Towards a Relational Account of Spacetime Symmetries and Structural Scales: An Axiomatic Framework and Algebraic Minimal Realization Based on Observation–Feedback Closure

This work presents a two-stage first-principles construction for foundational physics. In the first stage, an axiomatic framework is introduced in which physical objecthood is defined exclusively through participation in observation–feedback (OF) processes. At this axiomatic level, no background spacetime, metric, Hilbert space, or symmetry group is assumed a priori. In the second stage, a minimal faithful realization of this framework is adopted, consisting of a set of explicitly stated, controlled algebraic choices that support finite operational distinguishability. Within this minimal realization, a hierarchy of physically significant structures is consistently represented: an internal O(3) symmetry with oriented SO(3) sectors; a Lorentz-type kinematical structure with invariant group SO⁺(3,1) (the proper orthochronous Lorentz group) and an associated invariant propagation scale that occupies the structural role of the conventional speed c; and a minimal closure scale that, under standard action-dimensional normalization, plays a structural role analogous to that of the reduced Planck constant ℏ. This construction thus provides a unified relational setting in which the core kinematical architectures of special relativity and quantum mechanics admit a consistent, operationally grounded representation, realized under explicitly stated minimal assumptions. No derivation of dynamical equations or direct identification with empirical spacetime geometry is claimed.