AI agents need personal data across the domains of a person's life, but the data lives in systems that model these domains in incompatible ways. Every agent vendor that persists user context builds its own private personal-data model, paying the integration tax independently and producing systems that cannot reliably interoperate. Language models can translate between schemas at query time, but translation is the wrong layer for guarantees that must be deterministic, checkable, and durable: provenance, consent, audit, selective disclosure, portability, and conformance all require stable record shapes and shared semantics that hold independently of any single model or vendor. The Sygil Protocol specifies the semantic layer that the Model Context Protocol does not. Where MCP standardizes how agents connect to data sources, Sygil standardizes what the data is and how it is to be interpreted. It defines content-addressed records under JCS canonical serialization, ten production cross-domain namespaces aligned to dominant single-domain standards (FHIR, FDX, vCard, AT Protocol, Schema.org), a minimal query grammar, proof objects for provenance and authorization, federation primitives, lossless export, and a conformance architecture open to third-party implementations. The protocol composes from MCP, LinkML, DIDs, JCS, ODRL, and DPV; imports rather than replaces domain-specific standards; and remains orthogonal to storage, governance, identity, and runtime. The paper makes a structural claim, not a deterministic adoption claim: if agents are to operate reliably across personal-data domains with provenance, consent, audit, portability, and conformance guarantees, a shared semantic substrate of this kind is required. The paper specifies that substrate and draws the boundary between what the protocol guarantees, what runtimes must enforce, and what adoption must still prove.