Motivation. Public administrations across Europe deploy algorithmic decision-making systems for social welfare, housing, and care. These systems present an accountability challenge that existing approaches cannot address: a system may satisfy every individual fairness constraint while systematically producing unjust outcomes at the population level over time. Problem. Existing fairness definitions-individual fairness, equal opportunity, counterfactual fairness-define fairness as a static property measurable at a single snapshot. None models the feedback loop between human judgment and model retraining-the central vector of temporal injustice. Method. We present ARIA and the Temporally Fair Arbitration System (TFAS) definition comprising five independently falsifiable conditions. The four-subsystem architecture is specified via SysML and BPMN 2.0 [18]. Analysis follows the SSM/CATWOE methodology with explicit adversarial stakeholder modelling. Results. We prove the Temporal Injustice Theorem: if the feedback coefficient δ ≥ 1, decision distributions across demographic groups diverge monotonically regardless of local correctness. We verify analytically (induction) and empirically (n=100,000 applications, B=200 bootstrap replications, multi-group extension to |G|=4). A 15×10 sensitivity analysis characterises violation rates across the (δ, β) space; δ≤0.6 produces the lowest violation fractions. Contribution. TFAS is the first fairness definition incorporating bounded human-reviewer feedback as a formal system parameter. Executable Python implementations of SS1 (SPC monitor), SS2 (escalation FSM), and SS4 (Merkle audit log)-the three formally verified subsystems-provide 30/30 passing unit tests; SS3 is specified in SysML/BPMN and awaits a future HMI prototype. The CI/CD deployment gate provides 1:1 TFAS condition coverage and implements EU AI Act Article 14.