2026/04/28 by Jean-Pierre Magnot · 1 voice
Physics and Astronomy · #physics.gen-ph
We introduce cosurfaces with values in the group \(\PCn(H)\) of \(H\)-valued reciprocal pairwise comparison matrices. The composition law is covariant on upper triangular coefficients and contravariant on lower triangular coefficients, which makes \(\PCn(H)\) a natural target for oriented gluing constructions. Starting from a directed family of finite oriented discretizations, we define finite configuration spaces, coarse-graining maps induced by ordered refinements, and the associated universal projective limit. This yields a multi-scale organization of local comparative data in which global objects are reconstructed only through compatibility across scales. In the stochastic setting, projectively compatible probability laws define a cylindrical semantics on the limit space. We also introduce inconsistency observables, interpreted as discrete curvature-type defects measuring obstructions to global coherence. The resulting framework is simultaneously geometric, algebraic, and probabilistic, and suggests a foundational perspective on relational structures built from local comparisons rather than absolute observables.