reductionFactor_band
plain-language theorem explainer
The theorem pins the per-cycle bioremediation reduction factor between 0.87 and 0.89. Pilot engineers and RS modelers cite this interval to bound the exponential decay of contaminants under the identity-tick protocol. The proof unfolds the definition reductionFactor = 5/2 - phi and feeds the established bounds 1.61 < phi < 1.62 into linear arithmetic.
Claim. $0.87 < 5/2 - phi < 0.89$, where $phi = (1 + sqrt(5))/2$ is the golden ratio.
background
In the Identity-Tick Bioremediation Pilot module the reduction factor is defined as 5/2 - phi, which equals 1 - J(phi) for the J-cost function that lowers the activation barrier. This quantity sets the per-cycle degradation multiplier for PFAS and microplastics in phantom-cavity setups. The module states that residual fraction after n cycles is (1 - J(phi))^n and is exponential in n. Upstream lemmas supply the tight numerical bounds 1.61 < phi < 1.62 that are invoked directly.
proof idea
The proof is a one-line wrapper. It unfolds reductionFactor to 5/2 - phi, obtains the phi bounds from phi_gt_onePointSixOne and phi_lt_onePointSixTwo, and applies linarith twice to split the conjunction into the two strict inequalities.
why it matters
This bound supplies the numerical interval required by bioremediation_one_statement, which packages the full one-statement claim for the pilot certification. It closes the engineering derivation step in the J8 track, confirming that the RS-native reduction factor lies inside the stated engineering tolerance. The result touches the open question of pilot-scale validation against the falsifier of inconsistent degradation rates.
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