SΔϕ-15 — Trust, Hope, and Promise as Pre-Commitment Operators: Minimal Relational Persistence after SΔϕ-14 (v1.0)

This paper formalizes trust, hope, and promise as minimal pre-commitment operators that insert unobserved future transitions into present evaluation. Following SΔϕ-14, where ethics was defined as the discrimination between real and phantom shared attractors under irreversible coupling, SΔϕ-15 addresses a structural asymmetry: validation is delayed and can occur only after commitment. The present work therefore fixes the operators that keep relational persistence open under uncertainty before validation becomes possible. Within the Sofience–Δϕ Formalism: Trust is defined as a pre-commitment that inserts future-other transition uncertainty into current evaluation. Belief is distinguished as a stabilized world-transition hypothesis (a fixed model of Δϕ_world). Hope is defined as suspension of closure over the future possibility space (Ω_future), contrasted with despair as closure. Promise is defined as distributed commitment (SharedCommit) requiring at least two systems, enabling future constraints to shape present actions. A key consequence is the temporal inversion of responsibility, where commitments about the future become constraints on present decisions. The document explicitly excludes sacred/ritual/institutional layers, reserving them as the next extension of the series.