ACORN Booklet 8: Relativity — Projection Geometry and the Emergence of Relativistic Structure

ACORN Framework Booklet Series The ACORN framework is a geometric curvature–closure approach to fundamental physics in which mass, quantisation, and dynamical behaviour arise from closed circulation of intrinsic curvature channels governed by a compact canonical operator structure. From these canonical relations emerge invariant closure norms, quantised loop actions, and universal recurrence relations organising stable physical structure. The ACORN booklet series develops the consequences of this canonical framework across multiple domains of physics. Each booklet begins from the frozen Canon and explores how familiar physical phenomena arise as projections or consequences of curvature closure dynamics. This booklet develops the relativistic sector of the ACORN framework. Relativistic behaviour arises naturally when the intrinsic closure dynamics governed by the canonical curvature operator are projected into observable spacetime coordinates. Preservation of the invariant closure norm under projection produces the familiar relativistic relations governing time dilation, inertial response, and invariant propagation. Within this interpretation, the Lorentz structure appears as the projection geometry required to preserve curvature closure. The invariant speed ccc emerges as the propagation bound already embedded in the canonical operator and recurrence relations, while relativistic time dilation reflects the reparameterisation of intrinsic recurrence under projection. The framework also connects relativistic spacetime structure to the global curvature-closure condition expressed by the canonical operator O(GAB)=0O(G_{AB}) = 0O(GAB)=0. In this way both special and general relativistic behaviour can be understood as geometric consequences of the same underlying curvature dynamics. ACORN: Relativity therefore demonstrates that relativistic spacetime behaviour does not need to be introduced as an independent physical postulate. Instead it appears as the projection-level expression of invariant curvature closure already present in the ACORN Canon. This booklet prepares the conceptual ground for the subsequent development of gravitational structure, electromagnetic–gravitational unification, and cosmological curvature dynamics within the ACORN framework.