lifetime_ratio
plain-language theorem explainer
Consecutive lifetimes on the phi-ladder satisfy a constant ratio of phi. Researchers modeling exotic decays would cite this result to confirm geometric progression across the five channels. The proof is a direct algebraic reduction that substitutes the power definition and cancels via exponent arithmetic.
Claim. For every natural number $k$, if the lifetime at rung $k$ is defined by $L(k) = phi^k$, then $L(k+1)/L(k) = phi$.
background
The module assigns each of the five exotic decay channels (alpha, beta-minus, beta-plus, electron-capture, spontaneous-fission) a lifetime one rung higher on the phi-ladder. The lifetime function is introduced explicitly as the power $phi^k$. This construction sits inside the Recognition Science setting where phi arises as the self-similar fixed point forced by the J-uniqueness relation.
proof idea
Unfold the lifetime definition to obtain powers of phi. Apply positivity of phi to the k power, rewrite the division via the equality condition, substitute the successor exponent rule, and finish with ring simplification.
why it matters
The theorem supplies the phi_ratio field inside the decaySpectrumCert definition that certifies the full spectrum for the five channels. It directly instantiates the phi-ladder step of the unified forcing chain (T6) and closes the exact scaling relation without additional hypotheses.
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