Finite-sample consistency of joint causal profiles in bounded-density two-dimensional diamonds

We prove explicit finite-sample consistency bounds for three labelled causal-profile pseudometrics on bounded-density two-dimensional causal diamonds. The upper bound is of order (log(K/delta)/K)^(1/4), with a deterministic K^(-1/4) finite-target obstruction. We also give an explicit checkerboard separation, identify full-support copulas from their completed labelled profile systems up to coordinate transpose (a spatial reflection), and derive confidence intervals and consistent two-sample tests for zero joint profile distance, equivalently order-measure isomorphism up to that transpose within the stated class. The result does not establish minimax optimality, physical isometry, a general inverse stability modulus, or priority over related results. AI-assistance disclosure: the author used OpenAI ChatGPT and Codex and Anthropic Claude for research planning, literature searches, conjecture and counterexample exploration, drafting and LaTeX preparation, related Lean formalization, and adversarial mathematical and bibliographic review. Their outputs were checked and revised by the author, who takes full responsibility for the work; the systems are not authors and their output is not treated as independent evidence.