Personal Causal Fingerprint: Invariant Directed Acyclic Graph Topologies via Pearl's Do-Calculus and Confounder-Free Structural Verification

Contemporary biometric and continuous behavioral authentication mechanisms operate strictly at the associational level (L1) of Pearl's Causal Hierarchy, estimating static observational distributions P(Y|X). Consequently, they remain structurally vulnerable to zero-day adversarial imitation, deepfake synthesis, and generative diffusion cloaking. This technical report presents the mathematical and algorithmic foundation of Falcon Impossibility F09: the Personal Causal Fingerprint. By elevating security verification to Pearl's interventional level (L2) through structural causal models (SCM) and graph surgery G_{X}, the system challenges interactive human-machine interfaces via imperceptible, deterministic do-calculus perturbations. We prove that authentic biological agents preserve strict directional separation (d-separation) and invariant Markov boundary topologies governed by neuromuscular latency constants, which cannot be synthesized by observationally trained generative models. We formulate a non-parametric independence criterion in reproducing kernel Hilbert spaces (RKHS) and provide a deterministic, zero-heap, constant-time C99 verification kernel (SHAHEEN-ALG-2026-F09) for real-time edge security.