A Forced Geometric Invariant for Discrete–Continuum Compatibility (COSMIC-273: Paper 1)
Fuente:
Zenodo
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Sprache: | Englisch |
| Veröffentlicht: |
Zenodo
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866901557163851776 |
|---|---|
| author | France, Josephine |
| author_facet | France, Josephine |
| contents | <p>This work introduces a geometric solution to the incompatibility between discrete lattice substrates and continuous rotational field theories. A discrete lattice possesses only finite rotational symmetry, while physical fields transform under the continuous group SO(2). Reconciling these two regimes requires a geometric correction that allows a discrete boundary to support continuous curvature without distortion.</p> <p>By analysing the minimal region in which discrete and continuous descriptions must coincide, the paper derives a unique dimensionless stiffness invariant, Λ₀ = 4/π ≈ 1.2732. This value is not assumed or fitted; it is forced by geometric necessity. Λ₀ quantifies the ratio between the minimal orthogonal boundary capable of enclosing a unit interaction and the maximal rotationally invariant bulk region at the same scale. The result establishes Λ₀ as the fundamental modulus governing discrete–continuum compatibility.</p> <p>Once Λ₀ is fixed, it propagates through the geometry of the lattice and generates a natural hierarchy of higher‑order corrections. As an example, the paper applies Λ₀ to the torsion action of a minimal non‑contractible vortex. The resulting stiffness polynomial, S = 100Λ₀ + 6Λ₀², evaluates to S ≈ 137.05, matching the inverse fine‑structure constant α⁻¹ with high precision. This suggests that electromagnetic coupling strengths may emerge from geometric constraints rather than being arbitrary parameters.</p> <p>The work forms the first part of the COSMIC‑273 programme, which develops a geometric field theory built on discrete substrates. Future papers extend the framework to operator structures, spectral hierarchies, and long‑range geometric residues. The central claim is that Λ₀ is not merely a vacuum parameter but the generator of a broader geometric architecture with physical consequences.</p> <div>This paper presents a geometric resolution to the incompatibility between discrete lattice substrates and continuous rotational gauge fields. By analysing the boundary conditions required for a rotationally invariant field to propagate coherently on a hexagonal lattice, we derive a dimensionless stiffness invariant, Λ₀ = 4/π ≈ 1.2732. This invariant is shown to be a forced geometric necessity rather than an adjustable parameter: it quantifies the minimal correction required for discrete–continuum compatibility.</div> <div> </div> <div>Applying Λ₀ to a topological vortex configuration yields a stiffness polynomial whose numerical value reproduces the inverse fine‑structure constant α⁻¹ ≈ 137 with high precision. The result demonstrates that Λ₀ imposes a natural spectral hierarchy on vacuum torsion and suggests that fundamental coupling constants may emerge from geometric constraints of the discrete vacuum.</div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20110190 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Forced Geometric Invariant for Discrete–Continuum Compatibility (COSMIC-273: Paper 1) France, Josephine geometric invariant, Λ₀, 4/π, vacuum stiffness, discrete–continuum compatibility, geometric field theory, lattice field theory, geometric renormalization, spectral hierarchy, COSMIC‑273, torsion, vortex topology, fine‑structure constant, α inverse, lattice mechanics, vacuum impedance <p>This work introduces a geometric solution to the incompatibility between discrete lattice substrates and continuous rotational field theories. A discrete lattice possesses only finite rotational symmetry, while physical fields transform under the continuous group SO(2). Reconciling these two regimes requires a geometric correction that allows a discrete boundary to support continuous curvature without distortion.</p> <p>By analysing the minimal region in which discrete and continuous descriptions must coincide, the paper derives a unique dimensionless stiffness invariant, Λ₀ = 4/π ≈ 1.2732. This value is not assumed or fitted; it is forced by geometric necessity. Λ₀ quantifies the ratio between the minimal orthogonal boundary capable of enclosing a unit interaction and the maximal rotationally invariant bulk region at the same scale. The result establishes Λ₀ as the fundamental modulus governing discrete–continuum compatibility.</p> <p>Once Λ₀ is fixed, it propagates through the geometry of the lattice and generates a natural hierarchy of higher‑order corrections. As an example, the paper applies Λ₀ to the torsion action of a minimal non‑contractible vortex. The resulting stiffness polynomial, S = 100Λ₀ + 6Λ₀², evaluates to S ≈ 137.05, matching the inverse fine‑structure constant α⁻¹ with high precision. This suggests that electromagnetic coupling strengths may emerge from geometric constraints rather than being arbitrary parameters.</p> <p>The work forms the first part of the COSMIC‑273 programme, which develops a geometric field theory built on discrete substrates. Future papers extend the framework to operator structures, spectral hierarchies, and long‑range geometric residues. The central claim is that Λ₀ is not merely a vacuum parameter but the generator of a broader geometric architecture with physical consequences.</p> <div>This paper presents a geometric resolution to the incompatibility between discrete lattice substrates and continuous rotational gauge fields. By analysing the boundary conditions required for a rotationally invariant field to propagate coherently on a hexagonal lattice, we derive a dimensionless stiffness invariant, Λ₀ = 4/π ≈ 1.2732. This invariant is shown to be a forced geometric necessity rather than an adjustable parameter: it quantifies the minimal correction required for discrete–continuum compatibility.</div> <div> </div> <div>Applying Λ₀ to a topological vortex configuration yields a stiffness polynomial whose numerical value reproduces the inverse fine‑structure constant α⁻¹ ≈ 137 with high precision. The result demonstrates that Λ₀ imposes a natural spectral hierarchy on vacuum torsion and suggests that fundamental coupling constants may emerge from geometric constraints of the discrete vacuum.</div> |
| title | A Forced Geometric Invariant for Discrete–Continuum Compatibility (COSMIC-273: Paper 1) |
| topic | geometric invariant, Λ₀, 4/π, vacuum stiffness, discrete–continuum compatibility, geometric field theory, lattice field theory, geometric renormalization, spectral hierarchy, COSMIC‑273, torsion, vortex topology, fine‑structure constant, α inverse, lattice mechanics, vacuum impedance |
| url | https://doi.org/10.5281/zenodo.20110190 |