V5p33 — Explicit weight system on sl_2 chord diagrams for the V5 oscillation programme (TQNT)
Year: 2026
Type: preprint
Abstract: V5p32 derived the integer factor 4 in delta = -4 ln d_{1/2}(k=135) via two independent routes (Bar-Natan Vassiliev v_4 and Reshetikhin-Turaev Wilson 4-loop). V5p33 closes the V5p27-V5p33 series by writing down the explicit weight system on the five sl_2 chord diagrams that contribute to v_4 on a 3-component link. Explicit coefficients. Using the Casimir eigenvalue of the spin-1/2 representation of sl_2 (exactly C_2 = 3/4) and the 4T relations, we obtain the following weights for the five primitive 3-link chord diagrams: w(D_K) = 1/8 — Kontsevich diagonal w(D_B) = 9/16 — pair-coupling correction w(D_T) = 3/16 — single-triangle w(D_S) = 81/32 — symmetric three-body w(D_X) = 1/8 — crossed three-body Closure check. Summing the contributions of these five diagrams with their multiplicities on the three crossing-count directions of an asymmetric link triplet reproduces exactly the V5p29 multiplicative factor prod_{i<j
Author: Cariou, Lilian, Alexandre
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165186957
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