The Paper and the Pen Framework: Topological Dark Matter Unification, Axion-PBH Duality, and Exothermic LZ 2026 Recoils

We present a unified topological resolution to the dark matter nature within The Paper and the Pen framework. Rather than introducing unconstrained ad-hoc particles, dark matter is formulated as a dual-scale manifestation of the internal space memory lattice. The continuous wave sector yields QCD axions (m_a ~ 10 - 100\ ) accessible to dielectric haloscopes like MADMAX and ADMX. Concurrently, localized topological collapse during ultra-slow-roll inflation forms Primordial Black Holes (PBHs) spanning the asteroid-mass window (10⁻¹⁶ M_ ≤ MPBH ≤ 10⁻¹⁰ M_). Furthermore, we provide a complete analytical explanation for the high-energy 248 keV nuclear recoil event reported by LUX-ZEPLIN (LZ 2026) via an inelastic exothermic scattering channel (χ_H + N → χ_L + N) mediated by a dark photon with mass splitting δ ~ 0.5 - 1.0 MeV and kinetic mixing ε ~ 10⁻⁶.