Motion-Breath-Exchange lll
Year: 2026
Type: article
Abstract: We introduce the Closed Shape: the unique geometric object that simultaneously admits a \mathbb{Z}_5-grading with dihedral D_5 symmetry, a dual-conjugate pair of faces related by a 36^\circ phase shift and inverse golden-ratio weights, discrete closed quanta whose fundamental mass window lies near 2.8–3.3\,M_\odot, and a single invariant sector to which every differentiation returns. This object is realised by the Ly-manifold equipped with the global Motion—Breath—Exchange action, the graded metric g^{ij}=\varphi^{-d_5(i,j)}, and the dual Dirac comb. The construction is offered in the spirit of Einstein's Spinozist affirmation of the orderly harmony of what exists. It supplies a concrete, falsifiable geometric structure whose internal logic realises the kind of rational self-similarity associated with that harmony. We state sharp observational criteria by which the framework can be confirmed or refuted, anchored in the lower compact-object mass region, hierarchical merger signatures, and residual large-angle features of the cosmic microwave background. The Closed Shape stands or falls by those tests. Keywords: Motion-Breath-Exchange; Closed Shape; \mathbb{Z}_5-grading; D_5 symmetry; golden ratio; discrete mass quanta; Słowik Hypothesis; hierarchical mergers; CMB anomalies --- Interpretive Stance The geometric construction developed in this paper is offered in the spirit of Einstein's affirmation of "Spinoza's God who reveals himself in the orderly harmony of what exists." It is compatible with a theistic-evolution / evolutionary-creation reading of natural history, yet the mathematical claims, the discrete mass quanta, and the observational predictions stand independently of that reading. The Closed Shape is advanced as a falsifiable geometric object; any theological interpretation remains secondary and optional.
Authors: Słowik, Marcin, Tully, Chloe J.
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204159705
FWCI:
Cites:
Cited by:
Related to: