Causal–Spectral Distinguishability Selection on a Conditional Round S³ Carrier

This work develops a causal–spectral selector on a conditional round S³ carrier. Its central point is the separation of four layers that are often confused: carrier distinguishability, spectral mode capacity, causal accessibility, and physically admissible code capacity. On a round carrier S³_R_curv, the causally accessible fraction is exact: η_R(T) = (τ − 1/2 sin(2τ)) / π, with τ = cT / R_curv for 0 ≤ T ≤ t_coh, and η_R(T) = 1 after the coherence time. For homogeneous shell-complete spectral projectors, causal spectral accessibility reduces to this same volume fraction, so the raw causal capacity becomes B_causal^(P)(ε,T) = b_P η_R(T) N_P(ε), where b_P = log₂ q_P converts finite alphabet states into bits. The key construction is the dimensionless gravitational selector η_grav^(P) = B_phys^(P) / B_causal^(P). Physical admissibility is imposed by gauge constraints, gravitational dressing, energy bounds, entropy bounds, and stability conditions. Under the safe ceiling estimate, B_phys^(P) ≤ min(B_causal^(P), B_Bek, B_holo), with B_Bek = 2π E_D r_D / (ℏ c ln 2) and B_holo = A_D / (4 ℓ_P² ln 2). Hence the selector is a controlled contraction, 0 ≤ η_grav^(P) ≤ 1. In the min-law diagnostic model this becomes the compact normal form η_grav^(P) = min(1, B_ceil / (b_P η_R(T) N_P(ε))). The spectral side supplies explicit computable capacities. For scalar modes on round S³_R_curv, N₀(ε) = M₀(M₀ + 1)(2M₀ + 1) / 6, with M₀ = √(1 + (R_curv/ε)²) and Weyl scaling N₀(ε) ∼ (R_curv/ε)³ / 3. In the early-time, fine-resolution regime, η_R(T) ∼ 2τ³ / (3π) and N_P(ε) ∼ C_P(R_curv/ε)³, so the curvature radius cancels from the joint asymptotic law: D_P ∼ (2 b_P C_P / 3π)(cT/ε)³. This gives a clean self-similar rule: in the filtered scalar Weyl regime, halving ε reduces the selector by the cubic factor η_grav(ε/2) / η_grav(ε) ≈ 1/8. The manuscript is deliberately conservative in status. It does not claim that physical space has measured S³ topology, that arbitrary objects are three-spheres, that Hopf fibers are automatically material rings, or that the selector alone derives classicality, quantum gravity, or the Standard Model. The round-S³ formulas may be used as a screen transform and comparison language: for any positive length r one may compute round-screen quantities such as V₃(r) = 2π²r³, R₃(r) = 6/r², and t_coh = πr/c. But a topology claim requires an independent topology theorem or a measured physical field invariant. The durable contribution is therefore the exact causal–spectral integration, the selector ratio, the threshold structure, and the finite-alphabet discipline that turns spectral multiplicity into physically bounded code capacity.