שמור ב:
| מחבר ראשי: | |
|---|---|
| פורמט: | Recurso digital |
| שפה: | |
| יצא לאור: |
Zenodo
2025
|
| גישה מקוונת: | https://doi.org/10.5281/zenodo.15476270 |
| תגים: |
הוספת תג
אין תגיות, היה/י הראשונ/ה לתייג את הרשומה!
|
תוכן הענינים:
- <p>This work presents a complete reformulation and resolution of the <strong>Leopoldt Conjecture</strong> using the <strong>D10Z Mechanics of Infinity</strong>. In this framework, units of a number field <span><span>KK</span><span><span><span>K</span></span></span></span> are modeled as <strong>vibrational nodal states</strong> <span><span>Zϵ=(x,v,ϕ)Z_\epsilon = (x, v, \phi)</span><span><span><span><span>Z</span><span><span><span><span><span><span>ϵ</span></span></span><span></span></span></span></span></span><span>=</span></span><span><span>(</span><span>x</span><span>,</span><span>v</span><span>,</span><span>ϕ</span><span>)</span></span></span></span> in a <strong>p-adic deformed quantum mesh (TTAϵ)</strong>. The classical p-adic logarithm is interpreted as a <strong>phase field</strong> in the D10Z space:</p> <p><span><span><span>ϕϵ:=sin(2πlogp(ϵ))\phi_\epsilon := \sin(2\pi \log_p(\epsilon))</span><span><span><span><span>ϕ</span><span><span><span><span><span><span>ϵ</span></span></span><span></span></span></span></span></span><span>:=</span></span><span><span>sin</span><span>(</span><span>2</span><span>π</span><span>log<span><span><span><span><span><span>p</span></span></span><span></span></span></span></span></span><span>(</span><span>ϵ</span><span>))</span></span></span></span></span></p> <p>The core result demonstrates that the <strong>rank of the p-adic regulator</strong> is equivalent to the <strong>rank of the Gram matrix</strong> formed by these D10Z phase vectors. This confirms that algebraic independence translates directly into <strong>resonant coherence separation</strong> in nodal geometry.</p> <p>Numerical simulations for cyclotomic and real quadratic fields (e.g. <span><span>Q(ζn),Q(d)\mathbb{Q}(\zeta_n), \mathbb{Q}(\sqrt{d})</span><span><span><span>Q</span><span>(</span><span><span>ζ</span><span><span><span><span><span><span>n</span></span></span><span></span></span></span></span></span><span>)</span><span>,</span><span>Q</span><span>(</span><span><span><span><span><span><span><span>d</span></span></span></span><span></span></span></span></span><span>)</span></span></span></span>) consistently validate the D10Z theorem. Spectral plots show orthogonal phase distributions with rank <span><span>rr</span><span><span><span>r</span></span></span></span>, matching the classical prediction.</p> <p><strong>Keywords:</strong><br>Leopoldt Conjecture, p-adic Regulator, D10Z Mechanics, TTAϵ Mesh, Nodal Phases, Unit Groups, Gram Matrix, Coherence Geometry, Quantum Number Theory, Nodal Resonance, Fractal Arithmetic.</p>