain-language theorem explainer
Energy density ratio between two rungs on the phi-ladder equals phi raised to the difference of their indices. Storage engineers comparing chemical and nuclear scales cite this when scaling across the hierarchy derived in EN-004. The declaration is a direct exponential definition drawn from the phi-ladder structure.
Claim. The energy storage density ratio between rungs $n$ and $m$ on the phi-ladder is $phi^{n-m}$.
background
Recognition Science sets energy as J-cost times the coherence quantum E_coh = phi^{-5} eV. The module EN-004 derives storage limits from the phi-ladder, with chemical rung at one quantum and nuclear rung at phi^k for k near 45, producing the 10^9 ratio. The upstream density definition states density(k) := phi^k, supplying the same exponential scaling.
proof idea
Direct definition: storage_density_ratio n m expands to phi raised to (n - m). No lemmas or tactics are invoked.
why it matters
This definition supplies the scaling used by higher_rung_denser and storage_density_ratio_pos in the same module. It implements the EN-004 claim that storage efficiency is quantized on the phi-ladder, consistent with the T6 phi fixed point and the predicted chemical-nuclear gap of phi^45. No open scaffolding questions are closed here.
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