| _version_ | 1866901074797920256 |
|---|---|
| author | Gang, Zhang |
| author_facet | Gang, Zhang |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19068927 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | An Asymmetric Dimensional Barrier in Causal-Set Link Dynamics Selects 3+1 Dimensions Gang, Zhang causal sets, link action, dimensional selection, BDG action, asymmetric barrier, Xi parameter, 3+1 dimensions, posets, linear extensions, discrete quantum gravity <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> |
| title | An Asymmetric Dimensional Barrier in Causal-Set Link Dynamics Selects 3+1 Dimensions |
| topic | causal sets, link action, dimensional selection, BDG action, asymmetric barrier, Xi parameter, 3+1 dimensions, posets, linear extensions, discrete quantum gravity |
| url | https://doi.org/10.5281/zenodo.19068927 |