1. Abstract

2. Catalysis Overview on SSNs: First Article Recap

   1. Aggregated Security Through Unified Abstraction

   2. Key Benefits to SSNs

   3. Reframing the SSN Security Stack

   4. Economic & Game-Theoretic Flows

3. SSN Cryptoeconomic Security

   1. The Four Types of Security Costs

   2. Reducing the Cost of Security Acquisition

   3. Raising the Cost of Corruption

4. Finding Equilibrium in SSP Allocations

   1. Modelling SSN-to-SSP Allocations Based on Perceived Utility, via QRE

   2. Calculating SSN-to-SSP Allocations Based Required Target Stake

   3. Additional Target Stake Considerations

5. Localized vs. Correlated SSN Slashing Modes

   1. Localized Slashing

   2. Correlated Slashing

   3. Modelling Localized & Correlated Slashing Modes

   4. Calculating Localized & Correlated Slashing Modes

6. Catalysis Rebalancing Feedback Engine

7. Conclusion

Note: The term “Shared Security Networks” will be used herein to represent the networks/services (AVSs, Networks, BSNs, etc.) that leverage restaked collateral to validate their infrastructure needs. And the term “Shared Security Protocols” will be used herein to represent the restaking marketplaces (EigenLayer, Symbiotic, Babylon, SatLayer, etc.) that aggregate this demand and supply security and validation to Shared Security Networks.

Catalysis is the first Security Abstraction Layer that unlocks unified access to $20B+ of ETH, BTC & SOL economic security for institutions & developers to tap into. It introduces a modular and programmable coordination layer for Shared Security Networks (SSNs), enabling them to flexibly source, rebalance, and optimize economic security across multiple restaking ecosystems.

Rather than anchoring SSNs to a single protocol, Catalysis aggregates validator sets, standardizes slashing semantics, and surfaces utility signals to guide stake allocation based on risk and yield tradeoffs. This paper presents a stake allocation simulation illustrating how utility asymmetries and correlated exposures create systemic inefficiencies, and how Catalysis enables SSNs to converge toward allocation equilibrium across SSPs through real-time routing and dynamic feedback. It concludes by formalizing two core slashing modes—localized and correlated—and modeling how their containment or propagation depends on system architecture.

Shared Security Networks (SSNs) such as Omni, Redstone, Cap, Ditto, and Hyperlane are progressively integrating with multiple Shared Security Protocols (SSPs)—including EigenLayer, Symbiotic, and SatLayer—to enhance their economic security base. This multi-platform restaking strategy adds distinct trust domains, increasing security robustness. However, it also introduces complexity: validator sets, slashing semantics, fault adjudication, and delegation infrastructure vary widely across SSPs.

Catalysis abstracts this fragmentation through a unified interface. Instead of integrating with each SSP individually, SSNs can source restaked security through a single validator set and programmable slashing layer. Such modular structure allows SSNs to retain uptime and security continuity, even when one or more SSPs experience validator degradation, slashing events, or yield volatility.

Catalysis introduces structural flexibility to SSN design and operations, allowing SSNs to function as modular market participants within a programmable security economy. It enables cross-platform validator coordination, customizable slashing semantics, and partial execution across SSPs—maximizing security configurability and fault isolation.

• Unified Integration & Validator Abstraction

  A single Catalyst SDK layer handles integration across all supported SSPs. Validator management is abstracted, enabling cross-SSP coordination while customizing slashing logic and failure domains—reducing launch time and complexity for new SSNs;

• Dynamic Stake & Risk-Aware Rebalancing

  Stake allocation adapts in real-time to operator performance, pricing, and slashing history. SSNs can proactively or reactively shift stake across SSPs to isolate faults, mitigate underperformance, and improve capital efficiency;

• Programmable Reward Distribution

  Rewards are routed directly across SSPs without cross-chain wrappers or bridges, minimizing slippage, simplifies flow logic, and reduces fragmentation by consolidating delegation, slashing, and payout mechanisms;

• Partial Execution & Custom Trust Models

  SSNs can selectively deploy logic across multiple SSPs, enabling hybrid trust models and fault-resilient execution. This facilitates experimentation with differentiated validator trust configurations;

• Market-Based SSP Selection

  Aggregated demand across SSNs pressures SSPs to compete on validator quality, uptime, slashing guarantees, and reward rates—aligning infrastructure incentives with AVS security needs;

• Developer Flexibility

  All security primitives are programmable via Catalysis, allowing developers to iterate on incentive structures and core business logic, automate strategy rebalancing, and integrate without bespoke infrastructure overhead.

As SSNs evaluate integration with Catalysis, three critical questions emerge—each of which the system explicitly addresses:

1. How much economic security is required?

   SSNs must consider potential corruption profit based on their set-up and how much cost (economic security) would be sufficient to deter an attack. Read more on the topic on our newly-released piece on Target Stake with Symbiotic.

   Catalysis reframes this question further with a deeper second-order one:

   Which sources of cryptoeconomic security (ETH from EigenLayer and Symbiotic, BTC from Babylon and SatLayer, BNB from Kernel, etc.) does an SSN need and wants align itself with?

2. What is the cost of acquiring and maintaining that security?

   Catalysis exposes a unified fee and reward benchmarking layer across SSPs, enabling SSNs to optimize for the lowest-cost, highest-resilience combinations. SSNs can minimize validator acquisition costs, streamline restaker onboarding, and amortize security costs across multiple use cases.

3. What fault conditions govern validator behavior?

   SSNs must specify what constitutes slashing-worthy behavior and how faults are processed. Catalysis makes this logic programmable—enabling fault adjudication and penalty enforcement across SSPs through one cohesive slashing engine. This ensures validator accountability is not lost in cross-platform complexity.

In essence, Catalysis creates a two-sided restaking marketplace: SSNs compete for reliable security, while SSPs and Operators compete for SSN onboarding.

Assuming the structural advantages introduced by Catalysis play out as expected, a broader set of SSNs would likely enter the system—driving up aggregate demand for restaked capital. This flywheel creates upward pressure on rewards for delegators (via LRTs or direct restakers), incentivizing greater participation and TVL growth. At the same time, increased SSN competition drives demand for high-performing validators, prompting operators to compete on uptime, reliability, and responsiveness.

From a cost-efficiency standpoint, Catalysis introduces a competitive restaking marketplace. SSNs can compare pricing across SSPs and allocate stake where security is cheapest and most stable. This drives downward pressure on security costs as SSPs compete for SSN onboarding and encourages them to improve internal economics and UX.

SSNs also gain more malleability to consider SSPs’ TVL stickiness—how durable and reactive each SSP’s capital base is under slashing, volatility, or adverse events. Those with more consistent capital retention will be perceived as more reliable security sources.

By concentrating demand and standardizing the security procurement process, Catalysis enhances the buying power of SSNs. SSPs are incentivized to compete not just on integration availability, but on economic efficiency, validator quality, and fault tolerance. In this way, Catalysis transforms restaking from a fragmented infrastructure layer into a coordinated, efficient security marketplace.

SSNs incur four core categories of security-related expenses. Catalysis mitigates cost pressure across each through abstraction, routing optimization, and shared infrastructure:

1. Delegator Rewards: Continuous payouts to restakers and LRT holders who supply economic security.
   → Higher security demand requires elevated yields to attract stake, particularly in competitive environments where AVSs must signal safety.

2. Security Rental from SSPs: Although not fully standardized today, future SSPs may charge usage fees (e.g., Symbiotic 3%, EigenLayer 4.5%).
   → Catalysis enables price discovery and blended sourcing across protocols, minimizing net cost per unit of security.

3. Task Execution Fees: Validators are compensated for protocol-specific services.
   → Competitive validator markets lower long-run execution pricing, compressing recurring operating costs.

4. Protocol Development & Security Overhead: Tooling, audits, and DevOps are required to onboard and secure SSNs.
   → Catalysis reduces this burden via a unified SDK and standardized validator and slashing logic across SSPs.

Catalysis reduces security acquisition costs by abstracting validator infrastructure, eliminating duplicative onboarding, and enabling price discovery and dynamic stake routing across SSPs.

• Unified Security Infrastructure: Validators are aggregated across SSPs, letting SSNs onboard once to access pooled security.
  → Reduces onboarding friction and improves validator reward saturation by consolidating demand.

• Dynamically-Optimized Stake Allocation: Stake flows to SSPs offering optimal tradeoffs between risk, yield, and validator quality.
  → Avoids degraded providers, lowers capital inefficiency, and better aligns with each SSN’s Target Stake.

• Reward Efficiency and Routing: Rewards are natively routed across SSPs without wrappers or bridges.
  → Cuts gas costs and slippage, simplifying integration logic.

• System-Level Cost Compression: Aggregated SSN demand creates buy-side bargaining power.
  → Improves validator pricing and amortizes fixed infra costs across a broader base.

• Feedback-Driven Delegation Logic: Stake rebalances dynamically in response to performance, slashing, or curator signals.
  → Stake reallocates in real-time, optimizing for current risk-reward landscapes.

• Validator Reuse Across SSNs: Validators serving multiple SSNs operate under shared infrastructure.
  → Avoids re-registration and stake fragmentation, unlocking capital efficiency and reducing idle capacity.

Catalysis materially increases the Cost of Corruption (CoC) by aggregating security and aligning incentives across SSNs. Whereas traditional architectures enable isolated validator compromise, Catalysis enforces interdependency and accountability at scale.

• Aggregated Security Layer: Restaked capital from multiple SSPs is unified under a single slashing abstraction.
  → Tens of billions in economic security are pooled, making coordinated exploits prohibitively expensive.

• Differentiated Validator Sets Per SSP: Validators are coordinated via Catalysis but form distinct sets per SSP.
  → Attacks must breach multiple operator sets simultaneously, raising both complexity and cost of coordinated corruption.

• Higher Stake at Risk per Attack: Corruption attempts now expose more total stake per validator action.
  → Amplifies slashing losses, increasing the minimum profitable attack threshold.

• Reputational and Long-Term Opportunities: Well-behaved validators gain stronger reputation and opportunities across all integrated and upcoming SSNs.
  → Creates a more feedback-driven, transparent flywheel for operator selection.

• Cross-SSN Risk Propagation Awareness: Catalysis exposes correlation risks across SSNs via shared validator metadata.
  → Enables proactive delegation modeling, deterring systemic exploits by surfacing propagation vectors.

Restaking introduces uncertainty, partial observability, and multidimensional risk tradeoffs that invalidate key assumptions of standard game-theoretic models. In particular, traditional Nash Equilibrium assumes fully rational agents with complete information, selecting strategies that maximize utility deterministically. In restaking environments this model breaks down as participants operate under noisy incentive signals, hidden risks, incomplete slashing semantics, and evolving market conditions. Nash equilibrium also fails to account for coordination frictions, feedback loops, and multi-reward routing that shape actual SSN behavior.

By contrast, Quantal Response Equilibrium (QRE) models decision-making under bounded rationality. Agents do not always select the utility-maximizing action; instead, they assign probabilities to each action via a softmax function over perceived utility. This methodology captures realistic agent behavior: higher-utility SSPs are more likely to attract stake, but suboptimal ones may still receive allocations due to noise, misperception, or hedging. QRE accommodates stochastic dynamics, informational asymmetries, and incentive gradients—core features of restaking ecosystems.

In Catalysis, QRE offers a more robust equilibrium model. Stake does not flow deterministically to the highest-yield SSP. Instead, allocations diffuse across SSPs proportional to their slashing-adjusted utility. At equilibrium, each SSP attracts stake such that no SSN—given its subjective utility estimates and rationality bounds—has incentive to reallocate. The framework enables smoother rebalancing, reduces concentration risk, and aligns with real-world delegation behavior shaped by asymmetric risk-reward signals.

This section models how SSNs allocate stake across SSPs using the QRE framework. It highlights how allocations evolve from noisy, misaligned states toward probabilistic equilibrium as SSNs refine their utility assessments.

At the core is the utility function:

where:

• $\text{Utility}_{SSP_j}^{SSN_i}$: Net expected value perceived by an SSN when allocating stake to a given SSP, accounting for the tradeoff between returns, costs, and risks under constrained rationality;

  • $\mathbb{E}[\text{Return}_{SSP_j}]$

Since SSNs operate under incomplete information and rationality, they don’t source capital deterministically. Instead, they convert raw utility into probabilistic preferences via the softmax formulation:

• Rationality (λ) scales how strongly agents react to utility differences when allocating probabilistically across options:

  • Low λ → Bounded Rationality / High Noise: SSNs behave erratically, weakly preferring high-utility SSPs; randomness dominates;

  • High λ → Deterministic Behavior: SSNs sharply favor SSPs with higher perceived utility; probabilistic error shrinks;

• Perceived Utility ($U’_{SSP_j}$) reflects this interplay—blending observed utility and the SSN’s current rationality level.

At time $t₁$ (non-equilibrium), SSNs' allocations are uncoordinated and near-random. SSNs disproportionately allocate to SSPs with higher apparent rewards, stronger brand recognition, or inertia, regardless of underlying risk exposure.

At time $t₂$ (near-equilibrium), Catalysis introduces risk and incentive feedback, nudging the system toward equilibrium. SSNs rebalance based on perceived utility gradients that incorporate slashing likelihood, validator-set quality, historical uptime, reward rates, and other metrics. Stake begins to redistribute probabilistically toward more defensible SSPs, even if they weren't initially preferred.

This is visualized in the utility response curves:

• SSP1’s curve rises steeply as SSNs recognize its superior risk-adjusted return profile;

• SSP2’s curve declines, reflecting reassessed risk due to previously hidden risk or reward downsides;

• SSP3, initially undervalued, gains traction under higher $\lambda$, as latent utility is revealed through rational inference.

A key inflection occurs around $\lambda$ = 4: SSNs transition from misinformed and erratic behavior to grounded preference formation. Rationality begins to meaningfully differentiate between SSPs. Catalysis and risk advisors' feedback and insights play a pivotal role in this shift.

By $\lambda$ = 9, SSNs express nearly full discernment, allocating in line with refined perceptions of utility. Stake flows align tightly with risk-adjusted rewards and utility.

Ultimately, Catalysis does not enforce uniform distribution. It offers transparency and steers the system toward a stable probabilistic equilibrium, where stake is allocated in line with relative perceived utility—and no SSN finds further reallocation rational, given available information and risk.

Unlike standard minimax approaches that solely consider worst-case slashing risk and overlook key tradeoffs, our model instead uses perceived utility as a composite function of multiple factors: reward competitiveness, cost efficiency, validator quality, slashing likelihood, and operational reliability.

The stake sourced by $SSNᵢ$ from $SSPⱼ$ is determined proportionally as:

where:

• $S_i$ is the stake sourced by $SSNi$ from $SSPj$;

• $U’_{SSP_j}$

This formulation achieves three objectives:

• Relative Utility Normalization: Stake is assigned based on comparative rather than absolute utility, ensuring efficient delegation even under incomplete information;

• Budget-Constrained Safety: Allocations are anchored to the Target Stake $T$, bounding systemic exposure and ensuring cost-aware deployment—avoiding overspend while preserving capital efficiency;

• Framework Extensibility: The logic is extensible beyond SSN-to-SSP flows. It applies equally to LRT-to-SSN or Operator-to-SSN delegation, if utility and target stake parameters are independently defined.

SSNs with elevated Profit-from-Corruption (PfC) potential must provision proportionally higher Target Stake $T$ to offset attack incentives. When adversarial returns exceed slashing penalties, the system becomes economically vulnerable. Raising $T$ increases the Cost of Corruption (CoC) and restores economic deterrence.

Catalysis amplifies capital efficiency for high-$T$ SSNs by aggregating restaked security across SSPs and enabling dynamic reallocation toward configurations with optimal cost-risk profiles.

A key parameter often overlooked to consider when benchmarking Target Stake is collateral quality. Volatile or illiquid collateral degrade the effective security budget, requiring higher nominal $T$ to preserve equivalent resistance to corruption.

For a deep dive check our work with Symbiotic on Target Stake assessments:

Modeling Target Stake Requirements

This research in collaboration with Symbiotic explores how networks can estimate the amount of stake (or collateral) required to operate securely under PoS or restaking-based models.

https://paragraph.com

Catalysis is structurally resistant to classical Byzantine Fault Tolerance (BFT) corruption attacks. Two core design elements raise the cost and coordination complexity of system-wide exploits:

1. Differentiated Validator Sets Across SSPs: While Catalysis presents a unified operator interface to SSNs, each underlying SSP can have its own distinct set of validators. For instance, some operators may be active only within specific SSPs. When an SSN leverages Catalysis, it interacts with a unified coordination layer, even though, under the hood, operator sets can vary across SSPs. This means that any successful corruption attempt will potentially have to compromise multiple, distinct validator sets simultaneously, significantly raising the cost and coordination complexity of an attack and making large-scale exploits logistically implausible;

2. Capital Scale: Catalysis aggregates restaked collateral potentially exceeding $20 billion across multiple ecosystems. An attacker aiming at cross-SSP compromise would require an economically irrational commitment of capital under realistic adversarial models, making large-scale coordinated attacks financially infeasible.

BFT attacks targeting dissimilar SSNs—those with independent validator sets, slashing logic, or infrastructure—form submodular attack surfaces, where each additional SSN increases attacker cost faster than it increases reward. Under Catalysis, this type of exploit is not just disincentivized—it is structurally infeasible. The heterogeneity across SSNs breaks exploit scalability and collapses return-on-attack curves.

Supermodular attacks, by contrast, exploit convergence: shared validators, identical slashing semantics, or common execution infrastructure across SSNs. These reduce marginal cost and amplify adversarial payoff. While theoretically more viable, Catalysis significantly blunts these vectors by enforcing unified (yet partially differentiated set per SSP) validator sets, incentivizing risk diversification, and amplifying system-wide cryptoeconomic security across all served SSNs—raising both detection likelihood and slashing exposure.

As a result, this section does not model catastrophic BFT-style exploits. Instead, it focuses on minor but still slashable faults—e.g., equivocation, liveness failures, or double-signing—and how their impact scope depends on the SSP's underlying slashing mode: whether faults are isolated (localized) or propagate across domains (correlated).

EigenLayer exemplifies localized slashing through its Unique Stake and Operator Sets architecture, introduced in ELIP-002:

Unique Stake guarantees that an Operator’s specific slashable stake can be allocated only to one AVS at a particular time. This single pairing strengthens the AVS's security without creating exogenous risk to other AVSs or the protocol at large. Operator Sets provide an in-protocol structure that enshrines the segmentation of Operators into local groups for the accounting, allocation, and slashing of staked security.

Each Operator Set registered under an SSN must deposit dedicated (slashable) stake, isolated from other SSNs—even if the same Operator Set is active elsewhere. This segmentation enforces fault containment:

• Slashable stake: Actively securing a specific SSN; subject to penalties based on that SSN’s slashing logic;

• Non-slashable stake: Idle or delegated elsewhere; remains untouched by unrelated slashing events.

This model defines Localized Slashing: faults are accounted for and penalized within AVS-specific boundaries, preventing risk from propagating across SSNs by default.

However, structural isolation does not eliminate all forms of slashing correlation. Some edge cases can still introduce indirect propagation pathways:

• DeFi Liquidation Contagion: If an LRT backed by a slashed operator is used as collateral in lending markets (e.g., Aave), a sharp NAV decline can trigger liquidations—particularly in high-LTV positions or thin-liquidity pools. Lending protocols that rely on slower or less responsive pricing—often derived from AMMs—may misprice risk during slashing events. In contrast, order book-based markets (e.g, Hyperliquid, dYdX) typically adjust more quickly, potentially containing price dislocations. This mismatch in price realization can accelerate liquidation cascades and lead to TVL erosion across the affected SSPs;

  For further analysis on this topic, refer to: LRT Slashing Risk.

  Drawing a parallel scenario to the LST ecosystem: A similar event happened in the 2022 Ankr exploit, where a hacker gained control of a compromised key and used it to mint 6 quadrillion aBNBc tokens—a derivative of Ankr Reward Bearing Staked BNB. Since these tokens were meant to represent a claim on underlying BNB, the exploit effectively created counterfeit BNB at scale. As the hacker offloaded the fake aBNBc, the price of liquid staking tokens like BNBx and stkBNB plummeted. Exploiting the chaos, the attacker used the counterfeit tokens as collateral to borrow stablecoins from Helio, ultimately draining the protocol and leaving it financially crippled. Ankr acknowledged a $5M direct loss.

Correlated slashing occurs when a single validator fault propagates beyond its local domain, impacting multiple SSNs through shared dependencies. Unlike localized slashing—where faults are isolated per AVS—correlated slashing reflects a failure of stake isolation, allowing systemic exposure across otherwise independent networks.

Its most critical form emerges from covariance across participants: when SSNs, operators, LRTs, and, under Catalysis, even SSPs, share validator infrastructure, slashing semantics, or capital pools. In this expanded surface area, one slashing event—if left unchecked—can trigger cascading penalties across networks with aligned exposure vectors.

Propagation channels include:

• Shared validator sets securing multiple SSNs;

• Overlapping LRT portfolios of SSNs with collateral tied to affected operators;

• SSPs that service structurally correlated SSNs, amplifying blast radius.

When isolation boundaries blur, a single fault domain can drain capital across multiple SSPs, degrade cross-network trust, and weaken Catalysis’ aggregate security posture.

Mitigation depends on preemptive containment:

• Strict operator segmentation across SSNs to reduce overlap;

• Robust, non-ambiguous slashing definitions to localize penalties;

• Dynamic rebalancing and portfolio caps to avoid systemic overexposure;

• Collateral diversity across LRTs, minimizing reflexive liquidations.

Catalysis enhances risk visibility across these dimensions—but maintaining slashing containment in correlated environments requires intentional design at the SSN, LRT, and SSP levels.

This section models how SSNs dynamically rebalance stake allocations across SSPs in response to localized and correlated slashing risks. The Sankey transition from non-equilibrium ($t1$) to near-equilibrium ($t_2$) captures how Catalysis nudges the system toward context-aware delegation based on perceived utility gradients and risk asymmetries.

Each SSN bar reflects its Target Stake—the minimum capital required for secure operation. SSN2 and SSN5 are flagged as riskier and depicted in yellow.

At $t₁$ (non-equilibrium):

• Over 50% of $SSP2$’s utilized stake is sourced from high-risk SSNs, creating exposure to correlated slashing events. A fault in either SSN could propagate through $SSP2$, impacting unrelated SSNs like $SSN1$ and $SSN3$. Although unlikely, SSP2 becomes a potential channel for supermodular attack surfaces—where shared infrastructure and protocol and portfolio overlap reduce marginal attack cost and compounds adversarial payoff. If $SSP2$ adopts a localized slashing architecture, SSN covariance risk is neutralized, and security posture largely becomes a function of

These dynamics define a non-equilibrium state, where risk is unevenly distributed, yield signals are misaligned, and capital flows inefficiently—revealing the highly misinformed, at times near-irrational allocation decisions that distort utility assessments. Catalysis detects these imbalances and surfaces slashing asymmetries and overexposure zones to prompt reallocation. SSNs can adjust proactively or reactively, absorbing post-event feedback or shifting positions as incentive curves evolve.

At $t₂$ (near-equilibrium):

• Aggregate stake across the system increases as more efficient utility routing raises delegation confidence. Catalysis TVL at $t_2$ exceeds $t_1$, reflected by the thickened bar at the center. More capital is secured, better aligned to perceived utilities and yield-risk profiles;

• $SSP1$ and $SSP3$ selectively onboard higher-risk SSNs

Catalysis acts not as a passive router but as an active coordination layer—surfacing latent risk, realigning delegation behavior, and driving the system toward a probabilistic equilibrium. Stake no longer flows blindly toward yield. It follows perceived-utility paths, shaped by Catalysis’ intelligence, validator metadata, slashing semantics, and real-time incentive design.

The result: an adaptive, self-correcting delegation topology that preserves capital efficiency while minimizing systemic slashing risk.

To model how slashing events propagate across SSNs via shared infrastructure, validator overlap, or LRT portfolio covariance, we extend our LRT risk model to compute compounded SSN-level exposure. The framework introduces an amplified temporal risk function that accounts for both baseline slashing risk and the duration-dependent propagation effect:

where:

• $R_{\text{SSN}A}$ is $\text{SSN}A$’s baseline risk score profile;

• $\mathcal{S} \in [0.1, 0.5]$ is a sensitivity coefficient that scales cascading risk magnitude;
  → Lower values imply localized containment; higher values reflect elevated systemic fragility due to covariance and shared exposure;

Refer to Restaking Networks Risk Evaluation for a technical deep-dive on SSN risk and to LRT Slashing Risk for more detail on LRT risk and the formula construction.

In a correlated, rather than localized, setting, slashing propagation does not terminate at the initial fault domain. If $\text{SSN} A$ is slashed and shares dependency vectors with $\text{SSN} B$, then $\text{SSN} B$ acquires conditional exposure to the upstream slashing event.

This can be modeled using conditional expectation:

where:

• $\mathbb{E}\left[ R'_{\text{SSN} \, B} \mid \mathbb{S}_{\text{SSN} \, A} \right] > \mathbb{E}\left[ \mathbb{S}_{\text{SSN} \, A} \right]$ denotes the expected amplified risk score for $\text{SSN} B$, given that the covariant $\text{SSN} A$ has been slashed. Notably, this condition

This formalism captures second-order propagation: slashing on $\text{SSN} A$ revises the real-time risk profile of $\text{SSN} B$. Such correlations emerge from validator co-dependencies, LRT/SSP portfolio overlap, or entangled slashing semantics.

Amplified events can trigger cascading reallocation, stake withdrawals, and portfolio de-risking behavior. In extreme scenarios, restaking platforms with high TVL—particularly those exposed to frail collateral options—may suffer from systemic trust degradation.

To contain this, protocols must adopt nonlinear risk transmission models and dependency-aware allocation strategies, including:

• Preemptive modeling of second-order propagation;

• Operator-level exposure segmentation;

• Collateral diversification buffers for highly connected SSNs.

Catalysis serves as an active coordination layer, continuously steering the system toward a stable probabilistic equilibrium. It does not enforce allocation rules. Instead, it surfaces asymmetric risk concentrations, informs incentive design, and enables stake to reorganize dynamically in response to evolving market conditions.

At time $t_1$, the system may exhibit unstable configurations—such as excessive correlated exposure to a single SSP (e.g., $SSP2$)—which amplify the risk of multi-SSN slashing propagation. Catalysis detects these patterns in real time, quantifies risk gradients, and guides corrective rebalancing through incentive-compatible mechanisms. $SSP1$, for example, may be prompted to onboard marginally riskier SSNs to absorb systemic imbalance and reduce covariance across validator clusters.

A core function of the engine is discriminating between localized and correlated slashing vectors. When fault dependencies—such as shared validator sets, infrastructure, or LRT portfolios—are detected across SSNs (e.g., $SSN1$, $SSN3$, and $SSN5$), Catalysis flags these as correlated exposure zones and adjusts delegation incentives to mitigate propagation risk.

The rebalancing logic is modular and extensible, leveraging a suite of programmable primitives:

• Portfolio-Aware Delegation Logic: Incentivizes stake redistribution away from SSNs with excessive validator overlap, reducing conditional exposure and localizing fault domains;

• Validator Caps: Enforces operator concentration thresholds across SSNs to avoid systemic reliance on dominant infrastructure actors;

• Collateral-Type Differentiation: Promotes heterogeneous collateral sourcing to contain DeFi contagion from LRT-backed liquidation cascades;

• Slashing Semantics Harmonization: Standardizes fault definitions across SSPs to ensure symmetry in penalties and reduce exploitability via slashing arbitrage.

Crucially, equilibrium under Quantal Response Equilibrium is not a point solution. It is a distributional outcome wherein each SSN, based on perceived utility, has no incentive to reallocate. Stake flows probabilistically, reflecting the bounded rationality, asymmetric information, and risk signals that define real-world delegation environments.

Catalysis operationalizes this by continuously mapping utility vectors, flagging slashing covariance, and delivering route-aware, risk-adjusted incentives. The system doesn’t just react—it curates. The result is a dynamic, resilient delegation marketplace that organizes around economic stability rather than static configuration.

Catalysis reshapes SSN security economics by embedding awareness of SSP-specific risk, reward, and cost into the core of SSN stake routing. Through unified validator abstraction and programmable delegation logic, it reduces capital inefficiencies, enables market-wide price discovery, and allows SSNs to adapt dynamically in real time.

A stake allocation simulation—modeled through Quantal Response Equilibrium and visualized via a Sankey transition diagram—illustrates the system’s progression from non-equilibrium to near-equilibrium. Stake no longer flows naïvely toward yield-maximizing venues, but reallocates proportionally across SSPs based on risk-adjusted utility curves and Target Stake requirements.

We show that localized slashing isolates faults within the originating SSN, maintaining strict fault containment. Correlated slashing, by contrast, arises from shared validator sets, infrastructure, or portfolio overlap—enabling faults to propagate laterally across SSNs, LRTs, operators, and SSPs. To evaluate this risk, we introduce temporal amplification and conditional propagation formulas that quantify second-order exposure and help guide risk-aware delegation strategies.

Catalysis reframes restaked security as an ongoing coordination game—where utility, risk, and capital efficiency are continuously co-optimized across modular restaking ecosystems.

• Catalysis Documentation: https://docs.catalysis.network/

• Economic Security of Multiple Shared Security Protocols, Abhimanyu Nag, Dhruv Bodani, Abhishek Kumar (Catalysis): https://arxiv.org/abs/2505.03843#

• Restaking Protocols Infra Risk Framework V2, Tokensight: https://paragraph.com/@tokensightxyz/restaking-protocols-infra-risk-framework-v2

• Restaking Network Risk Evaluation: Developing a Fundamental Approach, Tokensight & P2P: https://hackmd.io/@lCkxYGq-RPqCfyHwdlrqbg/HymUqWD7Jx

• Modeling Target Stake Requirements in PoS and Restaking-Based Networks, Tokensight & Symbiotic: https://paragraph.com/@tokensightxyz/modeling-target-stake-requirements

• LRT Slashing Risk, Tokensight: https://paragraph.com/@tokensightxyz/lrt-slashing-risk

Check Catalysis website and Twitter.

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