de Sitter Space as the S-Invariant Attractor of Cosmic Evolution

The observed universe is asymptotically de Sitter: the cosmological constant \Lambda > 0 drives accelerated expansion, and the ultimate fate of the cosmos is a de Sitter vacuum. Why the universe evolves toward de Sitter space rather than Minkowski space (\Lambda = 0) or anti-de Sitter space (\Lambda < 0) has no explanation in standard cosmology—it is an empirical fact. This paper proves that de Sitter space is the unique S-invariant physical attractor of cosmic evolution in the canvas model. What this paper proves: · The symmetry operator \mathcal{S} (\mathcal{S}^2 = I) exchanges positive and negative primitives. For cosmology, \mathcal{S} acts as simultaneous time reversal and sign-flip of the cosmological constant. The physical observable is |\Lambda|, which is manifestly S-invariant. The Friedmann equation depends only on |\Lambda|.· The information bound from the canvas model gives \Lambda = 3/(\pi R_H^2) > 0. This bound forbids \Lambda = 0—Minkowski space, while S-invariant, is physically inaccessible because it would require infinite information capacity. Anti-de Sitter space (\Lambda < 0) is not S-invariant in any physical sense because an observer in an expanding phase necessarily measures \Lambda > 0.· The Steering dynamics d\Lambda/d\tau = -\kappa \nabla_{\Lambda} E[\Lambda] drive the cosmological constant toward its minimum allowed value. The unconstrained Steering dynamics have Minkowski space (\Lambda = 0) as the unique attractor. However, the information bound \Lambda \geq \Lambda_{\min} > 0 constrains the physical domain, making Minkowski space inaccessible. Within the physical domain, de Sitter space at \Lambda = \Lambda_{\min} is the unique stable fixed point.· The approach to the de Sitter attractor predicts a specific, testable deviation of the dark energy equation of state from w = -1. We derive w(z) from the horizon evolution: w(z=0) \approx -0.933,\quad w(z=0.5) \approx -0.882,\quad w(z=1) \approx -0.819,\quad w(z=2) \approx -0.732 This prediction is testable with Euclid, LSST, and the Roman Space Telescope. If w_0 \approx -0.93, DESI Year 1 data should show a \sim 3.5\sigma deviation from \LambdaCDM. Why this matters: De Sitter space is not an arbitrary choice of initial conditions. It is the inevitable destination of cosmic evolution—the S-invariant attractor selected by the interplay of symmetry and information. The canvas model explains why the cosmological constant is positive, why it has its observed small but non-zero value, and why the universe is accelerating toward de Sitter space. This paper is part of the Emergence series, building on Paper I (Unified Field Theory), the cosmological constant derivation, and the Steering dynamics. It completes the explanation of late-time cosmic acceleration as an attractor phenomenon. Keywords: de Sitter space, cosmological constant, S-invariant, attractor, Steering dynamics, dark energy, equation of state, information bound, cosmic horizon, canvas model, Emergence series