Matthias Asare-Darko

A Solution to the Birch and Swinnerton-Dyer Conjecture via K 11 Network Matrices and ZIP-Helmholtz Operators in Big Boot Gauge Theory

This paper presents a formal resolution framework for the Birch and Swinnerton-Dyer(BSD) Conjecture by mapping the arithmetic and analytic properties of an elliptic curve ontothe adjacency matrix of a discrete K11 complete graph network within the Big Boot GaugeTheory (BBGT). By...

A Solution to the Birch and Swinnerton-Dyer Conjecture via K 11 Network Matrices and ZIP-Helmholtz Operators in Big Boot Gauge Theory

This paper presents a formal resolution framework for the Birch and Swinnerton-Dyer(BSD) Conjecture by mapping the arithmetic and analytic properties of an elliptic curve ontothe adjacency matrix of a discrete K11 complete graph network within the Big Boot GaugeTheory (BBGT). By...

A Solution to the Hodge Conjecture via K 11 Network Matrices and ZIP-Helmholtz Operators in Big Boot Gauge Theory

This paper presents a formal resolution framework for the Hodge Conjecture by integrating the Big Boot Gauge Theory (BBGT) with a discrete K_11complete graph matrix topology. By embedding complex projective varieties into octonionic ZIP space (OZIP) and implementing the ZIP-Helmh...

A Solution to the Hodge Conjecture via K 11 Network Matrices in Big Boot Gauge Theory

This paper presents a formal resolution framework for the Hodge Conjecture by integrating Matthias Asare-Darko’s Big Boot Gauge Theory (BBGT) with a discrete K11complete graph matrix topology. By embedding complex projective varieties into octonionic ZIP space (OZIP) under the ba...

Unified Big Boot Gauge Theory (BBGT): Macro-Action Quantization (h_n = 2^nh_z ), Non-Associative OZIP Geometries, and N-Fold Topological Locking Across Cosmic Scales

Standard General Relativity (GR) and Quantum Mechanics (QM) remain fundamentallyun-reconciled due to the omission of non-associative topological boundary constraints, singular division limits, and force-hierarchy scaling. In this paper, we formalize the completeBig Boot Gauge The...

The Macroscale Quantum Wave Equation: Transitive Logical Derivation of Non-Associative Macro-State Evolution in Big Boot Gauge Theory (BBGT)

{"Microscopic quantum dynamics is governed by the linear Schrodinger and Dirac equationsscaled by Planck’s constant (ℏ). However, continuous spacetime assumptions break downwhen attempting to describe macroscopic, topologically locked celestial systems without coordinate singular...

Full Darkon-Euler-Lagrange Equations of Motion and Field Dynamics of the Darkon-Allotey Macro-Wave Formalism in Big Boot Gauge Theory

We present a complete variational field theory derivation of the Euler-Lagrange Equationsof Motion (EoM) governing the Darkon-Allotey Macro-Wave Quantum Mechanics framework within Big Boot Gauge Theory (BBGT). By explicitly varying the non-associative Lagrangian density L_ZIP def...

Topological Entanglement Capacitance and Meson Mass Spectrum Formalism

Extending the Topological Entanglement Capacitance (TEC) and Big Boot Gauge Theory(BBGT) framework from SU(2)f to SU(3)f, the pseudo-scalar meson octet (π, K, η) mapsonto an expanded 6-node reduced interaction graph V octet= {u, u, d, ¯ d, s, ¯ s¯}.The valence strange quark intro...

Darkon-Yang-Mills Theory and the Mathematical Proof of the Yang-Mills Mass Gap (∆ > 0)

We present a rigorous proof of the Yang-Mills Existence and Mass Gap Problem establishedby the Clay Mathematics Institute using Big Boot Gauge Theory (BBGT) and its DarkonYang-Mills (DYM) non-associative geometric framework. Standard classical non-abelian gauge theories on R^4 po...