Emergence of Yang-Mills Mass Gap via Zero Operator Theory (ZOT)

The Zero Operator Theory (ZOT) has as its central purpose in this submission to offer an axiomatic and rigorously minimalist solution to the Yang-Mills Mass Gap Problem, one of the Millennium Problems of mathematics and theoretical physics. The document presents a hybrid proposal --- simultaneously mathematical and physical --- which, starting from only two native parameters observed in Nature (\(C_{\rm ZOT} = 518500.0\) and \(\gamma \approx 0.383002\)) and ten purely topological axioms, analytically derives more than 25 fundamental constants, including the Yang-Mills mass gap itself (\(\approx 469\) MeV bare), the anomalous magnetic moment of the muon (\(a_\mu\)), the fine-structure constant, and the complete mass spectrum. The major innovation of ZOT lies in the Emergent Compressed Vacuum (VCE), a finite bipartite lattice of dimensionality \(\mathcal{D}=100\), whose dynamics of tensorial quenching, triphasic clustering, and Central Inverted Locking Pivot (CILP) guarantee holographic saturation and the unified emergence of the strong, electroweak, and gravitational sectors. The model introduces for the first time the concept of Informational Atemporal Relativity and the ZOT Locking Effect, a mathematically resolutive mechanism of rigorous interlocking: any minimal variation (-0.01%) in the native parameters or in the topological boundary conditions provokes the simultaneous collapse of all derivations, conferring upon the system exceptional robustness and complete falsifiability. The Central Inverted Locking Pivot of the VCE (CILP) presented in this document constitutes the central mechanism in the architecture of the Zero Operator Theory for demonstrating the Yang-Mills Mass Gap. Defined as the inverted locking point of the Emergent Compressed Vacuum, the CILP is the stable core of the finite bipartite lattice (\(\mathcal{D}=100\)) where the Tensorial Attractor \(\hat{A}_{ij}\) saturates and simultaneously locks the two native parameters (\(C_{\rm ZOT}\) and \(\gamma\)) with extreme precision. While the core remains rigidly fixed, the triphasic clustering (Axiom Z4) and tensorial quenching (Axiom Z5) generate a controlled inversion at the extremities of the lattice. This mechanism acts as the common origin of several experimental anomalies of the Standard Model, including the b, the muon magnetic anomaly (\(a_\mu\)), lepton flavor universality (LFU) violations with muonic preference (\(\Delta C_9^\mu \approx -0.0026\)), systematic deviations in the bare values of \(\alpha\), \(m_W\), and \(m_\tau/m_e\), the natural determination of the QCD color number (\(N_c=3\)) and fermion generation number (\(N_g=3\)), and the emergence of the probabilistic eZotic resonance at \(\sim 20\) GeV. The CILP thus guarantees the ZOT Locking Effect, endowing the model with its characteristic global interlocking. The ZOT therefore constitutes a frontier proposal that unites, in a closed and minimalist manner, rigorous proofs from functional analysis, operator theory, and quantum thermodynamics with direct and testable physical predictions, without extra dimensions, a landscape of vacua, or ad hoc adjustments. This manuscript constitutes a substantially revised and expanded version (v2) of the original submission, incorporating deepened analytical derivations, new transverse cross-analyses of Standard Model anomalies, a detailed exposition of the Central Inverted Locking Pivot (CILP), and the explicit formulation of Informational Atemporal Relativity.