This work develops a fully explicit mathematical and computational framework to investigate a classical philosophical problem: whether objects can exist independently of observation in a purely relational setting. We construct a state space of graphs representing candidate “objects,” and define a Markovian dynamics based exclusively on structural similarity, without introducing any intrinsic properties, energies, or external criteria. In this baseline regime, the system converges to an approximately uniform stationary distribution, indicating the absence of privileged configurations and, therefore, the absence of intrinsic objects. We then introduce observers in a minimal and formal way as low-dimensional projections of the feature space, coupled with a memory parameter that biases the dynamics. Under these conditions, localized regions of stability emerge in the stationary distribution. These regions can be interpreted as proto-objects: coherent, reproducible structures that appear stable from the perspective of a given observer. The central result of the work is obtained through a large-scale bootstrap over the space of observers. By sampling hundreds of observers and comparing their induced stable regions, we find that: The overlap between proto-objects identified by different observers is typically negligible (mean ≈ 0.037, median = 0). Stable regions are robust within a given observer but highly unstable across observers. No non-trivial subset of states is invariant under changes of observer (no-go result). Furthermore, the geometry of observer space exhibits a percolation-like transition: for low similarity thresholds, observers form a single connected component, while for higher thresholds the space fragments into many small, weakly connected or isolated components. Crucially, no stable families of observers emerge that would support observer-invariant object classes. Taken together, these results show that object-like structures can emerge from relational dynamics, but they are inherently observer-dependent and fail to define invariant entities. In this precise sense, the model provides a constructive realization of the “object of negation”: an entity that appears stable under a given analysis but cannot be sustained as an invariant structure across all perspectives. The work connects to several domains: relational approaches in physics, gauge redundancy and representational equivalence, statistical non-identifiability, and philosophical analyses of intrinsic existence. All results are reproducible from the provided dataset and code, and the framework is sufficiently general to be extended to other relational systems. This contribution is not an interpretation but a construction: it demonstrates, within a rigorous and explicit model, that the search for observer-independent objects in a purely relational setting fails in a precise and quantifiable way.
Eduardo Gonzalez-Granda Fernandez (Mon,) studied this question.