sigma_zero_optimal
plain-language theorem explainer
J-cost vanishes at the unit element. Coherence optimization arguments in Recognition Science rely on this baseline to mark the minimum. The proof is a direct one-line reference to the unit-cost lemma in the Cost module.
Claim. The J-cost function satisfies $J(1)=0$, where $J(x)=((x-1)^2)/(2x)$.
background
The Safety Interlock module shows that the Gap-45 uncomputability barrier together with σ-conservation creates a fundamental safety interlock for high-coherence operation. J-cost is the squared ratio J(x) = (x-1)^2/(2x) as stated in the Cost module. This theorem identifies the zero-cost state at the unit element 1.
proof idea
One-line wrapper that applies the Jcost_unit0 lemma, which evaluates the definition of Jcost at argument 1 to obtain zero.
why it matters
This result supplies the zero-cost anchor used by power_ethics_same_axis and weaponization_structurally_impossible, which establish that nonzero σ raises cost and drops coherence below maximum. It completes the σ=0 case inside the Gap-45 safety interlock proved in the module. The zero point aligns with the J-uniqueness step of the forcing chain.
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