Bergmann Bounce Drive 3.0: π as the Emergent Geometric Stabilizer and Regulator of Multi-Cycle Dynamics in the Bergmann Framework
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2026
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| _version_ | 1866901624914444288 |
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| author | Bergmann, Gordon |
| author_facet | Bergmann, Gordon |
| contents | <p>Building upon the Bergmann Bounce Drive 2.0, which introduced stochastic amplification via the Chaos Field δ_chaos, we present version 3.0 in which the transcendental constant π emerges as the fundamental geometric stabilizer. Using Gaussian Multiplicative Chaos on spherical bounce volumes, we derive that the volume-to-surface ratio (4/3)π exactly minimizes the renormalized action at the critical coupling γ → √8<span>⁻</span>. This fixes the effective Hubble parameter, suppresses runaway divergences, and guarantees eternal, self-consistent multi-cycle evolution. The central claim is that π is not an accidental mathematical constant but the unique attractor that turns a potentially unstable stochastic drive into a regulated, eternal propulsion mechanism. We provide full analytic derivations, updated effective equations, quantitative predictions for CMB anomalies, large-scale structure, and gravitational-wave signatures, as well as implications for retrocausal information transfer. BBD 3.0 represents a genuine paradigm shift: from chaotic amplification to geometrically stabilized eternal cycling.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19066154 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Bergmann Bounce Drive 3.0: π as the Emergent Geometric Stabilizer and Regulator of Multi-Cycle Dynamics in the Bergmann Framework Bergmann, Gordon <p>Building upon the Bergmann Bounce Drive 2.0, which introduced stochastic amplification via the Chaos Field δ_chaos, we present version 3.0 in which the transcendental constant π emerges as the fundamental geometric stabilizer. Using Gaussian Multiplicative Chaos on spherical bounce volumes, we derive that the volume-to-surface ratio (4/3)π exactly minimizes the renormalized action at the critical coupling γ → √8<span>⁻</span>. This fixes the effective Hubble parameter, suppresses runaway divergences, and guarantees eternal, self-consistent multi-cycle evolution. The central claim is that π is not an accidental mathematical constant but the unique attractor that turns a potentially unstable stochastic drive into a regulated, eternal propulsion mechanism. We provide full analytic derivations, updated effective equations, quantitative predictions for CMB anomalies, large-scale structure, and gravitational-wave signatures, as well as implications for retrocausal information transfer. BBD 3.0 represents a genuine paradigm shift: from chaotic amplification to geometrically stabilized eternal cycling.</p> |
| title | Bergmann Bounce Drive 3.0: π as the Emergent Geometric Stabilizer and Regulator of Multi-Cycle Dynamics in the Bergmann Framework |
| url | https://doi.org/10.5281/zenodo.19066154 |