Construction-Driven Injection: Linguistically-Grounded Edit-Based Code-Mixing Fingerprints for Large Language Models

Large language models (LLMs) are costly intellectual assets that remain exposed to unauthorized redistribution and commercial misuse. Injected fingerprints, i.e., trigger--target pairs embedded in model behavior, offer a practical, black-box-verifiable ownership signal, but existing methods decouple the two stages of the fingerprint life cycle: how a fingerprint is constructed and how it is injected. Existing fingerprinting frameworks suffer from two limitations. Natural-language fingerprints are prone to accidental activation, and garbled fingerprints are easily filtered by perplexity-based detection. Furthermore, decoupling construction from injection leaves the latter unaware of the trigger's linguistic structure, missing the opportunity for targeted optimization. We argue that fingerprint construction should drive injection, and present a unified fingerprinting framework that jointly optimizes both stages. First, LCF constructs code-mixing fingerprints by combining low-resource languages under a semantic-density substitution rule and grammar-biased mixing, yielding triggers whose perplexity sits far below garbled baselines while avoiding the accidental-activation failures of natural-language triggers. Second, LCFEdit injects each fingerprint with a null-space projection derived from high-resource multilingual representations that preserves knowledge, augmented by a cross-lingual alignment step that steers the weight update toward the fingerprint language's representation subspace. This construction-aware injection ensures that the update is linguistically informed and therefore more stable. Extensive evaluations on imperceptibility, detectability, and harmlessness demonstrate persistent ownership verification with negligible impact on utility.