Black-Hole Singularities and the Perfect-Cancellation Boundary

A singularity theorem establishes causal geodesic incompleteness under specified assumptions; it does not by itself identify a microscopic physical state located “at” the singularity. We study this distinction in the Potential Antimatter Model (PAM), which treats spacetime as an effective organization of a deeper relational system. The model describes the vacuum through a matter-supporting component B_M, termed potential matter, and a complementary cancellation-oriented component B_A, termed potential antimatter. The latter denotes a proposed vacuum component, distinct from ordinary antiparticles. Their difference, Δ = (B_M − B_A)/2, measures departure from cancellation, while the bounded diagnostic q = 1 / [1 + (|Δ|/Δ_0)²], with Δ_0 > 0, measures cancellation depth relative to a fixed reference scale. Larger q corresponds to closer matching of the paired components. The physical hypothesis is that cancellation becomes deeper toward a black-hole centre. A localized black hole nevertheless remains distinguishable from its environment and is postulated to retain a central value q_c < 1. Exact perfect cancellation, q = 1, is reserved for global closure: the proposed limit in which the distinction between a region and its environment disappears and the emergent spatial description ceases to apply. We ask whether a smooth transition between a deeply cancelled centre and its environment can support black-hole horizons while retaining a regular centre. Using the mass-profile shape shared with a companion formation calculation, we construct an exact, time-independent, spherically symmetric Einstein benchmark. Its effective energy density is concentrated in the transition region and vanishes at the centre. For every finite, nonzero transition width and finite source strength, the geometry has finite polynomial curvature invariants, with curvature tending to zero at the centre. Above a calculable strength threshold, it admits inner and outer horizons. The required effective density and directional pressures violate the null energy condition in a central region, explicitly identifying the null-convergence hypothesis of classical singularity theorems that this geometry does not satisfy. At fixed total mass, narrowing the transition recovers the Schwarzschild geometry at every nonzero radius, while the maximum curvature diverges at analytically determined rates. This limit requires a simultaneous increase in source strength and therefore differs from narrowing the transition at fixed strength. The calculation establishes a family of regular interiors and a controlled geometric singular limit. Its proposed dynamical association with progressively deeper cancellation remains a PAM conjecture. Within this interpretation, finite local cancellation can be represented by a regular black-hole geometry, while exact perfect cancellation belongs to global closure beyond the domain of the emergent spatial description.