For squarefree n with ω(n) = k, let τ_⊥(n) be the number of adjacent pairs in the divisor ordering of n that are coprime, and let g_sf(k) = max_{ω(n)=k} τ_⊥(n) be the squarefree extremal function of Erdős problem #1100. Erdős and Simonovits proved (√2 + o(1))^k < g_sf(k) < (2-c)^k. We give an exact combinatorial identity expressing τ_⊥ as a count of unblocked balanced splits, and use it to reduce the problem, in a tight-band weight limit, to a sum of within-cardinality-layer adjacency counts N(k,j). A first-moment analysis indicates E[N(k,j)] ≍ C(k-j, j), so that sum_j E[N(k,j)] ≍ sum_j C(k-j, j) = F_{k+1} ≍ φ^k, the golden ratio. This targets g_sf(k) ≥ (φ + o(1))^k, φ = (1+√5)/2 = 1.61803..., raising the Erdős–Simonovits lower bound from base √2 = 1.41421... to φ. The identity and the reduction are proved here; the lower bound is conditional on a within-layer adjacency lemma (a companion note) and on the transfer from the tight-band model to prime weights, both of which we state explicitly as open. Numerical evidence is consistent with the prediction. We emphasize that φ is a floor: the true maximum already exceeds F_{k+1} at small k, so g_sf(k)^{1/k} > φ, and the growth rate remains undetermined.
Publication Date: 2026-06-20