ACORN Booklet 1: The Canon — Definition and Equations of The ACORN Framework

ACORN Framework Booklet Series The ACORN framework is a geometric curvature–closure approach to fundamental physics that originates from a simple structural observation: the inertial mass of matter may be expressed as a partition of two complementary curvature channels whose invariant combination preserves the observed mass norm. This relation naturally reveals a hyperbolic geometric structure linking mass, curvature participation, and dynamical exchange between orientable and non-orientable curvature channels. From this starting point the ACORN Canon emerges as a compact set of canonical equations governing curvature circulation, invariant closure norms, quantised loop actions, orthogonality conditions, and global curvature consistency. Quantisation therefore appears not as an independent physical postulate but as the arithmetic consequence of closed curvature recurrence. 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 presents the ACORN Canon itself.Beginning with the mass-partition observation, the booklet derives the canonical curvature operator, invariant closure relations, loop-action quantisation conditions, and recurrence structure that together define the ACORN framework. These relations establish the minimal geometric structure required for stable closed curvature circulation. The ACORN Canon therefore serves as the structural anchor of the framework. Subsequent booklets examine how the same closure architecture produces the structures associated with matter, electromagnetism, radiation and quantisation, relativity, gravitational interaction, and cosmological dynamics. In this way the ACORN programme seeks not to replace established physical theories but to clarify the deeper geometric structure that connects them.