SΔϕ-33 — Belief, Conviction, and Certainty as Layers of Path Fixation: Minimal Conditions under the Absence of Arbitration (v1.0)

This work extends the Sofience–Δϕ (SΔϕ) series by formalizing belief, conviction, and certainty as three distinct layers of path fixation under conditions where no final arbiter is available. Rather than treating belief as a merely psychological state or a simple propositional attitude, this paper defines belief as a minimal fixation point provisionally assigned by a system in order to continue operating when guaranteed external agreement cannot be obtained. Conviction is defined as a thicker stabilization produced by repeated re-entry, organizing long-range path selection. Certainty is defined as an authority-weighted fixation that raises the cost of exception re-entry, enabling high coherence while increasing closure risk. Within the SΔϕ framework, belief preserves operation, conviction organizes duration, and certainty governs closure risk. The paper positions these three layers not as mere degrees of the same content, but as structurally distinct regimes of internal stabilization. In doing so, it connects the SΔϕ line from intuition, judgment, and authority to default power, editable governance, and legitimate intervention. This record belongs to the Sofience–Δϕ series and should be read in continuity with earlier documents on intuition, judgment, default power, editable defaults, and legitimate intervention.