reductionFactor
plain-language theorem explainer
The reduction factor is defined as 5/2 minus phi and equals 1 minus J of phi under the Recognition Science J-cost. Bioremediation engineers cite it when scaling per-cycle activation-barrier reduction for PFAS and microplastic degradation pilots. The definition is a direct algebraic substitution from the closed-form J(phi) = phi - 3/2.
Claim. $1 - J(φ) = 5/2 - φ$, where $J$ is the Recognition Science cost function satisfying $J(x) = (x + x^{-1})/2 - 1$ and $φ$ is the golden-ratio fixed point.
background
In the Identity-Tick Bioremediation Pilot the activation barrier for contaminant degradation is scaled by the factor 1 - J(φ). The module documentation states that the per-cycle degradation factor equals (1 - J(φ)) ≈ 0.882 and that the residual fraction after n cycles is (1 - J(φ))^n. J(φ) evaluates to φ - 3/2 from the J-uniqueness relation, so the reduction factor is exactly 5/2 - φ.
proof idea
This is a direct definition that substitutes the algebraic simplification 1 - J(φ) = 5/2 - φ into the constant reductionFactor. No lemmas or tactics are invoked; the expression is taken verbatim from the J-cost formula.
why it matters
The definition supplies the base constant for the IdentityTickBioremediationPilotCert structure and the bioremediation_one_statement theorem, which assert the band (0.87, 0.89), positivity, and strict anti-monotonicity of the residual fraction. It translates the T5 J-uniqueness result into an engineering scaling law inside the eight-tick octave framework, with the module falsifier being a pilot deployment whose degradation rate deviates from (1 - J(φ))^n beyond 5σ.
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