The Borda–Milan Principle: Emergent Spacetime from Finite Relational Structures

This work introduces the Borda–Milan Principle, a foundational framework proposing that spacetime, gravity, matter, and probabilistic behavior may emerge from finite relational structures governed by local compatibility and contractive refinement dynamics.Rather than assuming spacetime as a fundamental background, the model explores how geometric structure can arise as the stabilized limit of iteratively refined compatibility relations. Within this framework:spatial distance emerges as a compatibility cost,time corresponds to the progression of convergence toward structural stability,gravity arises from gradients in compatibility density,matter appears as persistent coherence attractors,energy corresponds to the rate of structural convergence,probabilistic behavior emerges from fluctuations among competing refinement paths.The proposal is formulated using concepts from metric geometry, graph structures, and contractive mappings, connecting emergent physical structure with fixed-point theory.This manuscript presents a conceptual and mathematical architecture together with falsifiable predictions, including residual geometric fluctuations and stabilization limits replacing singularities. The work is intended as an exploratory contribution to the foundations of physics and is offered to encourage analysis, critique, and further development.Scientific ContextThe framework relates to ongoing research programs investigating emergent spacetime, relational physics, and discrete geometric models, while introducing a distinct mechanism based on contractive refinement dynamics.Intended AudienceResearchers in:theoretical physicsmathematical physicscomplex systemsgeometry and dynamical systemsfoundations of science