This article presents a critical–propositional analysis of Symmetries and Motions in Manifolds, by J.W. van Holten and R.H. Rietdijk, originally published as NIKHEF-H/92-08 and available on arXiv with DOI https://doi.org/10.48550/arXiv.hep-th/9205074. The study examines the article’s treatment of symmetries, motions, Lie algebras, Killing vectors, Killing tensors, Noether’s theorem, scalar particles, spinning particles, and motion in curved spacetime, especially in relation to the Schwarzschild metric. The analysis places van Holten and Rietdijk’s mathematical-physical formalism in dialogue with the Theory of Objectivity (TO), by Vidamor Cabannas and Denivaldo Silva. It evaluates possible compatibilities and tensions with TO’s modal axioms, phenomenic elements, Inducer Effects, cosmogonic theorem, and cosmological Eras. Special attention is given to the interpretation of conserved quantities as structural information and to the recent TO formulation according to which the transcendent element corresponds to knowledge or information produced in atomic relations, equivalent to atomic radiations. The article argues that Symmetries and Motions in Manifolds does not provide a cosmogonic model or a theory of cosmic origin, but it offers a technically significant field of dialogue with TO by showing how physical motion, conservation, and dynamic identity depend on formal structures of symmetry, boundary, invariance, recursion, and conserved information. The analysis concludes that the article has strong technical-dialogical relevance for TO, especially regarding structural conservation, the singularization of the physical element through spin, formal boundary, and mathematical recursion. This analytical study received analytical support from ChatGPT. Keywords: Theory of Objectivity; Vidamor Cabannas; Denivaldo Silva; J.W. van Holten; R.H. Rietdijk; Symmetries and Motions in Manifolds; Killing vectors; Killing tensors; Noether’s theorem; curved spacetime; spin; Schwarzschild spacetime; modal ontology; phenomenic elements; Inducer Effects; cosmogonic theorem; cosmological Eras; conserved information; atomic radiation; philosophy of physics.