This deposit provides a minimal existence proof and technical specification for a closed curve that appears trefoil-like under planar projection while remaining topologically unknotted in ℝ³. The construction utilizes a monotone traversal over two full cycles (t ∈ [0, 4π]), using sink–source spiral dynamics defined by r(t) = r₀ + a cos(1.5t + π). The model demonstrates that knot-like visual complexity can emerge from two-cycle indexing and depth separation (z(t) = cos(t/2)) rather than topological entanglement. It includes canonical parameters for a "midground balance" suitable for visual identity and diagrammatic use. This record contains two complementary documents describing a single construction. (1) Main Paper:"Existence of an Unknotted Closed Curve with Trefoil-Like Projection via Two-Cycle Spiral Dynamics" This paper establishes the theoretical motivation and existence proof. (2) Canonical Primitive / Design Note:"Spiral Unknot (Canonical Definition)" This supplementary document fixes the minimal parametric form, phase ordering, and projection rules for implementation and design use.