The Paper and the Pen Framework: Foundational Derivations of Four-Volume Dynamics, Vacuum Energy Scale, Dark-Sector Energy Exchange, Neutrino Mass Drift, Baryogenesis, and Black-Hole Information Unitarity

We present the fully unified foundational manuscript of The Paper and the Pen Framework. The framework establishes a rigorous mathematical bridge connecting structural record-preservation mechanics, a signed Henneaux–Teitelboim (HT) canonical variable, accumulated spacetime four-volume dynamics, and internal topological memory. We demonstrate that the initial Poisson record-fluctuation law (HB Law), scaling as , inherently fixes the physical cosmological constant order of magnitude (), agreeing with observed dark energy density without scale fine-tuning. We formally distinguish this initial Poisson counting regime from the macro-coupling inverse-linear width law (). Using a fully variational HT-axion action, we derive the exact covariant energy exchange rate between dark energy and dark matter without vacuum density contradictions. Furthermore, we provide first-principles mathematical derivations for: (i) accumulated past light-cone four-volume saturation in FLRW geometry; (ii) redshift-dependent Majorana neutrino mass evolution ; (iii) dimensionally exact CTP noise kernel normalization for non-equilibrium baryogenesis; (iv) USR primordial black hole formation and inelastic LUX-ZEPLIN recoil kinematics; and (v) exact preservation of the record operator , proving black hole evaporation unitarity alongside a Poisson-averaged Page entropy envelope.