Quantum Scale Emergence: Relational Time, Weyl Geometry, and Conformal Cyclic Boundaries (Preprint v1.0)

Abstract. Physics describes one universe through separate grammars. General relativity makes time a dynamical property of geometry; quantum mechanics treats it as an external parameter. Cosmology invokes inflation, dark matter, and dark energy as distinct ingredients whose common origin remains unexplained. These are not three unrelated gaps. They share a single unresolved assumption: that distances, durations, and masses are available before the laws that govern them.The Conformal Emergent Reality Model (CERM) removes that assumption. Conformal geometry — causal structure without absolute scale — is taken as fundamental. A single scalar field, Omega, generates physical spacetime by combining a local response to Weyl curvature with Chronos, an accumulation of curvature-weighted history along a realised cosmic path. Scale is not a backdrop; it is the universe's evolving memory of how it was reached. Within stated limits the construction recovers familiar physics: an effectively classical metric yields the Einstein approximation, and a sufficiently classical geometric clock cancels its own rate factor to yield ordinary quantum evolution in physical proper time. The same scale dynamics faces cosmological tests across an aeon: conditional inflation with a dynamical exit, curvature-dependent Omegon excitations as a dark-sector mechanism, and accumulated Chronos as a possible source of late acceleration without a fundamental cosmological constant. Geometric expansion enlarges the information-bearing capacity of spacetime, linking the arrow of time to the growth of the physical carrier. Near conformal completion, mass and clock standards fade and selected boundary information may seed a new aeon — a mechanism inspired by Penrose's Conformal Cyclic Cosmology, realised here through distinct field-theoretic processes.Status of this version. Preprint v1.0. The mathematical derivations and technical appendices are complete; the prose is undergoing final editorial revision. Revised versions will be posted to this record as new versions.Keywords: emergent scale; conformal geometry; Weyl geometry; relational time; quantum gravity; Chronos; Omegon; geometric entropy; conformal cyclic boundaries; hierarchy problem; dark matter; geometric inflation.