Z-Algebra Black Hole Theory: Zero-Surface Unification, Holographic Sealing, and Intrinsic Einstein Structure

Within the priority-axis Z-algebra axiomatic system (V10.1), this paper merges three lines of work—black-hole ontology, the zero-surface area law, and the unified zero-surface picture—into a single algebraic framework for black-hole physics. The frozen-active dichotomy yields an orthogonal direct-sum decomposition, and the spectral rigidity theorem implies the cross-scale law f·kτ = 1/π. The bracket connection on the Lorentzian physical tangent space span{τ, i, j} produces an intrinsic Einstein structure of constant curvature K = −1, with Ric = −2η, R = −6, Λ = −2 and G = +η, fully consistent with the signature convention. The zero surface Q = 0 uniformly describes light cones, confinement walls, atomic shells and event horizons. The χ-Peirce sector isolation Z₊·Z₋ = {0} and the zero-surface area law form a dual-track holographic mechanism, conditionally yielding the Bekenstein-Hawking entropy S = A/(4G) (the 1/4 coefficient remains at the conditional level). Information sealing and singularity boundedness thereby acquire an algebraic interpretation. All incremental propositions are verified by the accompanying author-provided exact symbolic-verification script (36 tests, 36 passed, with strictly zero residuals; script attached and publicly reproducible), while core formulas are covered by the companion 53-item protocol. The axiomatic emergence of the Hawking temperature and of field equations is listed as open problems.