As large language models (LLMs) are increasingly redistributed, adapted, and served behind opaque APIs, model ownership can no longer be established reliably by inspecting model internals or deployment records. This creates a need for behavioral signatures that remain observable through black-box interaction. Yet most existing black-box fingerprints instantiate ownership signals through fixed query-key associations, reducing model identity to sparse memorized associations detached from ordinary behavior and limiting both robustness and stealth (e.g., fine-tuning or quantization) and stealthiness. A stronger fingerprint should instead be distributed, naturally elicited, and expressed at a higher semantic level. To this end, we introduce PROSE (Provenance through Relational Organization of Semantic Expression), replacing fixed query sets with a target semantical domain and brittle response keys with semantic structures internalized as domain-conditioned response behavior. Specifically, the fingerprint is encoded in how the model semantically organizes its in-domain conclusions, rather than in particular tokens or prescribed outputs. PROSE constructs a private bank of domain-specific semantic templates, internalizes them through mixed fine-tuning on structurally verified and clean responses, and verifies ownership by detecting the designated structures in responses to held-out natural queries. Extensive experiments across multiple model architectures, scales, and target domains show that PROSE achieves a 100% fingerprint detection rate on unmodified models with no observed false positives, preserves model utility, and retains strong detectability under downstream modifications and output transformations.