A levered AAPL perpetual held through the weekend may be margined and liquidated at the fixed point of venues reading one another's marks. Tick data cannot reveal the underlying topology. Seo and coauthors prove the claim, and the proof holds up.
A closed-window mark as a fixed point
Seo and coauthors split each venue's index target into two blocks. External anchors form one block: cash close, extended-hours prints, index futures and vendor feeds. Same-underlying derivative marks form the other, covering both the venue's own mark and its peers'. The paper calls the adjustment rate K, the intensity of funding and mark control that pulls marks toward the target.
With drift set to zero, the closed-window mark becomes the fixed point of the full reference graph. No single edge determines the result. External exposure instead comes from the network-level map between anchors and marks. A venue can therefore place a small direct weight on a vendor feed yet follow that proxy closely because peers import it along longer paths.
K disappears from the fixed point entirely.
Funding aggression and tight mark control determine how quickly the mark reaches its oracle target. They do not determine the target itself. Hard mark control makes a mis-anchored venue efficiently wrong rather than safer.
Both impossibility results come from this algebra. Every admissible peer topology can reproduce any observed reduced form from anchors to marks after the external loading block is re-scaled. The static mapping identifies nothing. The path-law argument goes further: reparameterising the adjustment matrix preserves the full conditional law of mark paths given the anchors. Setting the peer matrix to zero makes every admissible network path-law equivalent to a purely external model. Even with continuous error-free data, Hasbrouck and Gonzalo-Granger information shares, lead-lag tests and Granger tests have power exactly equal to size.
Rule text supplies the identifying restrictions. A disclosed line saying each venue adjusts only its own mark identifies the normalised peer row from the drift coefficients. Disclosed forbidden anchors, caps and weights can then pin the row, falsify it, or leave an admissible class. Its dimension equals the count of permitted peer inputs minus the rank of the relevant reduced-form submatrix.
The empirical work uses a frozen public battery from April to June 2026. It contains five-minute mark and index candles from Binance, Bitget, Gate and OKX; cash and extended-hours bars from Yahoo; and ES, NQ and BTC futures as comovement anchors and placebo. The four underlyings are AAPL, NVDA, TSLA and AMZN. There is no strategy, no return series and nothing to size. For a clearinghouse or regulator, the payoff is a disclosure checklist rather than a price test.
Where discrimination comes from
The authors seed a three-venue network, then construct purely external wiring and a directed peer cycle with spectral radius 0.77. Both share the same reduced form by construction. Their mark paths coincide to a maximum gap of 1.1e-13. Each has proxy R-squared of 0.9997, cross-venue agreement of 0.970 and a lead-lag information-share proxy of 0.007.
Adding disclosures one at a time reduces the admissible row set from dimension 2 to 1 to 0. The true row, (0.3, 0.4), is then pinned. A false disclosed rule remains infeasible at projection distance 0.11, compared with 0 for the true rule.
It is a clean demonstration, and most of the paper's power to discriminate resides there. The variance-ratio endogeneity detector, the permutation reopen study rejecting a no-anchoring null at roughly 2e-4, and the oracle-incident echo all come from the authors' own seeded runs. They label the permutation p-value as simulation.
Can the row test distinguish real venues?
The available data do not let it do so, a limitation the paper concedes in both its opening and closing claims. The abstract says the disclosed OKX row survives pre-open falsification "while a pure-external baseline shows the test's limited power". The conclusion says the row survives for four underlyings "with the pure-external baseline confirming the check's limited power". In the measurement section, every real-data check is described as indirect support for a proposition rather than recovery of W. Calling the empirical section a survival exercise consequently gives the result more force than the test delivers.
Across four underlyings and two frozen rule captures, the row test covers 186 to 195 five-minute timestamps over three NYSE days. Cap projection distance for the disclosed row ranges from 0.0024 to 0.0886. Fixed-weight residuals span 0.0036 to 0.1261, while the no-own-mark variant runs from 0.0040 to 0.0505. The zero-peer baseline lies between 0.0151 and 0.1275. Those figures are of the same order, and their ordering is mixed across underlyings.
Survival says almost nothing about topology here. The limitations section explains why plainly. Public perpetual candles stand in for the Hyperliquid and own-perpetual components, while stale-feed and active-branch labels remain unobserved. The test therefore establishes compatibility under a closure assumption.
The abstract also presents an eight-week deep-closed panel with cash-reopen validation, intended to bound how much closure variance comes from live external inputs. The panel covers 11 April to 9 June 2026 and contains 9,809 deep-closed timestamps per underlying across six venue series. Marks continue moving: median deviation from the last cash close ranges from 20 to 123 bps. Regressing deep-closed mark returns on ES and NQ produces R-squared as high as 0.42, while the BTC placebo stays below 0.07. Deep-closed drift has the same sign as the eventual cash open in 156 of 192 series-reopens, or 81.3%.
Several comovement and reopen checks are contemporaneous, as the authors concede. They show marks snapping to anchors already used by the oracle rather than discovering those anchors. We read the 0.42 as a single-window, in-sample statistic on four US mega-caps.
The reopen study spans five NYSE opens and 104 venue-series rows. Pooled median transition error against the matched cash move is 4.49 bps. A wrong-underlying control records 28.68 bps, while a same-underlying time-shift placebo ranges from 16.9 to 142.0 bps. Beating a different stock sets a low bar. The linked-pair dispersion speaks more directly to peer reference: 13.39 bps against 6.62 bps at Welch p of 0.042. The paper calls that result descriptive.
A thinner disclosure lever
The frontier result requires a venue permitting p peer inputs to publish p independent exclusions, weights or normalisations before its row is identified. Gate names its constituents without publishing weights. Documentation alone therefore leaves its row admissible set at dimension 1 to 4, which is a non-identification verdict.
OKX publishes more. Its public AAPL-USDT index component row replays with Hyperliquid Oracle at 0.343, OKX Linear Perpetual at 0.057, Binance Index at 0.171 and external vendor feeds at 0.429. Those feeds are Pyth, Ondo and dxFeed. The same weights apply to the other three underlyings, with a replay residual of 0.260 bps.
One provenance decision controls whether most of the mark is derivative-sourced. Treating the Hyperliquid oracle as a peer gives 0.571 under the as-parsed peer coding; the conservative coding gives 0.228. The paper carries both codings throughout. Its rules come from dated help-center captures from June 2026. They pin permitted inputs without fixing fallback weights, leaving the identifying information able to change without notice. Under the model's constant-affine regime, clamps, medians and stale-feed branches enter as unobserved regime labels and residuals.
A proper test requires the venue's own equity-perpetual mark, its oracle component row and its funding feed. We have spot crypto series and none of those. Cash equities cannot be substituted without destroying the feedback mechanism studied by the paper.
Tight cross-venue spreads and high proxy correlation do not establish that a weekend mark is anchored. In the paper's three-venue simulation, opposite topologies produce the same 0.970 cross-venue agreement and the same 0.007 lead-lag share. Deep-closed windows in the real panel also show wider cross-venue dispersion than the regular session.
The practical response is to demand the rule, count its independent restrictions and classify a venue that names constituents without weights as unidentified. Empirical evidence would become persuasive if the row test separated two venues on out-of-sample price data and ranked them consistently against the zero-peer baseline across underlyings, replacing the mixed ordering found here. Rule text already separates them through the frontier result. Until such evidence arrives, the theorem carries the paper and the panel illustrates it.
We made a related complaint about a volatility paper that specified its estimator exactly while staying silent about which model anyone would trade (our note). Seo and coauthors are exact about what cannot be identified, and their own falsification test demonstrates the limitation.