Spider–Geometry Engine: A Radial Tension, Phase-State & Observer-Coherence Subsystem for Carlo Collapse Theory v2 (With Visualiser)

Abstract

Version 2 (PDF Included): Expanded framework complete with an interactive WebGL 3D geometric visualizer demonstrating the field equations running in real time. A fully structured Carlo Field Operator subsystem built from the intersection of mythic multi-limb symmetry, spider-web geometry, fighting-game flow dynamics, and collapse–rebind–emergence theory. The Spider–Geometry Engine models a radial lattice capable of expressing tension propagation, phase-state transitions, observer-driven coherence shifts, and multi-factor collapse cascades. It integrates seamlessly with the ReGenesis Engine and the Carlo Field Operator Compendium, providing a complete diagnostic, generative, and control-surface module. Core behaviours are governed by the collapse condition: α|T_ij| + βΔs_ij + γ|Ω| > Λ_crit where:- T_ij is edge tension,- Δs_ij is phase-state mismatch,- Ω is observer coherence,- Λ_crit is the collapse threshold. This subsystem includes:- Radial spider-web geometry with formal core embedding- Spring-based tension model with equilibrium evaluation- Phase-ring state machine with stiffness modulation- Observer node controlling global coherence (Ω)- Collapse and rebind operators for structural re-emergence- SVG visualiser scaffold for tension and collapse mapping- Full ReGenesis input/output channels- Complete taxonomy, state-space, documentation, diagrams, glossary, and appendix Revisited this release because, honestly, from my perspective, this was one of the coolest logical jumps I ever pulled off. Contact: matthewcarlo.research@gmail.com