#personhood-proof (1 article)

The Cost-Benefit Matrix of Uniqueness Proof and Sybil Resistance: From Worldcoin to zkPassport

Sybil resistance is formalised as an impossibility triangle IT' = ¬∃ S [ U(S) = max ∧ D(S) = min ∧ I(S) = max ], equipped with nine sub-dimensions and five boundary conditions. The analysis disaggregates, one by one, the corner-case trade-offs of Worldcoin, BrightID, Gitcoin Passport, zkPassport, and Proof of Humanity across the three axes of uniqueness, disclosure cost, and inclusion. The CAP–IT' analogy is characterised as medium-strong and provides design guidance without licensing formal inference; the PACELC extension yields the IS-AUEL-D weak-level methodology. The impossibility triangle shares a conjunctive structure with the three-wall argument of article 03 (H1') and the three-element conjunction of article 04 (T), though it operates at a different logical level.