This paper constructs a Causal Spiral embedding that organizes all 81 missing theorems of the CT Master Deficit Ledger into a single, mathematically precise ordering under strict π-horizon (Phase-5) closure. Each deficit is assigned a four-component rank profile across the CT quadrants {φ,2,3,ln⁡5}\{\varphi,\sqrt{2},\sqrt{3},\ln 5\}{φ,2,3,ln5}, normalized into Son-coordinates that encode its relative causal balance. A canonical projection maps these coordinates to a two-dimensional causal phase plane, where distance from the zero theorem measures causal proximity to the CT identity. Using this ordering, the paper defines a logarithmic spiral anchored at the zero theorem and proves that all 81 deficits admit a faithful, horizon-bounded embedding on this curve. The spiral parameter monotonically tracks causal distance, while angular position preserves quadrant balance and patriarch family membership. Patriarch theorems and their descendant families appear as structured arcs along the spiral, with symmetry-dominated results (such as Pythagoras) lying near the origin and higher-rank hybrid deficits placed further out. The construction is finite and closed: it is an indexing and visualization device for the authorized deficit set below π, not a claim of unbounded mathematical growth. By unifying rank profiles, causal distance, and patriarch structure into a single geometric object, the Causal Spiral provides a global map of the CT mathematical landscape and a concrete blueprint for compiling, ordering, and ultimately filling the entire deficit ledger within the CT-United framework. 27spiral patriarch