The Universal Model Framework: Prime-Fractal Renormalization Group with Mass-Energy-Information Equivalence and Rigorous Prime-Weighted Lagrangian as the Complete Theory of Emergent Reality
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2025
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| _version_ | 1866902096748478464 |
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| author | Gericke, Marco |
| author_facet | Gericke, Marco |
| contents | <p>We present the complete Universal Model Framework (UMF)—a mathematically rigorous unified theory establishing that spacetime, matter, energy, and consciousness emerge from a discrete prime-fractal substrate governed by five axioms of distinction logic. Through comprehensive integration of eight renormalization group analyses (RG-1 through RG-8), we demonstrate parameter-free derivation of fundamental constants and phenomena across quantum, gravitational, and cosmological domains.</p> <p>Key achievements include: (1) Fine-structure constant α⁻¹ = 137.035999084 with 0.0013% accuracy through autonomous RG flow; (2) Complete gauge consistency verification (5/5 PASS) across U(1), SU(2), SU(3), diffeomorphism, and chiral symmetries via prime congruence classes; (3) Cosmological constant suppression to 93% of observed value (Λ_eff = 10⁻¹¹³ Planck units) through seven-stage parameter-free cascade; (4) Gravitational evolution showing 56% anti-screening enhancement from Planck to atomic scales; (5) Holographic universality with critical exponents ν = 2.0 ± 0.1, η = 1.0 ± 0.1 confirming area-law scaling; (6) Dark matter explanation as prime-structured cosmic information accounting for 27.8% of total energy density; (7) Consciousness quantification through integrated information Φ ≈ 4.6 bits with information-mass coupling; (8) Saddle-manifold RG topology with d_eff = 1 dimensional reduction.</p> <p>The framework provides explicit experimental predictions across 13 orders of magnitude: CMB prime multipole enhancement (ℓ = 223, 541, 809), gravitational wave discrete frequencies, quantum coherence advantages in prime-timed systems, neural oscillation power at prime frequencies, and information mass detection signatures. Three mathematical theorems establish exponential continuum convergence, complete anomaly cancellation through p ≡ 1 mod 6 constraint, and prime sum convergence. All analysis code, parameter fits, and validation protocols are provided with fixed random seeds ensuring full reproducibility.</p> <p>This represents the culmination of the UMF research programme, synthesizing quantum foundations, holographic geometry, Riemann spectral analysis, and multi-scale empirical validation into a single falsifiable information-theoretic paradigm where physical law emerges from computational self-consistency of prime-indexed distinction networks.</p> <ul> <li>This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author.</li> <li>Dedicated to Peter Plichta, who envisioned the code before it could be computed.</li> </ul> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17475189 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Universal Model Framework: Prime-Fractal Renormalization Group with Mass-Energy-Information Equivalence and Rigorous Prime-Weighted Lagrangian as the Complete Theory of Emergent Reality Gericke, Marco prime-fractal renormalization group Prime numbers Statistical mechanics Mathematical logic mathematical physics gauge unification Universal Model Framework UMF holographic principle quantum gravity <p>We present the complete Universal Model Framework (UMF)—a mathematically rigorous unified theory establishing that spacetime, matter, energy, and consciousness emerge from a discrete prime-fractal substrate governed by five axioms of distinction logic. Through comprehensive integration of eight renormalization group analyses (RG-1 through RG-8), we demonstrate parameter-free derivation of fundamental constants and phenomena across quantum, gravitational, and cosmological domains.</p> <p>Key achievements include: (1) Fine-structure constant α⁻¹ = 137.035999084 with 0.0013% accuracy through autonomous RG flow; (2) Complete gauge consistency verification (5/5 PASS) across U(1), SU(2), SU(3), diffeomorphism, and chiral symmetries via prime congruence classes; (3) Cosmological constant suppression to 93% of observed value (Λ_eff = 10⁻¹¹³ Planck units) through seven-stage parameter-free cascade; (4) Gravitational evolution showing 56% anti-screening enhancement from Planck to atomic scales; (5) Holographic universality with critical exponents ν = 2.0 ± 0.1, η = 1.0 ± 0.1 confirming area-law scaling; (6) Dark matter explanation as prime-structured cosmic information accounting for 27.8% of total energy density; (7) Consciousness quantification through integrated information Φ ≈ 4.6 bits with information-mass coupling; (8) Saddle-manifold RG topology with d_eff = 1 dimensional reduction.</p> <p>The framework provides explicit experimental predictions across 13 orders of magnitude: CMB prime multipole enhancement (ℓ = 223, 541, 809), gravitational wave discrete frequencies, quantum coherence advantages in prime-timed systems, neural oscillation power at prime frequencies, and information mass detection signatures. Three mathematical theorems establish exponential continuum convergence, complete anomaly cancellation through p ≡ 1 mod 6 constraint, and prime sum convergence. All analysis code, parameter fits, and validation protocols are provided with fixed random seeds ensuring full reproducibility.</p> <p>This represents the culmination of the UMF research programme, synthesizing quantum foundations, holographic geometry, Riemann spectral analysis, and multi-scale empirical validation into a single falsifiable information-theoretic paradigm where physical law emerges from computational self-consistency of prime-indexed distinction networks.</p> <ul> <li>This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author.</li> <li>Dedicated to Peter Plichta, who envisioned the code before it could be computed.</li> </ul> |
| title | The Universal Model Framework: Prime-Fractal Renormalization Group with Mass-Energy-Information Equivalence and Rigorous Prime-Weighted Lagrangian as the Complete Theory of Emergent Reality |
| topic | prime-fractal renormalization group Prime numbers Statistical mechanics Mathematical logic mathematical physics gauge unification Universal Model Framework UMF holographic principle quantum gravity |
| url | https://doi.org/10.5281/zenodo.17475189 |