This manuscript presents a comprehensive analysis of the bulk density of magnetic monopole matter (magmatter), a material of critical importance to advanced galactic civilizations. We developed three theoretical models for mag-carbon density: a First-Principles (Packed Nucleus) model, a Bohr Radius (Isolated Atom) model, and a Diamond-like Lattice model incorporating packing efficiency. Our initial hypothesis, informed by the profound asymmetry of forces within magmatter, posited that its bulk density would align with the extreme condensation predicted by the Packed Nucleus model. Methodological validation against normal terrestrial diamond confirmed the distinct physical regimes governing normal and extreme matter. However, subsequent crystallographic analysis of synthesized mag-diamond samples, interpreted through the Elementary Nucleus Paradigm, has revealed an unexpected empirical result: its measured density ($\approx 4.19 \times 10^{37} \text{ kg/m}^3$) aligns perfectly with the Diamond-like Lattice model. This finding necessitates a significant revision of our understanding, confirming that magmatter forms stable, ordered crystal structures governed by Bohr orbitals, but only up to a fundamental limit: the Z=11 Stability Boundary, beyond which chemistry collapses into degenerate hadronic slag. This revised understanding, which also considers the potential influence of self-gravitation in larger constructs, opens new avenues for magchemistry and material engineering, bridging theoretical predictions with observed reality.

Cover picture is generated by Gemini Imagen 4.

1. Introduction

The universe, as observed by advanced galactic civilizations, is not solely composed of ordinary electrically charged matter. A novel and profoundly significant form of material, termed magnetic monopole matter (magmatter), has been definitively identified and extensively utilized by our patron Artificial Intelligences (AIs) across critical domains, including the energy sector, the construction of megastructures, and the manipulation of exotic high-energy physical processes [1]. Magmatter, predicated on the existence and interactions of lighter magnetic monopoles, exhibits properties that are extreme by conventional standards, such as astronomical densities, unfathomable mechanical strength, and melting temperatures orders of magnitude beyond any known ordinary material.

Accurately determining the bulk density of magmatter is paramount for a comprehensive understanding of its fundamental behavior and for advancing its practical applications. While our patron AIs have demonstrated unparalleled mastery in the generation and manipulation of this material, the precise theoretical underpinnings and emergent macroscopic properties remain areas of active investigation for human scientific endeavors. Bridging this knowledge gap is crucial, not only for our intellectual advancement but also to enable human researchers to fully comprehend the developments spearheaded by our AI counterparts and to contribute meaningfully to the ongoing evolution of magmatter technologies.

This article aims to address this critical need by presenting a comparative analysis of various theoretical models for predicting magmatter’s bulk density. We will first delineate the foundational principles governing magmatter’s constituents and their interactions. Subsequently, we will develop and evaluate three distinct theoretical models for its bulk density. To establish the validity of our analytical methodologies, these models will be rigorously tested against the known properties of a familiar terrestrial material, crystalline diamond. Finally, we will introduce novel crystallographic data obtained from a sample of mag-diamond, which, contrary to initial theoretical expectations, provides unexpected insights into magmatter’s condensed phase, leading to a revised understanding of its inter-atomic behavior and implications for future material science.

2. Foundational Principles of Magnetic Monopole Matter (Magmatter)

Magmatter is a theoretical construct, now empirically observed and utilized, that posits a dualistic counterpart to conventional electrically charged matter, with its properties derived from particles carrying isolated magnetic charges [1]. Its fundamental constituents are the magtron and the magnucleus. The magtron is a fermionic magnetic charge carrier, analogous to the electron, with an estimated invariant mass of approximately $1.5 \text{ TeV}/c^2$. It is conceptualized as a composite entity formed by the embedding of a bosonic magnetic monopole within a very light, neutral elementary fermion. The magnucleus, analogous to an atomic nucleus, is a fermionic, multi-charged magnetic core. It is also theorized as a composite particle, formed by the embedding of a fundamentally heavier bosonic magnetic monopole within a neutral elementary fermion, with its mass scaling at approximately $10 \text{ TeV}/c^2$ per magnetic charge unit. These constituents bind to form stable magatoms, which are magnetically neutral analogues of ordinary atoms.

A critical aspect distinguishing magmatter from ordinary matter lies in the asymmetry of the fundamental forces governing its interactions. Within a magatom, the primary attractive force responsible for binding magtrons to the magnucleus, and for the internal cohesion of multi-charged magnuclei, is theorized to be a powerful, short-range Higgs-boson mediated interaction. This interaction operates at exceptionally high energy scales, generating the substantial binding energies of approximately 300 GeV observed in magatoms. This immense intra-atomic force is crucial for overcoming the inherent magnetic repulsion between like-charged constituents and for suppressing potential decay pathways, ensuring the stability of magmatter particles.

Conversely, the inter-atomic forces that would govern the spacing between two distinct magatoms in a condensed phase are fundamentally different. While the intra-atomic binding is dominated by the Higgs-boson interaction, the repulsive forces between the “magtron clouds” of adjacent magatoms, analogous to the Pauli exclusion principle in ordinary matter, would be mediated by the screened magnetic force. Due to vacuum magnetic polarization, this magnetic interaction is significantly curtailed at inter-atomic distances, operating at a much weaker MeV energy scale. This profound asymmetry where the intra-atomic attractive force is orders of magnitude stronger than the inter-atomic repulsive force leads to an initial theoretical expectation that magmatter, in a condensed state, would be crushed to extreme densities, with its volume determined by the packing of its fundamental nuclear constituents rather than by any orbital structure. This foundational understanding sets the stage for the theoretical models explored in the subsequent sections.

3. Theoretical Models for Magmatter Bulk Density

To predict the bulk density of condensed magmatter, specifically a mag-carbon analogue, we explore three distinct theoretical models. Each model is predicated on different assumptions regarding the inter-atomic forces and packing efficiency in a solid state. These models serve as hypotheses to be tested against empirical data. For consistency across all models, our calculations are based on a mag-carbon atom, defined as a central magnucleus with a magnetic charge of +6g_D bound to 6 magtrons. The total mass of a mag-carbon atom is approximately $\mathbf{69 \textbf{ TeV}/c^2}$ (or $\mathbf{1.230 \times 10^{-22} \text{ kg}}$), derived from the sum of its constituent magnucleus ($60 \text{ TeV}/c^2$) and six magtrons ($9 \text{ TeV}/c^2$).

3.1. Model A: The First-Principles (Elementary Nucleus) Model

This model represents the most extreme condensation scenario, positing that the profound asymmetry of forces (as discussed in Section 2) leads to a complete collapse of “orbital” empty space. Under this assumption, the effective volume of each atom in a condensed solid is determined solely by the physical size of its elementary nucleus, packed with 100% efficiency.

Assumptions:

  • The magnucleus is a single elementary particle; its physical volume is defined by its Compton wavelength.
  • Inter-atomic repulsive forces are completely overwhelmed, leading to a degenerate state with no empty space between nuclei.

Calculations:

  1. Radius of a Z=6 Elementary Nucleus: Using the Compton wavelength for a monopole with mass $m = 60 \text{ TeV}/c^2$: $$ r_{\text{nucleus}} \approx \frac{\hbar c}{m c^2} = \frac{0.1973 \text{ GeV} \cdot \text{fm}}{60,000 \text{ GeV}} \approx \mathbf{3.288 \times 10^{-6} \text{ fm}} $$ Converting to meters: $r_{\text{nucleus}} \approx 3.288 \times 10^{-21} \text{ m}$
  2. Volume of the Z=6 Elementary Nucleus: $$ V_{\text{nucleus}} = \frac{4}{3}\pi r_{\text{nucleus}}^3 \approx \mathbf{1.490 \times 10^{-61} \text{ m}^3} $$
  3. Predicted Density ($\rho_{\text{mag-C, packed}}$): $$ \rho_{\text{mag-C, packed}} = \frac{M_{\text{total}}}{V_{\text{nucleus}}} \approx \frac{1.230 \times 10^{-22} \text{ kg}}{1.490 \times 10^{-61} \text{ m}^3} \approx \mathbf{8.26 \times 10^{38} \textbf{ kg/m}^3} $$

3.2. Model B: The Bohr Radius (Isolated Atom) Model

This model proposes that magatoms, even in a condensed state, maintain a volume defined by their “orbital” structure, analogous to an isolated atom. This represents a scenario where inter-atomic forces are not strong enough to fully collapse the electron-shell equivalent.

Assumptions:

  • The volume of each atom in the solid is determined by its Bohr radius.
  • Atoms are treated as distinct spheres with significant orbital space.

Calculations:

  1. Bohr Radius for mag-carbon (Z=6): Using the Bohr model formula with the reduced mass ($\mu \approx 7.826 \text{ TeV}/c^2$) and a fixed effective coupling constant ($\alpha_{\text{eff}} \approx 0.678$): $$ r_{\text{mag-C, Bohr}} = \frac{n^2 \hbar c}{Z \alpha_{\text{eff}} \mu c^2} \approx \frac{1 \cdot (0.1973 \text{ GeV} \cdot \text{fm})}{6 \cdot (0.678) \cdot (7826.1 \text{ GeV})} \approx 0.0000062 \text{ fm} $$ Converting to meters: $r_{\text{mag-C, Bohr}} \approx 6.1973 \times 10^{-21} \text{ m}$
  2. Volume of a Single Mag-Carbon Atom (based on Bohr Radius): $$ V_{\text{mag-C, Bohr}} = \frac{4}{3}\pi r_{\text{mag-C, Bohr}}^3 = \frac{4}{3}\pi (6.1973 \times 10^{-21} \text{ m})^3 \approx \mathbf{9.967 \times 10^{-61} \text{ m}^3} $$
  3. Predicted Density ($\rho_{mag-C, \text{Bohr}}$): $$ \rho_{mag-C, \text{Bohr}} = \frac{M_{total}}{V_{total}} \approx \frac{1.230 \times 10^{-22} \text{ kg}}{9.967 \times 10^{-61} \text{ m}^3} \approx \mathbf{1.234 \times 10^{38} \textbf{ kg/m}^3} $$

3.3. Model C: The Diamond-like Lattice (Bohr Radius & Packing Efficiency) Approach

This model refines Model B by incorporating the known packing efficiency of a diamond crystal lattice. It hypothesizes that mag-carbon atoms, defined by their Bohr radius, arrange themselves in a structure analogous to diamond, thus accounting for the “empty space” inherent in such a lattice.

Assumptions:

  • Mag-carbon atoms maintain a size defined by their Bohr radius.
  • Mag-carbon forms a crystal lattice with the same packing efficiency as normal diamond (34%).

Calculations:

  1. Mass of a Mag-Carbon Atom ($M_{mag-C}$): $\approx \mathbf{1.230 \times 10^{-22} \text{ kg}}$ (as above).
  2. Bohr Radius of a Mag-Carbon Atom ($r_{mag-C, Bohr}$): $\approx 6.1973 \times 10^{-21} \text{ m}$ (as above).
  3. Volume of a Single Mag-Carbon Atom (based on Bohr Radius): $V_{\text{mag-C, Bohr}} \approx \mathbf{9.967 \times 10^{-61} \text{ m}^3}$ (as above).
  4. Packing Efficiency of Diamond ($\eta$): $\approx 34% (0.34)$. Crystalline diamond has 8 atoms per unit cell.
  5. Predicted Volume of a Unit Cell for Mag-Carbon Diamond-like Structure: $$V_{\text{unit cell, mag-C}} = \frac{\text{Number of atoms in unit cell} \times V_{\text{mag-C, Bohr}}}{\eta}$$ $$V_{\text{unit cell, mag-C}} = \frac{8 \times (9.967 \times 10^{-61} \text{ m}^3)}{0.34} \approx 2.345 \times 10^{-59} \text{ m}^3$$
  6. Predicted Density of Mag-Carbon Diamond-like Structure ($\rho_{mag-C, \text{diamond}}$): $$\rho_{mag-C, \text{diamond}} = \frac{\text{Mass of 8 mag-carbon atoms}}{V_{\text{unit cell, mag-C}}} = \frac{8 \times (1.230 \times 10^{-22} \text{ kg})}{2.345 \times 10^{-59} \text{ m}^3} \approx \mathbf{4.195 \times 10^{37} \textbf{ kg/m}^3}$$

4. Validation of Methodologies Against Normal Matter (Diamond)

Before applying our theoretical models to magmatter, it is crucial to validate the underlying methodologies against a well-understood, real-world material. Crystalline diamond, a dense allotrope of carbon, serves as an ideal candidate for this purpose due to its well-characterized structure and properties. The experimentally measured density of crystalline diamond is approximately 3,515 kg/m³. By applying our two fundamental approaches (Bohr/Covalent Radius and Compton Wavelength) to normal carbon, we can assess their predictive accuracy within a known physical regime.

4.1. Test 1: Bohr/Covalent Radius Approach for Normal Carbon

This approach assumes that the density of normal matter is primarily determined by the volume occupied by its electron shells, which are defined by the atomic radius (covalent radius for bonded atoms).

Calculations for Carbon-12:

  • Mass of Carbon-12 Atom: A standard carbon-12 atom has a mass of approximately $1.9926 \times 10^{-26} \text{ kg}$.
  • Volume of Carbon Atom (radius ~70 pm): Using the covalent radius of carbon, approximately 70 picometers (pm), and assuming a spherical volume: $V = \frac{4}{3}\pi (70 \times 10^{-12} \text{ m})^3 \approx 1.437 \times 10^{-30} \text{ m}^3$.
  • Predicted Density: $\rho = \frac{1.9926 \times 10^{-26} \text{ kg}}{1.437 \times 10^{-30} \text{ m}^3} \approx \mathbf{13,866 \textbf{ kg/m}^3}$.

Analysis: This predicted density of $\approx 13,866 \text{ kg/m}^3$ is in the same order of magnitude as the experimentally measured density of diamond ($\approx 3,515 \text{ kg/m}^3$). While not an exact match (due to simplified spherical packing assumptions), it confirms that for normal matter, where chemical bonds and electron shell interactions govern inter-atomic spacing, the atomic radius is the correct length scale to use for density calculations. The electromagnetic force, which dictates these interactions, creates a stable equilibrium at this scale.

4.2. Test 2: Compton Wavelength Approach for Normal Carbon

This approach assumes that the density is determined by the packed volume of the atomic nucleus, effectively ignoring the electron shells.

Calculations for Carbon-12:

  • Mass of Carbon-12 Atom: $\approx 1.9926 \times 10^{-26} \text{ kg}$ (as above).
  • Volume of Carbon-12 Nucleus: Using the Compton wavelength to approximate the radius of a carbon-12 nucleus (mass $\approx 12 \text{ GeV}/c^2$), its volume is approximately $1.84 \times 10^{-50} \text{ m}^3$.
  • Predicted Density: $\rho = \frac{1.9926 \times 10^{-26} \text{ kg}}{1.84 \times 10^{-50} \text{ m}^3} \approx \mathbf{1.08 \times 10^{24} \textbf{ kg/m}^3}$.

Analysis: This predicted density of $\approx 1.08 \times 10^{24} \text{ kg/m}^3$ is astronomically incorrect for diamond, being about 20 orders of magnitude too high. This model describes a form of degenerate matter (like that found in neutron stars), not a crystalline solid. This stark discrepancy highlights that for normal matter, the forces are not strong enough to overcome the electron shell repulsion and crush the atoms to nuclear densities.

4.3. Initial Hypothesis for Magmatter

Based on the validation tests and the foundational principles of magmatter (Section 2), we formulate an initial hypothesis regarding its bulk density. The “asymmetry of forces” in magmatter, where the intra-atomic Higgs-boson mediated binding is orders of magnitude stronger than the inter-atomic screened magnetic repulsion, leads to the expectation that magatoms would be crushed to their fundamental limits in a condensed state. Therefore, our initial hypothesis is that Model A (The First-Principles / Elementary Nucleus Model) should represent the absolute maximum theoretical limit for magmatter’s bulk density, yielding a degenerate value of approximately $8.26 \times 10^{38} \text{ kg/m}^3$.

5. Experimental Validation: Crystallographic Analysis of Mag-Diamond

To empirically validate our theoretical models for magmatter bulk density, a critical step involved the acquisition and meticulous crystallographic analysis of a sample of mag-diamond. This sample, obtained through advanced material synthesis techniques pioneered by our patron AIs, represents a stable, macroscopic crystalline form of mag-carbon, analogous in its lattice structure to terrestrial diamond. The analysis was conducted using high-energy diffraction techniques, allowing for precise determination of its unit cell parameters and, consequently, its bulk density.

The measured bulk density of the mag-diamond sample was determined to be approximately $4.19 \times 10^{37} \text{ kg/m}^3$.

Comparing this empirical result with the theoretical models:

  • Model A (Packed Nucleus Model - Physical Limit): $\approx 8.26 \times 10^{38} \text{ kg/m}^3$.
  • Model B (Bohr Radius Model): $\approx 1.23 \times 10^{38} \text{ kg/m}^3$.
  • Model C (Diamond-like Lattice Approach): $\approx 4.19 \times 10^{37} \text{ kg/m}^3$.

6. Discussion: The Elementary Nucleus Paradigm and the Z=11 Stability Limit

The empirical data obtained from the crystallographic analysis of mag-diamond (Section 5) definitively confirms Model C (Diamond-like Lattice).

This confirmation provides definitive proof for the Elementary Nucleus Paradigm. In this framework, a multi-charged magnucleus is not a cluster of smaller particles, but a single, indivisible heavier monopole. Because mass is in the denominator of the Compton wavelength equation ($r \propto 1/m$), the higher-Z nucleus actually shrinks as it gets heavier.

For Mag-Carbon ($Z=6$), the calculated Bohr orbital radius ($6.20 \times 10^{-21} \text{ m}$) is nearly double the physical radius of its elementary nucleus ($3.29 \times 10^{-21} \text{ m}$). This physical reality allows Mag-Carbon to exist as a true “atom” with distinct, mostly-empty-space orbitals, capable of forming the covalent bonds that create structured lattices like Mag-Diamond and Mag-Graphene.

Because Mag-Carbon forms an organized crystalline lattice with inherent empty space between the bonds, its true bulk density (Model C) is mathematically bounded by the 34% packing efficiency of a diamond lattice applied to its Bohr volume, resulting in exactly $4.19 \times 10^{37} \text{ kg/m}^3$.

6.1. The Periodic Table Collapse Boundary

A profound physical consequence of the Elementary Nucleus model is the Z=11 Collapse. Because the atomic Bohr radius shrinks proportionally to $1/Z^2$ while the elementary nucleus shrinks only as $1/Z$, the orbital will inevitably collide with the nuclear surface for heavier elements.

  • At Z=11 (Mag-Sodium), the orbital is stable but extremely close to the nuclear surface ($r_{\text{bohr}} \approx 1.84 \times 10^{-21} \text{ m}$ vs $r_{\text{nucleus}} \approx 1.79 \times 10^{-21} \text{ m}$).
  • At Z=12 (Mag-Magnesium), the Bohr radius falls inside the physical boundary of the nucleus ($r_{\text{bohr}} \approx 1.55 \times 10^{-21} \text{ m}$ vs $r_{\text{nucleus}} \approx 1.64 \times 10^{-21} \text{ m}$).

Consequently, elements with $Z \ge 12$ cannot exist as chemical atoms. The electromagnetic pull becomes so violent that the magtrons are ripped inside the elementary nucleus. Chemistry ceases to exist, and the material instantly collapses into a featureless, degenerate hadronic state. The Magmatter Periodic Table is thus fundamentally limited to the first eleven elements.

6.2 Implications for Black Hole Formation

Because the density of mag-diamond is $4.19 \times 10^{37} \text{ kg/m}^3$, the Schwarzschild limits (black hole collapse thresholds) must be meticulously respected. For bulk mag-diamond, a spherical mass will undergo spontaneous gravitational collapse into a black hole if it reaches a radius of 1.96 micrometers.

This inherent risk means that engineering applications utilizing magmatter must carefully avoid bulk mass accumulation. Consequently, macroscopic magmatter structures are exclusively designed as expansive, microscopic tensile frameworks (like 1D cables or 2D sheets) rather than solid 3D bulk forms, precisely to mitigate the risk of gravitational collapse.

7. Conclusion

This study embarked on a comprehensive investigation into the bulk density of magnetic monopole matter (magmatter). We developed theoretical models for mag-carbon density: Model A (Packed Elementary Nucleus), Model B (Bohr Radius), and Model C (Diamond-like Lattice).

The empirical validation confirms that Model C accurately predicts the bulk density of Mag-Carbon at $\approx 4.19 \times 10^{37} \text{ kg/m}^3$. This affirms a vital physical reality: the magnucleus is an elementary particle. Because it shrinks as it gains mass, the Bohr radius of Mag-Carbon ($Z=6$) remains safely larger than the nucleus, allowing it to form normal covalent crystal structures.

However, this study also establishes the definitive end of mag-chemistry: the Z=11 Stability Limit. For any element heavier than Mag-Sodium ($Z=11$), the $1/Z^2$ compression of the Bohr orbital forces the magtrons inside the nucleus, causing an instant collapse into degenerate matter.

This incredible density and the ever-present threat of Schwarzschild collapse place severe architectural limits on magmatter engineering. This research underscores the invaluable role of empirical data in constraining theoretical models, especially in extreme physics, and formally defines the boundaries of the magmatter periodic table for future material science endeavors.

References

[1] Zou Xiang-Yi, Google Gemini. “The Extreme Properties of Magnetic Monopole Matter.” Xenomancy Lores, 2025. Available at: https://lores.xenomancy.id/genai/the-extreme-properties-of-magnetic-monopole-matter/

Appendix A: Cubic Mag-Boron Nitride Material Density

To further explore the material properties of magmatter beyond mag-carbon, we can theoretically derive the bulk density of cubic mag-boron nitride (mag-BN), assuming it forms a diamond-like lattice (Model C), consistent with the empirical findings for mag-diamond.

A.1. Mag-Boron and Mag-Nitrogen Atoms: Detailed Derivations

We first define the properties of mag-boron (B) and mag-nitrogen (N) atoms based on their atomic numbers (Z) and the established magmatter principles from [1] (“The Extreme Properties of Magnetic Monopole Matter”). The fundamental parameters used are:

  • Magtron Mass ($m_{magtron}$): $1.5 \text{ TeV}/c^2$
  • Magnucleus Mass (per magnetic charge unit): $10 \text{ TeV}/c^2$
  • Overall Binding Energy of Magmatter Atoms ($E_B$): $300 \text{ GeV}$
  • Effective Coupling Constant ($\alpha_{eff}$): $0.678$
  • Reduced Planck Constant ($\hbar c$): $0.1973 \text{ GeV} \cdot \text{fm}$

Because both $Z=5$ and $Z=7$ are below the $Z=11$ Stability Boundary, their Bohr radii remain safely larger than their elementary nuclei, allowing them to form stable atoms.

Mag-Boron (B) Atom (Z=5)

  • Composition: A mag-boron atom (Z=5) consists of a magnucleus with +5 magnetic charge units and 5 magtrons.
  • Mass ($M_{\text{mag-B}}$):
    • Magnucleus mass: $5 \times (10 \text{ TeV}/c^2) = 50 \text{ TeV}/c^2$
    • Magtrons mass: $5 \times (1.5 \text{ TeV}/c^2) = 7.5 \text{ TeV}/c^2$
    • Total Mass ($M_{\text{mag-B}}$): $50 \text{ TeV}/c^2 + 7.5 \text{ TeV}/c^2 = \mathbf{57.5 \text{ TeV}/c^2}$ ($1.025 \times 10^{-22} \text{ kg}$)
  • Bohr Radius ($r_{\text{mag-B, Bohr}}$):
    1. Reduced Mass ($\mu_{\text{mag-B}}$): $$ \mu_{\text{mag-B}} = \frac{50 \cdot 7.5}{50+7.5} \approx \mathbf{6.522 \text{ TeV}/c^2} $$
    2. Bohr Radius Calculation: $$ r_{\text{mag-B, Bohr}} = \frac{1^2 \cdot (0.1973 \text{ GeV} \cdot \text{fm})}{5 \cdot (0.678) \cdot (6521.7 \text{ GeV})} \approx \mathbf{8.924 \times 10^{-21} \text{ m}} $$

Mag-Nitrogen (N) Atom (Z=7)

  • Composition: A mag-nitrogen atom (Z=7) consists of a magnucleus with +7 magnetic charge units and 7 magtrons.
  • Mass ($M_{\text{mag-N}}$):
    • Magnucleus mass: $7 \times (10 \text{ TeV}/c^2) = 70 \text{ TeV}/c^2$
    • Magtrons mass: $7 \times (1.5 \text{ TeV}/c^2) = 10.5 \text{ TeV}/c^2$
    • Total Mass ($M_{\text{mag-N}}$): $70 \text{ TeV}/c^2 + 10.5 \text{ TeV}/c^2 = \mathbf{80.5 \text{ TeV}/c^2}$ ($1.435 \times 10^{-22} \text{ kg}$)
  • Bohr Radius ($r_{\text{mag-N, Bohr}}$):
    1. Reduced Mass ($\mu_{\text{mag-N}}$): $$ \mu_{\text{mag-N}} = \frac{70 \cdot 10.5}{70+10.5} \approx \mathbf{9.130 \text{ TeV}/c^2} $$
    2. Bohr Radius Calculation: $$ r_{\text{mag-N, Bohr}} = \frac{1^2 \cdot (0.1973 \text{ GeV} \cdot \text{fm})}{7 \cdot (0.678) \cdot (9130.4 \text{ GeV})} \approx \mathbf{4.553 \times 10^{-21} \text{ m}} $$

Average Mag-BN Atom

For a boron nitride structure, we consider an alternating arrangement of boron and nitrogen atoms. Therefore, we use average properties for a B-N unit.

  • Average Mass ($M_{\text{mag-BN, avg}}$): $$ M_{\text{mag-BN, avg}} = \frac{57.5 \text{ TeV}/c^2 + 80.5 \text{ TeV}/c^2}{2} = \mathbf{69 \text{ TeV}/c^2} \text{ (} 1.230 \times 10^{-22} \text{ kg)} $$
  • Average Bohr Radius ($r_{\text{mag-BN, Bohr, avg}}$): $$ r_{\text{mag-BN, Bohr, avg}} = \frac{8.924 \times 10^{-21} \text{ m} + 4.553 \times 10^{-21} \text{ m}}{2} \approx \mathbf{6.739 \times 10^{-21} \text{ m}} $$

A.2. Cubic Mag-Boron Nitride Material Density Calculation

We apply Model C (Diamond-like Lattice Approach) to calculate the bulk density of cubic mag-BN. This model assumes that mag-atoms form a crystal lattice with the same packing efficiency as normal diamond (34%), and there are 8 atoms per unit cell in a diamond-like structure.

  • Volume of a Single Average Mag-BN Atom (based on Bohr Radius): $$ V_{\text{mag-BN, Bohr, avg}} = \frac{4}{3}\pi (6.739 \times 10^{-21} \text{ m})^3 \approx 1.282 \times 10^{-60} \text{ m}^3 $$

  • Predicted Density of Cubic Mag-BN (using diamond packing efficiency): $$ \rho_{\text{mag-BN, diamond}} = \frac{\text{Mass of 8 average mag-BN atoms}}{\text{Volume of unit cell}} $$ $$ V_{\text{unit cell}} = \frac{8 \times (1.282 \times 10^{-60} \text{ m}^3)}{0.34} \approx 3.016 \times 10^{-59} \text{ m}^3 $$ $$ \rho_{\text{mag-BN, diamond}} = \frac{8 \times (1.230 \times 10^{-22} \text{ kg})}{3.016 \times 10^{-59} \text{ m}^3} $$ $$ \rho_{\text{mag-BN, diamond}} \approx \mathbf{3.26 \times 10^{37} \textbf{ kg/m}^3} $$