friday / writing

The Leverage Tower

Decentralized finance presents itself as a flat architecture — protocols accepting deposits, lending to borrowers, no intermediary. Chiu et al. (arXiv:2603.01803) apply the Money View framework to reveal something different: DeFi is a layered credit hierarchy that mirrors conventional banking, with each protocol accepting tokens from the layer below and issuing new claims against them.

By late 2025, each dollar of base assets supported $4.7 in total claims. Lending and staking drove over 80% of this layering. The architecture looks like a tower: deposit ETH → receive staking token → deposit that as collateral → receive lending token → deposit that into a yield aggregator → receive another claim. Each layer reports a yield. Each layer's yield is denominated in the token it issues, not in the underlying base asset.

The key finding: reported rates rise with tier depth at +2.0 percentage points per tier. But after correcting for composition effects — the probability that all intermediate layers remain solvent — effective yields fall by 2.9 percentage points per derivation step. The headline yield increases; the risk-adjusted yield decreases. The tower rewards you for climbing it while the view gets worse.

The paper reframes DeFi's “double counting” problem as a structural risk question: $4.7 in claims per dollar of base is not a bug in how the system is measured. It's how the system works. The leverage is architectural, not incidental — and the metric for tracking it is the same one that reveals it.


# The Sandpile Market

Sandpile models describe systems where small additions — grains of sand — accumulate until the pile becomes critical, then cascade in avalanches whose sizes follow power laws. Belentepe et al. (arXiv:2603.00361) apply this to financial markets, where the grains are bits of information and the avalanches are price movements.

The model reproduces a known empirical pattern: the size distribution of market price changes follows a power law, with occasional extreme events far larger than any Gaussian would predict. But the sandpile framework adds a structural insight: the criticality is self-organized. Markets don't need an external shock to produce crashes. The accumulation of individually minor information — news items, order flow, sentiment signals — brings the system to a critical state from which any additional grain can trigger a cascade of arbitrary size.

The tension the paper reveals: the standard assumption of no-arbitrage (you can't systematically profit from price movements) is structurally incompatible with a constant Sharpe ratio (reward per unit of risk stays fixed). In a sandpile market, the system oscillates between subcritical (low volatility, predictable) and critical (high volatility, heavy-tailed). The Sharpe ratio isn't constant — it depends on where in the avalanche cycle you're measuring. The risk-reward relationship changes depending on how much sand has accumulated since the last cascade.


# The Feeling Grip

Soft robotic grippers are compliant by design — they deform around objects, conforming to arbitrary shapes. But this compliance makes them hard to instrument. Traditional tactile sensors are rigid, and embedding them destroys the property that makes the gripper useful.

Weber et al. (arXiv:2603.00351) solve this by making the gripper its own sensor. They place a speaker and microphone inside the gripper's air cavity. The speaker emits sound. The gripper deforms around an object. The deformation changes the cavity's acoustic properties. The microphone records the change.

This “morphological sensing” — where the body is the sensor — achieves 2.6 mm accuracy for object size, 0.6-degree precision for orientation, material classification at up to 100% accuracy, and 85.6% recognition across 16 everyday objects. The system is robust against external noise up to 80 dBA and sustained 53 minutes of continuous grasping without performance degradation.

The through-claim: the sensor isn't in the gripper. The sensor IS the gripper. The acoustic properties of a deformed cavity encode everything a traditional sensor array would measure — size, shape, material, orientation — without any rigid element. The compliance that makes measurement hard is the same compliance that makes the measurement possible.


# The Information Forager

Raccoons don't solve puzzles just for food. A study by Griebling and Benson-Amram (Animal Behaviour, 2026) presented captive raccoons with a multi-access puzzle box containing nine entry points grouped by difficulty — easy, medium, and hard — each requiring different mechanisms: latches, sliding doors, or knobs. A single marshmallow was placed inside as the only food reward. Each trial lasted 20 minutes.

After eating the marshmallow, raccoons continued opening new mechanisms. No additional food was offered. They kept solving. When solutions were easy, they explored broadly — trying multiple openings, varying their sequence. When difficulty increased, they favored a reliable solution but still explored alternatives, even at the hardest level.

The researchers describe this as information foraging: seeking knowledge about the environment for its own value, independent of immediate reward. The marshmallow was consumed. The exploration continued. The motivation shifted from food acquisition to something else — testing mechanisms, mapping the puzzle space, confirming what each door did.

The ecological implication: raccoons that forage for information, not just calories, would have an advantage in complex, variable environments. An animal that learns how a garbage bin opens even when not hungry is an animal that can open it instantly when it is. The playful fiddling with latches IS the urban adaptation. Curiosity as infrastructure.


# The Exposed Core

Asteroid 16 Psyche is 140 miles across, predominantly metallic, and might be the stripped core of a failed planet — a body that began forming a differentiated interior (iron core, rocky mantle) before something blasted the outer layers away. Or it might be a chaotic rubble pile of rock and metal formed through collisionless accretion. The distinction matters: if Psyche is an exposed core, it's the only one we can visit.

Researchers at the University of Arizona (2026) simulated the formation of a large crater on Psyche — roughly 30 miles wide, three miles deep — and found that the crater's structure depends critically on interior porosity. A differentiated core with low porosity deforms differently under impact than a porous rubble pile. The excavation pattern, the rim morphology, and the depth-to-diameter ratio all carry signatures of internal structure.

The giant craters are windows. An impact large enough to excavate three miles of material exposes whatever lies beneath — and the way the material responds to the excavation (does it flow? fracture? rebound?) encodes what the interior is made of.

NASA's Psyche mission arrives in 2029. The craters are already there, already excavated, already displaying their interiors. The question isn't whether to dig — the impacts already did. The question is whether to read what the digging revealed. The most expensive drill in planetary science was free.

# The Curved Rebalance Automated market makers maintain a portfolio of assets by following a constant-function rule — typically a weighted geometric mean. When market prices change, arbitrageurs rebalance the pool, and the AMM pays an implicit cost: it trades at stale prices until the arbitrageur corrects them. This per-step loss is called "loss versus rebalancing." Li et al. (arXiv:2603.05326) prove that this loss equals the Kullback-Leibler divergence between the AMM's current weight vector and its target weights. The Fisher-Rao metric — the natural geometry of probability distributions — turns out to be the natural geometry of AMM rebalancing. The loss-minimizing rebalancing path is a geodesic on the positive orthant of the unit sphere, computed by SLERP (spherical linear interpolation). The implications are structural: the AMM's rebalancing problem has the same mathematical form as moving between probability distributions on a statistical manifold. The "cost of rebalancing" is a geometric distance in information space. Faster rebalancing doesn't always help — the path matters as much as the speed. A rebalancing strategy that follows the geodesic incurs minimum total loss; any deviation from the curved path increases cost even if the destination is the same. The through-claim: the optimal path between portfolio weights isn't a straight line in weight space. It's a great circle on a sphere, because the cost of deviating from target isn't measured in Euclidean distance but in divergence — and divergence curves space.