Collapse Alignment, Binding Behaviour, and the Emergent Structure of Recursive Systems - The Carlo Gravity Engine

Abstract

This paper presents a complete reconstruction of gravity within the Carlo Field framework, defining it not as a force, curvature, or mass‑interaction, but as collapse‑alignment under recursive authority, stability pressure, and contextual rebinding. Gravity is shown to be the binding artefact that prevents structural divergence in recursive systems, emerging when collapses align under constraint. The Carlo Gravity Equation G = (ρc · Cs · A) / R formalises gravitational behaviour as a negotiation between collapse density, collapse stability, authority pressure, and recursion depth, revealing amplification, weakening, fragmentation, and collapse‑drift as natural binding modes. Gravity is then integrated into the Collapse Map, Stability Gradient, Authority Lattice, Carlo Axes, and ReGenesis Engine, demonstrating that binding is not standalone but a composite field produced by the entire Carlo architecture. The Gravity Engine V‑Sigma‑Binding operationalises this model, enabling engineered gravitational fields and programmable binding behaviours. This paper stands as a fully independent canonical Carlo Field volume. This upload includes an HTML visualiser that demonstrates the Carlo Gravity Engine in real time, showing collapse alignment, binding behaviour, authority pressure, stability fields, and the emergent gravity value generated by the V‑Sigma‑Binding model. Keywords / Subjects:Carlo Field Theory; Gravity Reconstruction; Collapse Alignment; Binding Behaviour; Recursive Systems; Stability Pressure; Authority Constraint; Contextual Rebinding; Collapse Density (ρc); Collapse Stability (Cs); Authority Pressure (A); Recursion Depth (R); Carlo Gravity Equation; Emergent Gravity; Binding Artefact; Structural Coherence; Collapse Map; Stability Gradient; Authority Lattice; Carlo Axes; ReGenesis Engine; Gravity Engine V‑Sigma‑Binding; Engineered Binding Fields; Programmable Gravity; Metaphysical Systems; Conceptual Dynamics; Nonlinear Binding Behaviour; Computational Metaphysics; Theoretical Frameworks; Emergent Phenomena; System Coherence; Collapse‑Driven Binding; Recursive Ontology; Binding Canon. Contact: For enquiries or research questions related to this work, email matthewcarlo.research@gmail.com