This work extends the foundational framework by introducing operators acting on sections of the fibered structure, enabling relational geometry across the base space. A connection operator is defined: ∇ : Γ(E) → Γ(T*O ⊗ E) Curvature is introduced as: R(v, w)s = ∇v∇ws − ∇w∇vs A fiberwise metric structure is defined to provide measurement: gα : Fα × Fα → ℝ All operators are defined in a strictly algebraic, non-differential setting, without assuming a smooth manifold structure. Variation is interpreted structurally rather than through infinitesimal calculus. Compatibility conditions ensure: • Fiber preservation • Projection invariance • Structural consistency across layers This layer establishes a complete relational geometric system while remaining within the constraints of the foundational structure.
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Ivan Petrov Pasev
United Institute of Informatics Problems
Digital Science (United States)
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Ivan Petrov Pasev (Mon,) studied this question.
www.synapsesocial.com/papers/69c7724e8bbfbc51511e2a4f — DOI: https://doi.org/10.5281/zenodo.19237961