Tone Theory and the Hubbard Model on the Honeycomb Lattice
Anthony SANTANA
Published Oct 7, 2026• 0 citations
Abstract
Abstract This paper establishes a fully causal, real-space geometric reformulation of multi-body transport,excitonic binding stability, and energy shifts within the Grand Unified Theory (GUT) context of theTension-Optimized Newtonian Entropy (TONE) framework. By replacing abstract, non-local quantumwavefunctions, electron-hole probability matrices, and configuration-space abstractions with continuousreal-wave currents moving across a discrete honeycomb lattice baseline, we show that two-body boundstates emerge natively from physical torque gradients and metric twists. Under this framework, themulti-particle states collapse via the Law of Large Numbers, forcing non-commuting background noiseto average out to zero and cancel completely. This leaves a deterministic net energy flow governed by aconserved Hamiltonian across the pixelated pores of the space-time canvas. We evaluate the empiricaltransport parameters—the bipartite tight-binding hopping parameters, the multi-particle dispersion en-ergy relations, and the exact two-body energy shifts relative to non-interacting thresholds—as explicitmechanical reactions governed by localized hydrostatic fluid-shear stresses and Planck-length geomet-ric limits (lP ). This approach organically eliminates infinite ultraviolet divergences and non-physicalprobability collapses by providing an absolute geometric floor, demonstrating that topological trans-port invariants and attractive particle-hole correlations are macroscopic manifestations of hydrodynamicresonance and coordinate path tracking within a granular, elastic space-time matrix. PACS Numbers: 71.35.-y, 02.70.Ss, 05.30.Fk, 11.15.HaKeywords: TONE Framework, Quantum Monte Carlo, Honeycomb Lattice, Hubbard Model, ExcitonBinding, Geometric ContainmentCopyright Notice: Copyright Pending © 2026 Anthony Santana. All Rights Reserved.DOI: 10.5281/zenodo.23201226
- DOI
- 10.5281/zenodo.23201225
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