reductionFactor_pos
plain-language theorem explainer
The theorem establishes that the reduction factor 5/2 - φ is strictly positive. Engineers modeling PFAS and microplastic degradation in identity-tick bioremediation pilots would cite it to guarantee that each cycle strictly lowers the residual contaminant load. The proof is a one-line term that unfolds the definition and combines the bound φ < 1.62 with linear arithmetic.
Claim. $0 < 5/2 - φ$, where the reduction factor equals $1 - J(φ)$ and $φ$ denotes the golden ratio.
background
The Identity-Tick Bioremediation Pilot module treats phantom-cavity remediation as an engineering derivation that lowers the activation barrier from $E_a$ to $E_a · (1 - J(φ))$. The reduction factor is defined directly as 5/2 - φ, which equals 1 - J(φ) and supplies the per-cycle multiplier ≈ 0.882. The module then forms the residual fraction as (5/2 - φ)^n after n cycles. Upstream, the lemma phi_lt_onePointSixTwo supplies the concrete bound φ < 1.62 obtained from √5 < 2.24.
proof idea
The proof is a one-line wrapper. It unfolds reductionFactor to the expression 5/2 - phi, invokes the lemma phi_lt_onePointSixTwo, and closes with linarith.
why it matters
Positivity is required by the identityTickBioremediationPilotCert record and by the three residualFraction theorems (positivity, strict decrease, and the bound less than one). It completes the engineering step in track J8 of Plan v5, ensuring the exponential decay model is well-defined. The result rests on J-uniqueness and the phi fixed point from the forcing chain; the module falsifier is a pilot deployment whose degradation rates deviate from (1 - J(φ))^n scaling beyond 5σ.
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