κ-Identity: Behavioral Fingerprinting for Continuous Verification of LLM Agents

We introduce κ-Identity, a primitive for the continuous behavioral identity of autonomous LLM agents in production. κ-Identity is the specialization to LLM agents of a broader framework, developed here, in which the identity of any mutable-substrate process is the persistent correlational structure between that process and its environment, integrated over time. The framework is operationally defined as conditional mutual information between past and future behavior given environment, exceeding a non-trivial threshold over a minimum temporal window; it admits cross-domain instantiations — to quantum systems via persistent correlations under repeated measurement, to humans via behavioral biometrics, to computer processes via runtime integrity attestation, and to LLM agents as κ-Identity — and exposes four structural limits that any practical implementation must face: the indistinguishability of systems sharing all observable statistics, the inability of behavioral channels to measure intention, the failure of substrate-access strategies to recover identity at a deeper layer, and the requirement of multi-modal composition for operationally defensible attestation. κ-Identity is measured by behavioral fingerprinting: a privacy-preserving method that extracts low-resolution structural features of each input-output event client-side, learns a per-agent baseline distribution from organic traffic, and runs windowed two-sample tests against that baseline to detect model substitution, sustained injection, and drift — without access to model weights, raw prompts, or raw responses. Verdicts about κ-Identity are issued as κ-Proofs: signed JSON Web Tokens that any third party can verify offline against a public JWKS, without an account with the verifier and without sight of the underlying events, making behavioral attestation portable across organizational trust boundaries. We present the framework, its cross-domain instantiations, its hard limits, the measurement method, and the attestation architecture. The contribution is conceptual and architectural rather than empirical; quantitative claims about detection performance against adversarial drift on real LLM traffic are out of scope here and reserved for a follow-up report. A production instantiation under the name Metalins Drift Detection is referenced in Appendix A.