Incomplete Causal Transactions: Black Holes as Permanently Frustrated Couplers and the Physical Independence of Entropy and Generative Capacity

The black hole information paradox has been substantially resolved: entropy is preserved in Hawking radiation, as established by the Page curve, replica wormhole calculations, and the island formula. We argue, however, that this resolution addresses only one of two physically distinct properties of quantum information states. The Shannon–Bekenstein framework formalises entropic content S(σ), but lacks representation for a second property: the capacity of a state to causally influence future configurations of external systems. We term this generative capacity G(σ) and establish that it is formally independent of S(σ). The central result is that even in a fully unitary resolution, I(ρ_rad, ρ_E) ≤ C·S_BH·2^{−S_BH/2} → 0 after the scrambling time for any system E in prior causal contact with an infalling state, while S(ρ_rad) follows the Page curve. A unitary resolution restores entropy; it does not restore causal influence capacity. We demonstrate this in the JT gravity + bath model via the decoupling theorem. Eight technical contributions support this framework: formal proof of S–G independence via the Rindler family; proof that the Bell state saturates the supremum in G(σ,d) via the entanglement-assisted channel capacity theorem; three explicit benchmark calculations; covariant reformulation of G bounded above by an area law; distinction of the causal residue from BMS soft hair charges; and time-dependent causal sterilization at rate κ = 2πT_H = λ_L, saturating the Maldacena–Shenker–Stanford bound on quantum chaos [35]. Theorem C.2 establishes that classical correlations survive the Rindler horizon completely while quantum entanglement is destroyed — the horizon acts as a quantum-classical separator. The framework introduces the causal quality index κ ∈ [1,2] as a potentially observable signature distinguishing accretion histories with identical mass, charge, and angular momentum.