- T. Koslowski, P. Naranjo, and A. Vassallo. Pure shape dynamics: general framework.
*Classical and Quantum Gravity*, DOI 10.1088/1361-6382/ac9725, 2022.

The paper puts forward a general framework for describing relational physical theories. This framework’s novel take on relationalism is its insistence on describing any dynamical system by means of the intrinsic geometry of its associated curve in the suitable relational configuration space of the theory, namely shape space, whereby the corresponding equation of state of the curve expresses the ratio of change of one of its geometric degrees of freedom with respect to another one. The mathematical structure underlying the equation of state is a local section over a natural generalization of the unit tangent bundle, called shape phase space.

- A. Vassallo, P. Naranjo, and T. Koslowski. The physics and metaphysics of pure shape dynamics. In A. Vassallo, editor,
*The Foundations of Spacetime Physics: Philosophical Perspectives*, chapter 4, pages 108–132. Routledge, 2022.

The goal of this essay is twofold. First, it provides a quick look at the foundations of modern relational mechanics by tracing its development from Julian Barbour and Bruno Bertotti’s original ideas until present-day’s pure shape dynamics. Secondly, it discusses the most appropriate metaphysics for pure shape dynamics, showing that relationalism is more of a nuanced thesis rather than an elusive one. The chapter ends with a brief assessment of the prospects of pure shape dynamics in light of quantum physics.

- A. Vassallo, P. Naranjo, and T. Koslowski. A proposal for a metaphysics of self-subsisting structures. I. Classical physics.
*Synthese*, DOI 10.1007/s11229-022-03865-x, 2022.

The paper proposes a novel structural realist metaphysics for physics implemented using the theoretical framework of Pure Shape Dynamics, which provides a completely relational description of physical systems.

- A. Vassallo, D. Romano. The Metaphysics of Decoherence.
*Erkenntnis*, DOI 10.1007/s10670-021-00469-8, 2021.

The paper investigates the type of realism that best suits the framework of decoherence taken at face value without postulating a plurality of worlds, or additional hidden variables, or non-unitary dynamical mechanisms. It is argued that this reading of decoherence leads to an extremely radical type of perspectival realism, especially when cosmological decoherence is considered.

- A. Vassallo. Does General Relativity Highlight Necessary Connections in Nature?
*Synthese*, DOI 10.1007/s11229-020-03009-z, 2021.

The paper discusses the physical role that the Bianchi identities play in general relativity and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense.

- T. Bigaj, A. Vassallo. How Humean is Bohumianism?
*Foundations of Physics*, DOI 10.1007/s10701-020-00361-5, 2020.

The paper considers a Humean reading of the laws of physics applied to the particular case of Bohmian mechanics. It is argued that this “Bohumian” strategy saves the letter but not the spirit of the Humean doctrine of supervenience. The conclusion is that the best defense for Bohumians is to question the fundamental existence of complex physical systems and their states by treating any reference to them as a convenient description of the underlying collection of Bohmian particles.

Furthermore, here are the two papers that paved the way to the present project:

- A. Vassallo. Can Bohmian mechanics be made background independent?
*Studies in History and Philosophy of Modern Physics*, 52:242–250, 2015.

The paper investigates whether the structure of Bohmian mechanics is compatible with the best-matching procedure, which lies at the heart of shape dynamics.

- A. Vassallo and P. H. Ip. On the conceptual issues surrounding the notion of relational Bohmian dynamics.
*Foundations of Physics*, 46(8):943–972, 2016.

A follow-up paper in which the structure of a non-relativistic Bohmian theory based on best-matching is sketched, and its metaphysical consequences are discussed.