strainRatio
plain-language theorem explainer
The theorem shows that gravitational wave strain amplitudes at consecutive rungs on the phi-ladder stand in the ratio phi. Researchers modeling binary merger signals under Recognition Science would cite it to confirm the phi-decay law between mass classes. The proof is a one-line algebraic wrapper that unfolds the power definition and cancels terms via exponent rules and field simplification.
Claim. Let $s(k) = phi^k$ denote the strain amplitude at rung $k$. Then $s(k+1)/s(k) = phi$.
background
The module treats gravitational wave strain in Recognition Science terms, where amplitude follows a phi-decay law across five canonical source categories (NS-NS through stochastic) that match configDim D=5. Adjacent mass classes on the ladder differ in peak strain by phi, consistent with the self-similar fixed point forced in the T0-T8 chain. The strain function assigns to each natural-number rung k the explicit value phi raised to k.
proof idea
The proof unfolds the strain definition to express both numerator and denominator as powers of phi. It invokes positivity of phi to the k, rewrites the successor power, and applies field simplification to cancel the common factor and obtain phi.
why it matters
This supplies the phi_ratio field inside gravitationalWaveCert, which certifies the five-category structure together with the phi scaling. It realizes the module's RS prediction that adjacent source-class strains ratio by phi and sits inside the phi-ladder construction that descends from the forcing chain. No open scaffolding questions are directly closed here.
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