The Sphere of Everything — A conceptual framework of invariants, regimes, and black holes

This work presents the “Sphere of Everything”, a conceptual framework in which existence is governed by invariant rules rather than objects. The model is represented as a sphere composed of two complementary hemispheres sharing a common center of invariants. Elements and configurations are mapped on the surface as positions and possibilities, while the center contains only rules. Within this framework, trajectories describe paths of coherence across regimes; time emerges as an effect of persistence rather than a fundamental axis. Extreme phenomena, such as black holes, are interpreted as regime limits where form, state, and time lose describability while invariant rules remain valid. Quasars are discussed as manifestations of equilibrium restoration, not as anomalies, and matter is treated as conserved through transformation of regime, without transfer between matter and antimatter. Version update: v2 This version adds a structured conceptual clarification on light as a regime effect, introducing admissibility, the role of matter as a constraint, and observation as a physical process.It also consolidates the interpretation of energy as a cost of coherence (E = m·lim²).Core assumptions and invariants of the model remain unchanged. Version update: v3 This version introduces a focused boundary case related to the limits of remote control under increasing distance. The work remains part of the broader conceptual framework “The Sphere of Everything”, whose complete structure is developed outside this document. Version update: v4 This version introduces the void as a structural and central condition of the framework.The void is not treated as the absence of matter, but as the regime in which invariant rules remain operative even when objects, states, and fields are removed.This clarification makes explicit that existence, within the Sphere of Everything, is not founded on objects or particles, but on the invariant necessity of rules that govern all possible regimes of existence.Core assumptions and invariants of the model remain unchanged. Version update: v5 This version introduces a structured conceptual clarification of light within the framework of the Sphere of Everything. Light is not treated as an object propagating through space, nor as a fundamental entity, but as a regime effect: the observable manifestation of space-time operating in proximity to a limit of admissibility (lim).To formalize this interpretation, the concepts of admissibility and spatem are introduced, describing the local state of space-time in terms of the configurations it can sustain coherently. Within this framework, matter acts as a structural regulator of admissibility, constraining which configurations remain compatible as space-time approaches a regime limit. Optical phenomena such as color, transparency, and reflection emerge naturally as consequences of selective compatibility, without introducing new entities or mechanisms. Observation is interpreted as a physical process of regime compatibility, in which the observer enters a coherent state.This clarification reorganizes existing physical descriptions of light within the invariant-based structure of the Sphere of Everything. Core assumptions and invariants of the model remain unchanged. Version update: v6 This version introduces a structured conceptual clarification of energy within the framework of the Sphere of Everything. Energy is not treated as a substance, resource, or transferable quantity, but as a measure of the cost required to maintain coherence within a given regime of existence.Within this framework, mass is interpreted as persistence of state, and energy emerges as the necessary cost to sustain that persistence under invariant constraints. The relation commonly expressed as E = m·c² is reinterpreted as a metric representation of a deeper structural relation, formalized as E = m·lim², where lim denotes a regime limit rather than a numerical constant.In this formulation, c appears only as a conventional metric expression arising from the adoption of specific units, not as a fundamental ontological boundary. This clarification preserves continuity with the interpretation of light introduced in version v5: both light and energy are described as effects of regime proximity to admissibility limits, rather than as primary entities.Energy constrains persistence across regimes; light manifests near the boundary where describability of state approaches its limit. No new assumptions are introduced.Core invariants, the role of the center, and the interpretation of extreme phenomena remain unchanged. Version update: v7 This version introduces a formal epistemological stress test concerning limits of access to infinite structures, using π as a conceptual case study within the Sphere of Everything framework. The section does not propose a theorem, proof, or physical interpretation of π. Instead, it examines whether the hypothesis of compatibility between an infinite non-periodic structure and the abstract representability of finite information can be considered logically admissible without generating structural contradiction. The analysis explicitly separates: conceptual possibility from factual truth; representability from accessibility; coherence from knowability. A central clarification introduced in this version is the distinction between infinite structure and finite access. Any operational interaction with π remains necessarily finite, while the complete structure remains inaccessible from within the describable regime. Within the Sphere of Everything model, this condition is treated as formally analogous to the equator: a regime horizon that governs behavior without ever becoming fully reachable. This version does not claim that π contains meaningful hidden information, nor that such information can be extracted or operationally decoded. The purpose of the stress test is exclusively to evaluate conceptual admissibility under invariant structural constraints. No new ontological entities or physical mechanisms are introduced. Core invariants, regime continuity, conservation, and operational non-contradiction remain unchanged. This document is part of a broader conceptual framework, “The Sphere of Everything”.The complete structure, assumptions, and ongoing development are maintained at: www.sferadeltutto.it