A Parameter-Free, First Principles Dual Derivation of the Cosmological Constant: The 25/12 Consilience in Chrono Singularity Unification
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| Natura: | Recurso digital |
| Lingua: | inglese |
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2026
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| _version_ | 1866901916111339520 |
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| author | McCabe, Luke |
| author_facet | McCabe, Luke |
| contents | <p>We present a complete, parameter-free derivation of the cosmological constant through two mathematically independent pathways that converge on identical predictions within the Chrono-Singularity Unification (CSU) framework. The Holographic Pathway evaluates the Euclidean effective action on the horizon manifold S² x S¹, yielding the vacuum spectral weight W_vac = 25/12 from the Gauss-Bonnet topological invariant (χ(S²) = 2) and the CFT trace anomaly (c/12 = 1/12). This produces the timeless geometric ratio Ω_Λ = 25/36 ≈ 0.694, achieved at the Epoch of Holographic Saturation.</p> <p>The Multiplicative Pathway derives the dimensionless cosmological constant through exponential suppression: Ξ_Λ = e^γ · α^k, where k = 57 physical degrees of freedom emerge from the topological multiplet basis (66 generators minus 9 gauge constraints), and the fine structure constant α⁻¹ = 137 arises from the Newton series identity over this basis. The path integral Jacobian C = e^γ follows rigorously from the Euler-Maclaurin discrete-to-continuum correspondence.</p> <p>Both pathways yield Ξ_Λ ≈ 2.868 x 10⁻¹²², achieving 99.9% agreement with observation. The convergence of these independent derivations—one topological-holographic, one algebraic-multiplicative—constitutes a consilience providing compelling evidence for the underlying framework. The derivation resolves the 122-order-of-magnitude vacuum catastrophe without fine-tuning, supersymmetry, or anthropic selection. Falsifiable predictions include: (i) Dirac neutrinos (neutrino-less double beta decay forbidden), (ii) exactly three fermion generations, and (iii) exclusion of grand unified theories at M_GUT ~ 10¹⁶ GeV.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18954055 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Parameter-Free, First Principles Dual Derivation of the Cosmological Constant: The 25/12 Consilience in Chrono Singularity Unification McCabe, Luke cosmological constant quantum gravity holographic principle fine structure constant vacuum energy dual derivation Chrono Singularity Unification CSU ΛCDM Dark Energy general relativity Quantum physics Particle physics <p>We present a complete, parameter-free derivation of the cosmological constant through two mathematically independent pathways that converge on identical predictions within the Chrono-Singularity Unification (CSU) framework. The Holographic Pathway evaluates the Euclidean effective action on the horizon manifold S² x S¹, yielding the vacuum spectral weight W_vac = 25/12 from the Gauss-Bonnet topological invariant (χ(S²) = 2) and the CFT trace anomaly (c/12 = 1/12). This produces the timeless geometric ratio Ω_Λ = 25/36 ≈ 0.694, achieved at the Epoch of Holographic Saturation.</p> <p>The Multiplicative Pathway derives the dimensionless cosmological constant through exponential suppression: Ξ_Λ = e^γ · α^k, where k = 57 physical degrees of freedom emerge from the topological multiplet basis (66 generators minus 9 gauge constraints), and the fine structure constant α⁻¹ = 137 arises from the Newton series identity over this basis. The path integral Jacobian C = e^γ follows rigorously from the Euler-Maclaurin discrete-to-continuum correspondence.</p> <p>Both pathways yield Ξ_Λ ≈ 2.868 x 10⁻¹²², achieving 99.9% agreement with observation. The convergence of these independent derivations—one topological-holographic, one algebraic-multiplicative—constitutes a consilience providing compelling evidence for the underlying framework. The derivation resolves the 122-order-of-magnitude vacuum catastrophe without fine-tuning, supersymmetry, or anthropic selection. Falsifiable predictions include: (i) Dirac neutrinos (neutrino-less double beta decay forbidden), (ii) exactly three fermion generations, and (iii) exclusion of grand unified theories at M_GUT ~ 10¹⁶ GeV.</p> |
| title | A Parameter-Free, First Principles Dual Derivation of the Cosmological Constant: The 25/12 Consilience in Chrono Singularity Unification |
| topic | cosmological constant quantum gravity holographic principle fine structure constant vacuum energy dual derivation Chrono Singularity Unification CSU ΛCDM Dark Energy general relativity Quantum physics Particle physics |
| url | https://doi.org/10.5281/zenodo.18954055 |