Abstract This article introduces an ontological framework consisting of a geometric model and its associated formulation, challenging the Theory of Everything. The geometric configuration of the model – fundamental interrelationships model (IRM) – captures a set of interrelationships invariantly underlying transformation across domains. These interrelationships include, but are not limited to: serial–parallel relations, transition of state, critical point, continuation–discontinuation, convergence–divergence, contraction–expansion, singularity–plurality, commonality–difference, symmetry–asymmetry, dynamics–stability, order–disorder, limitation–without limitation, hierarchical structure, and interconnectedness. Crucially, unlike current ToE candidates, the IRM asserts that both lifeless laws and living processes are specific expressions of these fundamental interrelationships. Physical phenomena and their laws, biological evolution, cognitive processes, and social organization are not separate domains governed by unrelated principles, but differentiated manifestations of the same generative operators – the fundamental interrelationships. Built upon this foundation, a wide range of well-established physical theories can be reinterpreted as domain-specific expressions of these deeper invariants, including: Newton's laws of motion Laws of thermodynamics Space-Time relationship Uncertainty principle Noether's theorem Wavefunction Collapse Chaos theory Complexity theory Simultaneously, biological phenomena – adaptation, natural selection, increasing complexity, division of labour, cooperation, hierarchical organization – can be shown to express the same underlying interrelationships. On this basis, a novel hypothesis is advanced: the evolution of life follows the same fundamental laws that govern physical processes, thereby offering a conceptual bridge between cosmological evolution (including the Big Bang) and biological evolution. The Latest Development: Ontological–Mathematical Hybrid Formulation The most recent advancement in this research is that there is no counterexamples have been found in repeated falsification tests conducted by the major AI platforms, and the IRM rules appear to underlie all states, systems and domains. Given that the universe is dynamic and constantly changing, the universal applicability of the IRM rules across all domains indicates that these fundamental rules are cross-domain invariant. This discovery gives rise to a breakthrough interpretation: the continuous horizontal axis of the model is the geometric representation of the cross-domain invariant interrelationships – the universal constants, serving as generative operators, that govern everything in the universe. In contrast, the discontinued curved lines oscillating around the axis represent the variables of causal determining factors and the properties defining the resultant existing states. Building on this new interpretation and the geometric model, a formal formulation capturing the principles of IRM is introduced: Φ (α, β, λ…) → E (a, b, c…) Here: Φ represents the set of fundamental interrelationships. α, β, λ… represent causal variables or determining factors. E denotes an emergent state of existence. a, b, c… represent the properties characterizing that state. In this formulation, Φ functions not merely as a constant, but as a generative operator. It governs the trajectory of causal variables and produces emergent properties through structured transformation. Thus, the fundamental interrelationships are both invariant and operative: they are the long-sought universal constants and the operators governing generative processes across domains. This leads to a crucial distinction. Traditional mathematical models are state-bound: their precision derives from symbolic specification tied to particular conditions. When defining properties change, the equation must change. By contrast, the IRM is not confined to state-specific symbols. It is non-numerical and geometric, representing the invariant relational structure that governs transitions between states. Because it abstracts from specific numerical definitions while preserving relational invariance, the IRM possesses what may be termed a totipotent capacity – the ability to represent phenomena across all domains without being restricted to any single configuration. Just as totipotent stem cells can give rise to differentiated forms, the fundamental interrelationships generate increasingly specialized laws while retaining universality at the foundational level. Together, the IRM and its formal ontological–mathematical expression constitute a new type of framework: a universal ontological–mathematical hybrid formulation. Rather than searching for a single ultimate particle or field, this approach identifies the invariant relational operators that govern all transformations. If successful, this framework offers not merely a unification of physical forces, but a unification of physics and life itself – marking a significant step toward addressing the longstanding challenge of a comprehensive Theory of Everything.
Gavin HUANG (Mon,) studied this question.