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|ψ⟩ = α|0⟩ + β|1⟩

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P³¹ Labs Georgia 501(c)(3) · Determined May 2026

The only stable isotope.

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Π₁(d) = (1/d)|ψᵢ⟩⟨ψᵢ| where ⟨ψᵢ|ψⱼ⟩ = (dδᵢⱼ + 1)/(d + 1) — The geometry protects the signal.

P31 Labs, Inc. is a Georgia 501(c)(3) public charity (EIN: 42-1888158). Determination received May 2026. Donations are tax-deductible to the extent permitted by law.