Introducing Cascade Tensor: Mapping Live Leverage Topology

Cascade Tensor is the third module in the Vortex Research Suite. Its question is structurally different from the other two: where Diagnostics asks 'is this asset structurally healthy' and Capital Tensor asks 'where is capital sitting at equilibrium,' Cascade Tensor asks 'given the live position state across leveraged venues, how amplifying is the network — how would a shock propagate.'

The fitted object is a 4-dimensional tensor of position density indexed by (venue, asset, leverage_bucket, time). Each cell carries signed notional in USD: positive for net long, negative for net short, summed across positions in that cell at time t. For Phase 1 the dimensions are 6 venues × ~30 assets × 5 leverage buckets, sampled at 60-second intervals. The downstream surfaces — CSI, cascade trajectories, the Jacobian — are projections of per-tick snapshots of this tensor.

Position sources split into two regimes, distinguished by an is_observed flag on every position row. Hyperliquid and dYdX v4 publish per-wallet positions through their public APIs; we pull them for a curated leaderboard set. Hyperliquid emits liquidationPx natively; dYdX requires deriving liquidation price from the subaccount's equity and the per-market maintenance-margin fraction. Binance, Bybit, OKX, and GMX expose aggregate open interest plus top-trader long/short bias but not per-position state. Modeled positions are reconstructed from those aggregates using a calibrated leverage distribution, and rows carry is_observed = false so downstream consumers can filter to observed-only when they need it.

CSI — the Cascade Stress Index — condenses each per-tick snapshot into one scalar per asset by blending three components. Density at risk: how much notional sits within an N% price move of liquidation. Concentration: a Herfindahl-style measure on the venue × leverage_bucket distribution, so a one-venue concentration reads as more fragile than a spread one. Skew: the long-vs-short imbalance at the at-risk band, since a symmetric setup unwinds in either direction whereas a one-sided one cascades. CSI is the single number you read first; Pro and Elite get the per-component breakdown so the headline can be drilled into.

The Jacobian endpoint exposes the eigenvector decomposition of a linearised shock-propagation operator across assets. The dominant eigenvalue is the amplification factor; the corresponding eigenvector is the asset basket that would carry the shock furthest. The /simulate endpoint follows the same operator forward for a user-supplied seed shock to produce a wave-by-wave trajectory. Elite gets the custom-shock builder (any magnitude in [-50%, +50%]); Starter and Pro use canonical shock magnitudes (±3%, ±5%, ±10%) calibrated against historical liquidation cascades.

What Cascade Tensor doesn't do is predict cascades. The Jacobian decomposition describes the current network's sensitivity; it doesn't say the next shock will be of the kind the operator amplifies. The /simulate endpoint runs counterfactual trajectories — 'if shock X hit, here's how the operator would propagate it on this snapshot' — not forecasts. The module is a measurement of leverage topology, not a forecast of leverage events.