Concentration of Within-Layer Adjacencies: Almost all n in a prime-block ensemble attain the golden-ratio floor for coprime adjacent divisors

The conditional lower bound g_sf(k) ≥ (φ + o(1))^k for Erdős problem #1100 rests on a first-moment estimate [within]: the within-layer count N(k,j) of disjoint adjacencies among size-j subset sums has mean ≫ C(k-j, j). A first moment bounds the average; it does not say whether that average is produced typically or by rare spikes. We settle this by two second-moment estimates. First, the small-ball candidate count Z = #{disjoint pairs with |Δ| ≤ θ} concentrates, Var(Z)/(E Z)² = 1/(2(k-1)) + O(k^{-2}) + O(√j · 2^{-H(2β)k}); the whole estimate reduces to one expectation Q = E[(1-ρ²)^{-1/2}] in the gap correlation ρ, and the only delicate point, the near-diagonal ρ → 1, is sealed by the codimension-two device of [within, Prop. 3] one level up. Second, the blocked count concentrates: conditioning on a single pair gives the blocker count bounded conditional moments — indeed E[B_P | F_P] = 1/2 + o(1) on {|Δ_P| ≤ θ}, the window of [within] being tuned to exactly this — so its second moment collapses onto the first estimate, every near-diagonal class being exponentially suppressed (worst case O(φ^{-k})). Together these give the typicality theorem: for the prime-block ensemble of [primes], almost every squarefree n has τ_⊥(n) ≥ φ^{k-o(k)}. The result rests on the within-layer lemma [within] and one standard input, a multivariate local limit. It fixes the typical exponent at φ; the growth rate γ remains open in [φ, 1.88988...], closing γ = φ being a matter of lowering the upper bound [upper] to meet it. (This is a companion to A Reduction of the Squarefree Coprime Adjacent Divisor Problem and a Conditional Golden-Ratio Lower Bound.)