Carlo Geometry Compendium & System Extensions (Ω‑Tier Research Edition)

This deposit contains two core components of the Carlo Research Programme: (1) the official reading sequence for the Carlo Geometry Compendium, and (2) the first three system extensions expanding the framework beyond geometry. File 1 — HOW TO READ THIS COMPENDIUM — OFFICIAL ORDER This document provides the canonical reading order for the Carlo Geometry Universe. It organises all geometry families into a structured progression beginning with Classical Geometry and advancing through Collapse‑Driven, Carlo‑Native, Emergent, Exotic, and finally Ω‑Tier Geometry. The sequence is designed to support researchers in navigating the conceptual development of the Carlo system from established mathematical foundations to fully unified Ω‑tier constructs. The file concludes with the Geometry Universe Completion Page and an author’s note confirming full coverage of the geometry domain. File 2 — EXTENSION.txt This file introduces the first three extensions of the Carlo System: Carlo Physics, Carlo Dynamics, and Carlo Logic. Each extension is fully unfolded into ten sections, detailing the physical, dynamical, and logical behaviour of collapse, tension, topology, observer influence, phase‑state structure, fractal regimes, neutral zones, attractors, field theory, and Ω‑tier unification. These extensions form the operational and behavioural layers of the Carlo Universe and serve as the foundation for subsequent computational and cosmological tiers. Abstract: This deposit provides the foundational reading sequence and the first system extensions of the Carlo Research Programme. The reading order establishes a structured progression through the Carlo Geometry Universe, from Classical Geometry to Ω‑Tier unification. The extension file introduces the physical, dynamical, and logical layers of the Carlo System, detailing collapse behaviour, tension flow, topology evolution, observer influence, phase‑state structure, fractal regimes, neutral zones, attractors, field theory, and Ω‑tier unification. Together, these documents form the conceptual and operational basis for further study of the Carlo Universe across mathematical physics, complex systems, and computational geometry. Notes: These documents are part of the Carlo Omnibus series and represent the initial stages of the unified Carlo System. Subsequent tiers (Computation, Cosmology, Meta‑Layer, Closure) are published separately. This deposit is intended for researchers studying operator‑based geometry, collapse‑driven systems, emergent structures, and Ω‑tier unification. Contact: matthewcarlo.research@gmail.com Carlo Geometry Collapse‑Driven Geometry Ω‑Tier Geometry Carlo Physics Carlo Dynamics Carlo Logic Geometry Compendium Operator Systems Emergent Geometry Topology Mutation Observer Phase Phase‑State Geometry Fractal Regimes Unified Field Models Computational Geometry Frameworks Mathematics → Geometry & Topology Mathematics → Mathematical Physics Computer Science → Theory & Methods Physics → Theoretical Physics Physics → Complex Systems Interdisciplinary → Systems Theory Interdisciplinary → Computational Modelling