We introduce a minimal relational network model in which superconducting-like behavior emerges as a collective phase of constrained connectivity and phase coherence, without assuming microscopic electrons, phonons, or material-specific interactions. The model is formulated as a concrete instantiation of a previously introduced axiomatic relational–informational framework for emergent geometry and effective spacetime, in which geometry and effective forces arise from constrained information flow rather than from a background manifold. Mathematically, this construction is realized on a finite weighted graph with binary edge-activation variables and compact vertex phase variables, sampled through a Gibbs ensemble generated by an additive informational action. The system is represented as a finite weighted graph with weighted edges encoding transport or informational costs, augmented by dynamically activated low-cost channels and compact phase degrees of freedom defined at vertices. The effective edge costs induce a weighted shortest-path metric, providing an operational notion of emergent relational geometry. Using Monte Carlo simulations on two-dimensional periodic lattices, we show that the same informational action supports three distinct emergent regimes: a normal resistive phase, a fragile low-temperature–like superconducting phase characterized by noise-sensitive coherence, and a noise-robust high-temperature–like superconducting phase in which global phase coherence persists under substantial fluctuations. These regimes are identified using purely relational observables with direct graph-theoretic and statistical-mechanical interpretation, including percolation of low-cost channels, phase correlation functions, an operational phase stiffness (helicity modulus), and a geometric diagnostic based on relational ball growth. In particular, we extract an effective geometric dimension from the scaling of low-cost accessibility balls, using a ball-growth relation of the form B(r) ~ rdeff, revealing a clear monotonic hierarchy between normal, fragile superconducting, and noise-robust superconducting—like regimes. This demonstrates that superconducting-like behaviour in the present framework corresponds not only to percolation and phase alignment, but also to a qualitative reorganization of relational geometry. Robustness is tested via finite-size comparison between 8 × 8, 12 × 12 and 16 × 16 lattice realizations. Within this framework, normal and superconducting-like behavior arise from the same underlying relational mechanism and differ only in the structural stability of connectivity, coherence, and geometric accessibility under fluctuations. The aim of this work is structural rather than material-specific: we do not reproduce detailed experimental phase diagrams or microscopic pairing mechanisms, but identify minimal relational conditions under which low-dissipation, phase-coherent transport can emerge as a generic organizational regime of constrained relational systems.
Brumă et al. (Sat,) studied this question.