Boundary-Selected Weyl-Squared Gravity and EFT at Conformal Boundaries

Paper I: Boundary-Selected Weyl-Squared Gravity and Effective-Field-Theory at Conformal Boundaries This paper establishes the structural foundation of the framework by proving that the Weyl-squared operator is uniquely compatible with a well-posed variational principle at smooth conformal boundaries in four dimensions. It demonstrates the existence of a strictly hyperbolic radiative attractor that ensures smooth conformal extension across the boundary without requiring additional degrees of freedom. Paper II: Geometric Memory Transfer and Conformal Transitions in Boundary-Compatible Gravitational EFT It introduces the geometric memory functional (N), a conformally invariant quantity that captures the accumulated Weyl curvature of a cosmological phase. The work proposes a transition mechanism where inherited geometric radiation drives the Hubble rate above particle mass scales, enabling conformal transitions without assuming particle decay or modifications to the Standard Model. Paper III: Microscopic Accumulation of Geometric Memory via Dimension-8 Operators in Conformal Cosmology This study details the microscopic mechanism of memory accumulation through a dimension-8 operator coupling Weyl curvature to scalar field kinetic terms. It demonstrates how nonlinear structure formation, particularly from supermassive black holes, saturates the memory function to provide the boundary data that sets mass parameters for the subsequent cycle. Paper IV: Primordial Cosmological Perturbations in Boundary-Compatible Geometric EFT It derives the primordial scalar and tensor power spectra within the boundary-selected EFT regime. The paper predicts a universal correlated suppression of primordial amplitudes by a factor of -1. 046 ₇₃, while preserving the standard inflationary consistency relations at leading order. Paper V: Ultralight Dilaton Dark Matter from Near-Conformal Dynamics in Geometric EFT It identifies a dark matter candidate emerging from the near-conformal hidden sector responsible for generating the framework's Weyl coefficients. The model predicts an ultralight dilaton with a mass of approximately 10^-22 eV, naturally generated through non-perturbative scale-symmetry breaking, which reproduces fuzzy dark matter phenomenology.