FD-8_Evolution Equation of the Future-Direction Distribution and Unified Structure
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2026
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| _version_ | 1866901926104268800 |
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| author | Kuniyuki, Morita |
| author_facet | Kuniyuki, Morita |
| contents | <p>FD-8 provides the unified evolution equation of the FD-Series by combining the <br>three layers of the future-direction structure: the expectation value mu, the <br>statistical width Sigma, and the internal degrees of freedom kappa. While FD-1 <br>to FD-7 develop these components individually, FD-8 shows that they arise from <br>a single underlying distribution P(mu) whose evolution determines both classical <br>and quantum gravitational behavior.</p> <p>The unified evolution equation takes the schematic form<br> dP/dtau = L[mu, Sigma, kappa] P,<br>where the operator L encodes the geometric change of the future direction and <br>its fluctuations. Classical gravity emerges from the first-moment structure mu, <br>quantum behavior from the second-moment structure Sigma, and internal degrees <br>of freedom from the eigenstructure of the distribution. No additional fields or <br>postulates are required.</p> <p>In the classical limit Sigma -> 0 and kappa -> 0, the equation reduces smoothly <br>to the deterministic hierarchy FD-1 to FD-5. In quantum and near-quantum <br>regimes, the full structure of P(mu) becomes essential and provides a unified <br>description of gravity, quantum behavior, and internal structure.</p> <p>FD-8 completes the FD-Series by establishing the minimal unified framework for <br>classical and quantum gravity based on the geometry of the future direction.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20349128 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | FD-8_Evolution Equation of the Future-Direction Distribution and Unified Structure Kuniyuki, Morita future direction unified evolution equation distribution P(mu) Sigma tensor kappa structure quantum gravity classical limit geometric unification statistical structure FD-Series general relativity extension <p>FD-8 provides the unified evolution equation of the FD-Series by combining the <br>three layers of the future-direction structure: the expectation value mu, the <br>statistical width Sigma, and the internal degrees of freedom kappa. While FD-1 <br>to FD-7 develop these components individually, FD-8 shows that they arise from <br>a single underlying distribution P(mu) whose evolution determines both classical <br>and quantum gravitational behavior.</p> <p>The unified evolution equation takes the schematic form<br> dP/dtau = L[mu, Sigma, kappa] P,<br>where the operator L encodes the geometric change of the future direction and <br>its fluctuations. Classical gravity emerges from the first-moment structure mu, <br>quantum behavior from the second-moment structure Sigma, and internal degrees <br>of freedom from the eigenstructure of the distribution. No additional fields or <br>postulates are required.</p> <p>In the classical limit Sigma -> 0 and kappa -> 0, the equation reduces smoothly <br>to the deterministic hierarchy FD-1 to FD-5. In quantum and near-quantum <br>regimes, the full structure of P(mu) becomes essential and provides a unified <br>description of gravity, quantum behavior, and internal structure.</p> <p>FD-8 completes the FD-Series by establishing the minimal unified framework for <br>classical and quantum gravity based on the geometry of the future direction.</p> |
| title | FD-8_Evolution Equation of the Future-Direction Distribution and Unified Structure |
| topic | future direction unified evolution equation distribution P(mu) Sigma tensor kappa structure quantum gravity classical limit geometric unification statistical structure FD-Series general relativity extension |
| url | https://doi.org/10.5281/zenodo.20349128 |