Projective Narrowing Model: Observational Tests of a Constraint-Based Geometric Cosmology

We present the Projective Narrowing Model (PNM), a geometric framework in which spacetime structure arises from a constraint on admissible configurations rather than being assumed as a fundamental primitive. Observable states are required to satisfy a tripartite visibility condition Δx Δ𝛤 Δθ ≥ ℓ_P E_P, which imposes a minimal Planck-scale bound on combined spatial, projective-density, and angular spreads. When embedded in a relativistic setting, this constraint induces an effective geometric stress-energy contribution that remains covariant and reduces exactly to general relativity in the limit where projective effects vanish. We test the resulting framework across four independent observational domains: BAO residual structure (eBOSS DR16), Euclid Q1 galaxy alignments and entropy-resolution scaling, Planck CMB algorithmic complexity (temperature and lensing), and Pantheon+ supernova distance relations. Across these domains, PNM achieves statistical performance comparable to ΛCDM under equivalent model complexity, and in selected cases yields improved residual structure or information criteria. Within this framework, large-scale phenomena conventionally attributed to dark matter and dark energy arise as consequences of the geometric compatibility constraint itself, without introducing additional energy densities, fields, or free dark-sector parameters. Each observational test isolates a distinct implication of the tripartite constraint, rendering the framework explicitly falsifiable. PNM therefore proposes an empirically testable geometric generalization of relativistic cosmology derived from a constraint-based principle in projective phase space.