Two effects are tangled here, and the whole point is to separate them. Deep hedging beating delta is a generic frictions effect — it happens in any model. The roughness question is only the increment: does the rough market beat its own smooth control? Every honest check said no — and the checks were the hard part.
z = 5.6 → artifact
At c = 0.02 an apparent roughness edge of +0.362 (z = 5.6) emerged. It survived significance, 8/8 seed-consistency, two-budget reproducibility, an edge-convergence fix, and a baseline decomposition — and was still a residual-convergence artifact. A finer 3000-epoch check dissolved it to +0.033 (z = 0.7) while the untrained control held exactly constant. The hardest-won false-positive catch in the project.
Two guardrails behind the null. Frictionless anchor (GATE 1): with no costs the trained policy recovers Black–Scholes delta (mean|δ−Φ(d₁)| = 0.016, P&L-std ratio 1.03–1.04) and a look-ahead policy trips the causality guard — the framework is sound before any edge is claimed. Signatures: giving the hedger the whole path history (path-signatures) matches the simple Markovian (t, S, √V) state but never beats it, at ~2.5× the training cost — and an early signature “edge” of +0.167 (z = 2.2) was unmasked as uneven training (rough +0.146, smooth −0.021), not roughness.
frictions edge: +1.14 vs delta (8/8 seeds)
roughness increment: +0.06 ± 0.04 (z = 1.4)
← the edge is real; the roughness part isn't — and it stays null across c ∈ [0, 0.05]
This is the last of the five questions, and it closes the loop. Across the whole audit, roughness is hard to identify from price history (Q1) and from option surfaces (Q4), it isn't cheaply priceable by multilevel Monte Carlo (Q2), it gives no execution edge (Q3), and here it gives no hedging edge beyond frictions (Q5). Five routes, one answer: whether or not the roughness is real, you cannot turn it into an advantage. And every “no” was defended against the false positive that would have made a better headline — which is exactly why the verdict can be trusted.