ACORN: Unification for General Relativity and Quantum Mechanics - A Curvature–Closure Framework for General Relativity and Quantum Mechanics

This paper presents the architectural overview of the ACORN (Alternating Curvature Ontology of Relational Nature) framework, a geometric proposal connecting General Relativity and Quantum Mechanics through curvature closure and recurrence. In the ACORN framework, physical structure arises from curvature circulation within an intrinsic geometric domain referred to as T-space: X, Y, Z, T × C In this domain curvature evolves through two complementary channels: mNE (T) and mₑq (T) whose invariant closure norm is m² = mNE² − mₑq² Closed curvature circulation corresponds to stable matter, while open curvature propagation corresponds to radiation. Observable spacetime physics emerges through projection into the familiar spacetime domain (x, y, z, t) via an ACORN projection operator ΠACORN. Under this projection: • orientable curvature contributes to gravitational structure• non-orientable curvature contributes to electromagnetic structure• closed curvature modes appear as stable matter• open curvature propagation appears as radiation A key structural relation linking propagation and closure is the recurrence relation m c² T₀ = N h which connects relativistic energy (associated with the propagation constant c) with quantum action (associated with Planck’s constant h). Within this interpretation: • General Relativity reflects curvature propagation• Quantum behaviour reflects closure and recurrence of curvature circulation• Gravitation and electromagnetism emerge as complementary projections of the same curvature tensor The framework therefore proposes a geometric bridge between the relativistic and quantum descriptions of nature while preserving their established empirical laws. This paper provides the architectural overview of the ACORN framework. Detailed derivations and extended treatments are available in the ACORN technical volumes, booklets, and supporting papers previously archived by the author on Zenodo.