সংরক্ষণ করুন:
| প্রধান লেখক: | |
|---|---|
| বিন্যাস: | Recurso digital |
| ভাষা: | |
| প্রকাশিত: |
Zenodo
2026
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| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | https://doi.org/10.5281/zenodo.19068927 |
| ট্যাগগুলো: |
ট্যাগ যুক্ত করুন
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সূচিপত্রের সারণি:
- <p>We study the dimensional-selection problem in a finite ensemble of discrete causal partial orders (posets). A link-based causal action — the d=2 Benincasa–Dowker action S = N − 2C₀ — exhibits a 3+1-dimensional selection window, while the standard d=4 BDG action systematically selects 5D at every coupling tested.</p> <p>The key result is the identification of a dimensionless control parameter Ξ_{d→d+1} measuring the link-penalty cost per unit entropy gained at each dimensional boundary. The 4→5 barrier occurs at Ξ_{4→5} ≈ 10 across three independent generators (CV = 13.9%), substantially larger than lower-dimensional thresholds (Ξ_{3→4} ≈ 3, Ξ_{2→3} ≈ 2). This asymmetric barrier makes 3+1 dimensions a natural equilibrium point: the link-penalty cost of ascending from 4D to 5D is an order of magnitude steeper than any lower transition.</p> <p>Semi-analytical derivation yields Ξ_{4→5} = 11.8 (within 17% of numerical median), with root cause identified as entropy saturation combined with link-density gap persistence. Blind extrapolation to d ≥ 6 confirms the framework: predicted Ξ_{5→6} = 64.4 (measured 45.8), Ξ_{6→7} = 51.3 (measured 37.8).</p> <p>v1.5: Full LaTeX submission with 16 publication figures, 22 tables, analytical Ξ derivation, d ≥ 6 predictive validation. 31 pages.</p>