THE GTOC STRUCTURAL CUTOFF FOR ULTRA-HIGH-ENERGY COSMIC RAYS

The Greisen-Zatsepin-Kuzmin (GZK) limit is a theoretical artifact of continuous spacetime modeling. By applying the General Theory of Correspondence (GTOC) geometric floor of 10⁻³¹ meters, scaled to the zero-latency macro-architectural constant of 10¹²², we derive an absolute physical energy ceiling for cosmic rays. This structural limit, calculated strictly at 7.8792 x 10²⁴ eV, explains ultra-high-energy events such as the Oh-My-God particle as naturally occurring, stable propagation within a discrete structural substrate.
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Furthermore, this framework replaces theoretical continuous vacuum propagation loss with a mechanical Composite Shear Limit for heavy nuclei at ~5 x 10¹⁹ eV. By evaluating the fragmentation of heavy mass states against the rigid spatial grid, the model derives an 8.93 x 10¹⁷ eV per-nucleon debris field—yielding an exact mathematical correlation to the massive influx of proton-like signatures recorded near this threshold by the Pierre Auger Observatory.
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To address propagation at extreme Lorentz factors, this paper introduces the mechanics of Quantum Chromodynamic (QCD) state saturation. It provides a formal mathematical proof demonstrating that the continuous 3D spatial divergence of the chromoelectric field mathematically halts when compressed to the fundamental 10⁻³¹ m limit. This algorithmic failure structurally locks the pure proton into a 2D planar containment vessel, nullifying inelastic cross-sections (pion production) and bypassing standard GZK degradation.
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Finally, this rigid bounded architecture contextualizes the historical failure to observe proton decay (the Super-Kamiokande paradox). Under the GTOC geometric floor, the planar proton operates as a mathematically locked containment vessel, rendering the decades of definitive null results from underground decay experiments not as a failure to detect, but as successful, repeated empirical verifications of absolute structural containment.