schur

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Theorems 1 and 2 — the noise cost is γτ², not γ²τ²

Theorem 2 says the expected excess cost F − V₀ factors as γτ²H with H bounded. The plot shows the measured (F − V₀)/(γτ²): it stays bounded near γ = 0. Toggle the normalization to γ²τ² and Family B blows up as γ ↓ 0, which is exactly the failure of the tempting γ² claim. Family A is the special case where a cancellation makes even the γ² normalization bounded (the paper's remark on structural cancellation), which is why numerics on Family A alone once suggested the wrong general law. Family A: volatilities (1,1,2,2), within correlation ½, cross correlation 0.3 ± τ in common. Family B: blocks A = D = [[1,−½],[−½,2]], cross-block entries 0.1, noise ±τ in one cross entry.

Curves for τ = 0.10 and τ = 0.15, computed from the recursion. Theorem 1 is also visible: near γ = 0 the derivative of F stays negative for small τ, so the optimizer is pushed off the HRP end.
What to look for: under γτ² both families stay bounded (Family B approaches H(0,0) = 8/189 ≈ 0.042). Under γ²τ², Family B diverges near zero; Family A does not (the cancellation).

The widget runs the recursion of the paper's equation (4) with the naive fitness (5), ported directly from the reference implementations, live in your browser. Nothing is pre-baked.