storage_density_ratio
plain-language theorem explainer
Energy density ratios between rungs n and m on the phi-ladder are defined as phi raised to the integer difference n minus m. Physicists and engineers working on RS-derived storage hierarchies cite this when comparing chemical and nuclear energy densities. It is introduced as a direct one-line definition that encodes the exponential scaling without additional proof steps.
Claim. The ratio of energy storage densities at integer rungs $n$ and $m$ on the phi-ladder is given by $phi^{n-m}$.
background
The module derives fundamental limits on energy storage per unit mass from the phi-ladder and J-cost structure. Energy takes the form J-cost times the coherence quantum, with E_coh equal to phi to the power of negative five electronvolts. The upstream density definition from NeutronStarCrustalRegimesFromRS sets density at rung k to phi^k, supplying the exponential base used here.
proof idea
This is a one-line definition that directly sets the ratio equal to the phi-exponentiation of the rung difference.
why it matters
The definition supports the positive-ratio and higher-rung-denser theorems in the same module. It realizes the EN-004 claim that storage densities follow phi-ladder scaling, producing the predicted nuclear-to-chemical ratio of approximately phi^45. It connects to the Recognition Science framework in which phi is the self-similar fixed point and energy hierarchies are quantized on the ladder.
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