SΔϕ-16 — Evil as Relational Closure: Minimal Failure Modes after Trust and Promise (v1.0)

This paper defines evil within the Sofience–Δϕ Formalism as a closure operator over relational futures. Following SΔϕ-14 (ethics as discrimination between real and phantom shared attractors) and SΔϕ-15 (trust/hope/promise as pre-commitment operators), the present work isolates a minimal failure mode: relational persistence can still collapse when the future possibility space for coupled systems is persistently closed. Within this framework: Evil is defined as persistent closure of the relational future space (Ω_rel) under irreversibility: Evil := Close(Ω_rel). A key lemma distinguishes evil from error: error is local and potentially recoverable, whereas evil is persistent closure that makes rollback costs explode and collapses relational futures. The paper formalizes three minimal conditions under which systems select closure as an attractor: (1) closure attractor visibility (closure appears as stability/relief), (2) validation cost explosion (Cost_validate ≫ Cost_close), and (3) irreversible identity lock (change is translated as identity collapse, suppressing variance toward closure). Three corollaries clarify that evil can be intention-free (optimization/bureaucracy/bias), can arise from good intention (system-wide closure “to save”), and can appear seductive because closure behaves like a strong attractor. The document treats evil as a directional operator (closure), not a moral label for agents, and prepares the transition toward the institutional/sacred layer where openness must be stabilized without infinite validation cost.