Observation–Feedback Closure I: An Axiomatic Kinematical Existence Proof for Time, Structural Scales, Relational Space, and Lorentzian Kinematics

This paper is the first article in the Observation–Feedback (OF) Closure series. Without presupposing any spacetime manifold, metric, Hilbert space, symmetry group, or field equation, it presents an axiomatic kinematical existence proof for time, structural scales, relational space, and Lorentzian kinematics within the OF closure framework. Physical ontology is defined as a triadic relational system that can participate in admissible OF transitions and preserve its relational identity through its intrinsic closure-reserve structure. The paper establishes that the minimal positive closure magnitude plays the structural role of the reduced Planck constant under action-dimensional normalization, reconstructs effective relational space and Lorentzian kinematics from internal relational structure, and introduces a controlled realization hierarchy separating primitive ontology, representational kinematics, and emergent effective sectors. Under a controlled minimal positive-definite realization, the internal O (3) relational structure admits an effective relational externalization into a three-dimensional macroscopic spatial metric via lightlike comparison chains among stable systems, while the invariant propagation scale cₑff emerges as the effective Lorentzian propagation scale. In the early OF-dominated regime, where no stable spatial metric exists, inflation-like expansion is interpreted as a rapid growth of relational accessibility prior to stable metric reconstruction. What’s new in v1. 1. 1 (patch release): Strengthened mathematical foundation: the minimal positive-definite quadratic form (and hence O (3) symmetry) is now constructed from a binary OF response functional under stable symmetric comparison, replacing earlier provisional assumptions. Introduced a provisional internal gauge evolution parameter υᵢnt = ∂Cclo/∂E, reserved for future gauge-theoretic development in Paper II. All frozen results of v1. 1. 0 remain unchanged; this is a strictly additive and backward-compatible refinement. This version is intended as a developmental structural refinement of the OF Closure foundational program. No dynamical equations, field equations, coupling constants, interaction dynamics, or quantitative cosmological predictions are derived. Additional structural interpretations, including conjectural gravitational interpretations associated with closure-content variation, are designated as directions for future development.