The Factor 1/2 in the Cosmological Constant: A Causal Projection from the Observer's Causal Diamond

The canvas model predicts a cosmological constant Λ = 3/(πR_H²) from the information capacity of the cosmic horizon. Observation requires Λ = 6/(πR_H²)—exactly twice the prediction. This paper resolves the discrepancy by identifying its origin in the causal structure of de Sitter spacetime. Only half the cosmic horizon—the hemisphere causally connected to the observer's past light cone—can contribute to observable information. The effective information bound is therefore I_max,eff = 2πR_H²/ℓ_P² = A_horizon/(2ℓ_P²). Substituting this into the canvas model's Λ relation yields Λ = 6/(πR_H²), in exact agreement with observation. The factor 1/2 is not a fitted parameter. It is a causal projection factor grounded in the geometry of the observer's causal diamond, the arrow of time, and the projection factor ⟨cosθ⟩ = 1/2 over a hemisphere. The paper connects this result to established literature on de Sitter holography, causal diamond thermodynamics, and observer-dependent entropy. As a corollary, it shows that the observed value of Λ serves as a constraint that discriminates between different formulations of the holographic information bound. The canvas model's choice I = A/ℓ_P² (rather than the Bekenstein-Hawking entropy S = A/(4ℓ_P²)) is favored by observation. Open questions remain: the exact hemisphere in quantum geometry, the role of the causal wedge vs. entanglement wedge, first-principles derivation of I = A/ℓ_P² from canvas dynamics, and potential time dependence of the factor. These are addressed in the discussion. Keywords: cosmological constant, holographic principle, causal diamond, de Sitter space, information bound, canvas model, observer dependence