Decentralized verifiable credential systems have seen limited deployment in practice. Existing constructions, built on zero-knowledge proofs, are complex, application-specific, and largely restricted to predicates over structured data. We present Privately Inferred Credentials ($π$Creds): privacy-preserving, legacy-compatible, decentralized verifiable credentials generated by trusted LLM inference over authenticated data. LLMs' ability to semantically reason over unstructured data substantially expands the range of claims $π$Creds can certify over existing credential systems. The use of LLMs also introduces new application-level threats, which we formalize through two problems: the Source-Constrained Adversarial Example (SCAE) problem, which captures robustness against adversaries that manipulate authenticated data to obtain misleading credentials, and the Authenticated Covert Predicate Poisoning (ACPP) problem, which captures privacy leakage through adversarial model selection. We characterize applications of $π$Creds over user data, and a novel class of credentials over proprietary software that certifies properties of a service without revealing its source code. Our prototype supports issuing credentials over live financial, health, email, and code sources, and we empirically study the SCAE and ACPP threats on a product expertise credential over real financial data.

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