The operational spectral estimate runs +0.098 above a true 0.30, too much error for a tradable alarm. Theorem 1(i), however, is a result worth keeping. The pair (c_ij, theta phi_ij) is identified if and only if the sender's gain path has nonzero variance. On constant-gain simulation paths, the estimator reports non-identification 100% of the time.
Everything layered above that result, the spectral radius and rolling alarm, remains heuristic by the paper's own figures. Its sole positive empirical evidence comes from a two-channel Korean episode lasting less than three months. The regressor used there also falls outside the clean identification theorems.
The mechanism explains the attraction. Near the close, a leveraged fund with multiple m and assets A must trade A(m^2 - m)r in the same direction as the day's return. Aggregating funds on one underlying produces rebalancing capital K. Divide that by 20-day traded value and the actuation gain becomes gamma_j,t = K_j,t / ADV_j,t, disclosed daily through fund shares, NAVs and leverage multiples. Woo casts the closing auction as an algebraic fixed point. Each channel's mandated trade responds to its own full-period return, then moves every channel through a coupling matrix Phi. The feedback matrix is L_t = Phi diag(gamma_t). A known share theta of that displacement reverses overnight.
The identifying moment comes from this reversal. Conditional on the gain regime, project the overnight return onto the pre-window return and the result is C - theta M_t, with M_t equal to the resolvent minus the identity. A static lead-lag confound remains in the intercept, while the coupling varies with the gain. The estimator therefore runs a per-receiver OLS of overnight returns on sender returns, plus sender returns interacted with standardized gain. Coupling gives the interaction a negative sign, so inference uses a signed one-sided t-test.
The simulations set n = 5 and T = 750 across 200 Monte Carlo paths. They take theta = 0.85 as known, include four true off-diagonal couplings, put rho(L_t) between 0.3 and 0.55, and switch gains among {0.5, 1.0, 1.5}. Korea supplies the first real-data sample: sixteen single-stock LETFs (leveraged funds written on one stock) on Samsung Electronics and SK Hynix. Those funds launched 27 May 2026, and the sample was frozen 21 August 2026. One U.S. panel covers the MicroStrategy-Bitcoin-Coinbase complexes. Another uses fourteen TSLA, NVDA and AAPL funds launched across six dates in 2022-2023, with CRSP through December 2024 and N = 500 per regression.
The clean result
With constant gains, a line of observationally equivalent (coupling, confound) pairs remains. The estimator recognizes the problem, reporting non-identification on 100% of paths in that case. The obvious alternative fails differently. In scenario A, where gains follow a correlated staircase with a Gram condition number about 247 and the confound has the continuation sign, a level regression of overnight on pre-window returns records a false alarm rate of 0.04. Under independent gains in scenario D, reversing the confound sign sends that benchmark to 0.53. The interaction estimator stays at 0.12 in both independent-gain designs and reaches 0.22 under the correlated staircase. Variation in a known gain gives protection that a sign heuristic lacks.
Evidence from the two-regime variance-ratio comparison carries less weight. Untuned RMSE is 43.4 against 0.28. Tuning it in its own favor lowers the figure to 0.60, with 22% of paths inadmissible. The paper explicitly presents this as model mismatch rather than a refutation of heteroskedasticity identification, because the simulated shock variances are constant by design.
What does the regression recover?
Only at first order does the interaction coefficient recover the direct edge. Further out, it measures a sensitivity of the resolvent and responds to any reachable path. At rho(L) around 0.30, the signed detector flags structurally zero entries reachable in two hops 39% of the time. Size on unreachable pairs stays at 5.3%. When rho is about 0.45, the reachable-zero flag rate climbs to 84% and unreachable size drifts to 14%. At rho about 0.15, the flag rate drops to 7%.
Running the full n-squared interaction regression reduces the reachable-zero rate to 0.27 without changing size. That behavior helps when screening which channel imports another's innovation. It becomes a trap when the target is topology. The paper says as much and treats direct-edge recovery as a second-stage inverse problem, which it does not pursue empirically.
Spectral estimates remain heuristic
Entrywise estimates assembled into a matrix produce a spectral radius of 0.73 against a true 0.30. Applying the signed t-rule for sparsification barely changes it, yielding 0.72 because the detected entries contain the bias. Fixed-point inversion cuts the estimate to 0.47, or 0.42 when restricted to detected support. Oracle support still leaves +0.07, while delta-method coverage reaches only 61% at nominal 95%.
The preferred estimator projects the interaction slab onto a rank-one SVD. Conditional on successful root finding, its bias is +0.096 (sd 0.034) on 84 of 100 paths, again against a true 0.30. The remaining 16 root-failure paths go through the two-stage fallback. Across all 100 paths, that produces +0.098 (sd 0.058). This mixture has no calibrated inference. Exact nonlinear least squares performs worse from feasible starts, with spectral bias +0.66. Profiling out the confound leaves +0.54, and the final criterion is roughly 34 times its value at the truth.
The working bootstrap covers the true spectral radius on 90% of paths at nominal 95%. That result comes from 60 outer paths with B = 99, implying a Monte Carlo standard error near four points. Woo puts the figure in the abstract and identifies it as the remaining gap. Theorem 5 supplies the defence: pointwise validity for a design-preserving dependent-multiplier score bootstrap under thresholded consistent selection. The simulation uses neither condition. The paper argues that uniform local-to-zero validity is now the only open layer, and that layer continues to block a tradable spectral alarm. Delta-method intervals cover 45% to 61%, leaving too much uncertainty in the estimated distance from the monitoring boundary to size against it.
Multiplicity adds another problem. Across 20 edges and 151 overlapping windows, the null-arm false alarm rate is 0.90 at z = 2.576 under a two-window run rule. At that loosest setting, misses are 0 of 40. The most stringent tabulated setting, z = 3.72 with a three-window run rule, cuts the false alarm rate to 0.10. It also loses 18 of 40 detections within the horizon, based on 40 paths per arm and a binomial standard error of 0.05 to 0.08.
A monitor missing 45% of onsets within its horizon is still unfinished.
Three months carry the empirical case
The Korean result is contaminated by construction, as the paper concedes in Section VIII. Intraday bars begin only after launch. The regression therefore uses the close-to-close full-period return instead of the pre-window output required by the clean moment. Under this convention, even a static confound can acquire gain dependence. Woo calls the exercise contaminated screening.
Across three months of data, the launch-break contrast is z = -2.82 (Newey-West -2.72). It is more negative than all 182 ordered placebo pairs, giving rank 1/183 = 0.0055. The gain interaction is -0.106 (t = -2.29), while the standalone gain effect is insignificant. Estimated transmission is about 0.22 of the sender's innovation, compared with a receiver own-gain contribution of 0.24.
Fragility appears at the boundary. Using theta = 0.88 from another working paper gives a monitoring boundary of 1 - theta/2 = 0.56. The assembled rho is 0.610, which breaches the boundary, but the result depends entirely on a diagonal imported from the companion calibration. This sample's self-contained own-reversal estimate is 0.42 (z = -2.0) and stays below it. The paper reports both values and calls the comparison calibration-dependent. The alarm therefore depends on which diagonal is accepted: 0.61 or 0.42, against 0.56.
The U.S. evidence is null. All six MicroStrategy-Bitcoin-Coinbase directions have |z| <= 1.45, despite gamma reaching 1.72. In the staggered grid, one marginal cell out of twelve appears, AAPL to TSLA at t = -1.77, and it survives no multiplicity adjustment. Woo interprets this as the graded response surface of a low-impact closing venue, where gains reach only 0.53 to 0.54.
A useful diagnostic comes with those results. Although the funds launched on six dates, U.S. gain levels correlate between 0.81 to 0.91. For the rolling 250-day gain-Gram condition number, the median is 45 and the deciles run from 17 to 118. The simulations merely bracket those values: 12 under independent regime switching and 247 under correlated staircases. At 247, the false alarm rate rises to 0.22 from 0.12.
We could not run this. Constructing gamma_j,t requires daily disclosed fund shares, NAVs and leverage multiples for each underlying, data we do not carry. The clean moment also requires a pre-window output separated from the post-window reversal, along with a value for theta. Daily and minute bars provide neither.
There is no P&L in this paper, and none is claimed. I would change my view after seeing the same detector run on the pre-window regressor once enough intraday history accumulates on the Korean complexes.