Improved Lower Bound for the Linear Threshold of B₂: σ(B₂) ≥ 18/7

This deposit contains the data, code, proof notes, and preprint for the result σ(B₂) ≥ 18/7 in the extremal problem on the linear threshold exponent of the bipartite incidence graph B₂ of the complete 3-partite 3-uniform hypergraph K_{2,2,2}^{(3)}. The problem was posed as Oberwolfach Report 3/2024, Open Problems in Discrete Geometry, Problem 9 by Ji Zeng. The main theorem is: for every σ < 18/7, there exist B₂-free bipartite graphs G = (A ⊔ B, E) with |A| = m, |B| = m^σ, and |E|/|B| → ∞ as m → ∞. Consequently σ(B₂) ≥ 18/7. The proof is a first-moment deletion argument in a random bipartite graph; the threshold 18/7 is the natural exponent for this construction. The deposit also contains small-parameter computational calibrations (random bipartite search, 3-partite hypergraph deletion, and greedy construction). These experiments are illustrative only and do not establish the asymptotic theorem. Limitations: (1) the bound applies to t = 2 only; (2) no matching upper bound σ(B₂) ≤ 18/7 is proved; (3) Janzer's qualitative bound σ(B_t) < 3 remains non-explicit; (4) the construction is probabilistic and non-explicit for large m. Code is MIT licensed; data and JSON certificates are CC0 1.0 Universal; the deposit as a whole and the preprint are CC-BY 4.0. A PDF version of the preprint is included in the deposit; the Markdown and LaTeX sources are also included for archival purposes.