Reliablocks: Reliability Framework

• Reliablocks is a framework that quantifies reliability in block-based systems, addressing correlated failure risks in both blockchain and distributed storage.
• It employs on-chain oracle scoring, block-aware erasure codes, and DRBD formal analysis to enhance risk management and optimize recovery.
• The framework supports diverse applications, from optimistic rollups and dynamic interest rate settings to resilient data recovery in distributed architectures.

Reliablocks is a framework and protocol suite for quantifying, optimizing, and operationalizing reliability in systems that are subject to correlated block failures and dynamic finality risk. The term refers both to recent on-chain reliability metrics for optimistic rollups as well as broader “block-aware” erasure coding schemes in distributed storage. This entry focuses on three domains in which Reliablocks have arisen: (1) on-chain rollup reliability scoring (Das et al., 8 Nov 2025), (2) block failure resilient code design (Calis et al., 2014), and (3) formally verified reliability block diagram (RBD) analysis (Elderhalli et al., 2019).

1. Motivation and Formal Definitions

Reliablocks addresses reliability at the granularity of blocks—collections of components or nodes that share correlated failure domains (e.g., racks in a data center, blocks in blockchain rollups). In large-scale systems, traditional reliability models and codes fail to capture block-wise dependency and correlated failure modes. Reliablocks introduces explicit block modeling:

• In distributed storage, a block is a set of storage nodes with shared risk.
• In rollup protocols, a block is a chain segment whose economic finality is uncertain until fraud windows elapse.

The core operational objective is to attach to each block $b$ a reliability score $R(b)$ that estimates the probability of successful recovery or irrevocable commitment, quantified either formally (as in HOL-verified algebra (Elderhalli et al., 2019)), algebraically for coding-theoretic schemes (Calis et al., 2014), or empirically as a dynamic index on-chain (Das et al., 8 Nov 2025). This quantification enables transparent and block-aware risk management, adaptive rate setting, and automated policy enforcement.

2. On-Chain Reliability Scoring for Optimistic Rollups

Reliablocks introduces a permissionless oracle for non-finalized blocks in Optimistic Rollups, producing a reliability score $R(b) \in [0,100]$ for each block $b$ under Ethereum’s seven-day challenge window (Das et al., 8 Nov 2025). The score is computed as follows:

Let $E_b$ denote the set of fast-exit events (capital commitments) in $b$, each with value $v_i$, and a sensitivity parameter $\alpha > 0$:

$W_b = \sum_{i \in E_b} v_i$

$R_{\mathrm{raw}}(b) = 1 - \exp(-\alpha W_b)$

$R(b) = 100 \times [1 - e^{-\alpha \sum_i v_i}]$

The implementation aggregates signed reliability attestations $$\sigma_j = \mathrm{Sign}_{\mathrm{sk}_j}(b \,\|\, R_j(b))$$ from multiple operators, storing the on-chain score as a median of $t$ submissions:

$$R_{\mathrm{onchain}}(b) = \mathrm{median}\{R_1(b), R_2(b), ..., R_t(b)\}$$

The system consists of three architectural tiers:

• Layer AVS WASMI (off-chain, Rust, Cosmos-based, computes $R(b)$ from Ethereum data)
• EigenLayer AVS operators (off-chain, Node.js/Go, submit signed attestations powered by staked ETH with slashing)
• A Solidity ReliabilityRegistry contract (on-chain median aggregation and finality event emission)

This score is surfaced via a UI dashboard displaying $R_{\mathrm{onchain}}(b)$, total fast-exit value $W_b$, historical trends, and a recommended interest rate for liquidity providers, derived by

$$r(R(b)) = r_{\min} + (r_{\max} - r_{\min}) \, \exp(-\beta R(b))$$

with typical parameters $r_{\min}=1\%$, $r_{\max}=3\%$.

3. Block Failure Resilient Codes

Repairable Block Failure Resilient (BFR) codes structure data encoding and recovery around block-level erasure and repair (Calis et al., 2014). The system model partitions $n$ nodes into $b$ disjoint blocks, each of $c = n/b$ nodes. The primary parameters:

Parameter	Description
$b$	Number of blocks (failure domains)
$\rho$	Maximum blocks that can fail and still permit data recovery
$k$	Number of nodes the data collector (DC) contacts
$k_c$	Number of nodes per block ($k_c = k / (b - \rho)$)
$\alpha$	Symbols stored at each node

A $(n, b, \mathcal{M}, k, \rho, \alpha)$ BFR code supports:

• Data recovery from any $b_c = b - \rho$ blocks (reading $k_c$ per block)
• Node repair within failed blocks via minimal cross-block bandwidth

The file size is upper-bounded by a flow-cut bound:

$$\mathcal{M} \leq \sum_{\ell=0}^{b-1} \sum_{i=0}^{k_c-1} \min(\alpha, (d - \ell k_c - i)\beta)$$

Two extremal points are derived:

• BFR-MSR (Minimum Storage Regeneration):

$$\alpha_{\mathrm{MSR}} = \frac{\mathcal{M}}{k},\quad \gamma_{\mathrm{MSR}} = \frac{\mathcal{M} d}{k d - \frac{k^2}{b_c}(b_c-1)}$$

• BFR-MBR (Minimum Bandwidth Regeneration):

$$\alpha_{\mathrm{MBR}} = \gamma_{\mathrm{MBR}} = \frac{2 \mathcal{M} d}{2 k d - \frac{k^2}{b_c}(b_c-1)}$$

Explicit constructions leverage projective plane block designs for $b\ge3$, ensuring symmetric recovery and repair locality.

Within the Reliablocks design paradigm, BFR codes serve as the erasure-and-repair backbone. Block-aware local codes may be layered for intra-block repairs, and repair scheduling becomes policy-driven at the block level.

4. Formal Block Reliability Algebra and Verification

To reason formally about reliability for systems with block-based redundancy, a higher-order logic (HOL) algebra is devised for Dynamic Reliability Block Diagrams (DRBDs) (Elderhalli et al., 2019). The algebra introduces structure functions and reliability operators:

• Series (AND):

$R_{\mathrm{AND}}\ X\ Y = \min(X, Y)$

$R_{\mathrm{series}}(t) = \prod_{i=1}^n R_i(t)$

• Parallel (OR):

$R_{\mathrm{OR}}\ X\ Y = \max(X, Y)$

$$R_{\mathrm{parallel}}(t) = 1 - \prod_{i=1}^n [1 - R_i(t)]$$

• Spare constructs (e.g., for redundant spares, warm/cold/hot):

Warm spare:

$$R_{\mathrm{spare}}(t) = 1 - \int_{0}^{t}f_Y(y)F_{X_d}(y)dy - \int_{0}^t\!\int_{y}^t f_{X_a|Y=y}(x)dx f_Y(y)dy$$

Cold spare:

$$R_{\mathrm{cold}}(t) = 1 - \int_{0}^t\int_{y}^t f_{X_a|Y=y}(x)dx f_Y(y)dy$$

Hot spare:

$R_{\mathrm{hot}}(t) = 1 - (1 - R_Y(t))(1 - R_X(t))$

Main algebraic simplification laws (all formally verified in HOL4) include commutativity, associativity, distributivity, absorption, and case analyses on extended-real inequalities.

The approach enables entire system-level DRBDs—including spare, series, parallel, and nested constructs—to be automatically symbolically verified and reliability expressions mechanically derived.

5. Architectural Implementations

The Reliablocks on-chain system (Das et al., 8 Nov 2025) is architected along modular, economically secured lines:

• Off-chain compute:
  • WASMI module (Rust, Cosmos chain) and AVS operator Daemons (Node.js/Go), polling Ethereum block data, parsing fast-exit logs, and executing the reliability formula.
  • Each attestor signs the computed $R(b)$ and pushes it to the on-chain registry.
• On-chain aggregation:
  • The Solidity ReliabilityRegistry ensures only authorized (EigenLayer staked) submissions are counted.
  • Final score is the median of attested $R_j(b)$, and slashing is enabled for inconsistent submissions.
  • Gas usage per finalized block is kept under 200k, dominated by ECDSA checks and median computation.
• UI and utilization:
  • Dashboard surfaces $R(b)$ for each block, along with historical reliability, number of attestations, and economic parameters.
  • The interest rate formula enables immediate deployment in fast-exit markets, bridges, and lending.

For BFR codes (Calis et al., 2014), explicit constructions rely on combinatorial block designs (projective planes) or scalar “transpose” codes for $b=2$. The formal DRBD analysis (Elderhalli et al., 2019) is realized wholly within the HOL4 proof assistant, with less than 30 simplification lemmas required for generic reliability analysis.

6. Applications and Broader Implications

Reliablocks methodology supports:

• Automated risk quantification: Cross-chain bridges, exchanges, and fast-exit markets dynamically adjust confirmation requirements, fees, or interest rates based on the current $R(b)$.
• Lending and insurance: Protocols can denominate premiums, collateral, or rates directly in terms of block reliability, rather than opaque challenge windows.
• Provable system reliability: Distributed storage systems with block-aware erasure codes and DRBD-based reliability modeling achieve predictable protection under correlated failures.

A plausible implication is that the formalization of reliability at the block level creates a unifying substrate for both decentralized finance protocols (via on-chain scores and economic incentives) and data storage architectures (via BFR codes and DRBD algebras), aligning reliability optimization across seemingly disparate domains.

7. Cross-Disciplinary Synthesis

Reliablocks bridges operational, mathematical, and cryptoeconomic notions of reliability. On-chain scoring (Das et al., 8 Nov 2025) introduces real-time, economically meaningful reliability indices for smart contract platforms. BFR codes (Calis et al., 2014) provide a resilient coding framework for correlated failure domains, while dynamic DRBD algebra (Elderhalli et al., 2019) offers formal symbolic guarantees via theorem proving. The convergence of these threads defines Reliablocks as both a technical discipline and a suite of deployable mechanisms for next-generation reliable systems.