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Virtual-Real Interface: A Geometric Framework for Reasoning About Multi-System Interactions in Skeletal Biology

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Server
Preprints.org
DOI
10.20944/preprints202610.1797.v1

Biological systems achieve homeostasis through networked interactions among regulatory, transport, executive, and tuning components. However, existing frameworks typically capture only pairwise or axis-specific relationships, lacking a unified geometric language to characterize how these four functional roles assemble into robust alliances or expose fragile dependencies. Here we introduce the 'Virtual-Real Interface' (VRI)—a qualitative geometric-logical framework derived from the physical operation of folding a triangular sheet into a pseudo-tetrahedron. In this framework, the nervous (A), circulatory (B), target (C), and endocrine (D) systems are mapped onto the four vertices. The two geometrically closed faces (A–B–D and B–C–D) represent functionally self-sufficient subsystem alliances ('actual faces'), while the two open faces (A–C–D and A–B–C) expose systemic vulnerabilities ('virtual faces')—geometric nonexistence mapping onto functional non-autonomy. Using the skeletal system as a demonstrative case, we show that the framework (i) enumerates three etiological subtypes of osteoporosis based on the initial defect locus, (ii) predicts prognostic divergence by distinguishing whether the basal face is actual or virtual, and (iii) proposes multi-target repair strategies for postmenopausal osteoporosis. The framework extends to multi-organ interaction networks via co-point, co-edge, and co-face construction rules. Importantly, VRI is not a biological discovery per se, but a structurally derived and empirically testable methodological tool for network-based disease subtyping and therapeutic prioritization.

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