What is USL?

The Pi Squared Universal Settlement Layer

Pi Squared aims to enable the next generation of verifiable computing. This next era of computing will be both universal and scalable while maintaining an optimally minimal trust base. We are developing Pi Squared’s Universal Settlement Layer (USL) to realize this. USL is a modular blockchain architecture that not only facilitates Pi Squared but also promotes ​Universality, Trust Base, and Application Interoperability .

USL provides end-to-end correctness guarantees for generic computations, adhering to a blockchain system's typical constraints and minimizing the trust base. As a result, USL encourages the adoption of verifiable computing as the standard paradigm for distributed computing. This is achieved without requiring domain-specific languages (DSLs) or execution environments, all while being efficient and scalable.


USL supports all kinds of computations conducted off-chain, typically occurring at layers above it. Regardless of their complexity, these computations are versatile and adaptable to execute in any chosen language or virtual machine (VM) without necessitating compilers or language-specific VMs.

The computations can be expressed in any language or VM as long as formal semantics exists in K for that particular language or VM. This will ensure their correctness and trustworthiness.

You can learn more about K here.

USL is agnostic to computation methods, which allows upper layers to implement optimizations and utilize their preferred architectures. There are no restrictions on how computations are performed, as this falls outside the scope of USL's concerns.

For more information on USL limitations, refer to USL Limitations.

Trust Base

USL exposes any trust assumptions made by computations transparent for end-user awareness and trust base minimization. This is achieved primarily through correctness proofs. The trust base of USL is optimally minimal, consisting of only two components: the system’s formal semantics, where the computation is performed, and the Matching Logic proof checker circuit. These two components are rigorously vetted, both battle-tested and formally verified.

USL's network is permissionless, so nodes can join and leave without needing permission from a central authority or a designated committee. Finally, untrusted nodes choose to join the pool of provers to contribute to generating proofs of transaction blocks.


Computations processed by USL are mathematically proven correct before being accepted as valid. Based on underlying theories in K, these correctness proofs are generated using Matching Logic for each calculation. The proof is then transformed into a succinct zero-knowledge proof (ZKP), which attests to the existence of the mathematical proof. This approach allows USL to reduce the trust base needed to approve the state change caused by the computation.

USL also allows external entities to verify its state independently. This transparent method ensures users can use USL confidently, knowing that the integrity of the computation is maintained through strict mathematical computation.

Determinism and Reproducibility

The validation performed by USL is deterministic, as it is determined by a state transition function. The input state and incoming transaction (or claim) provide this function's inputs. The validation is reproducible and can be independently verified by any external entity that correctly implements USL’s state transition function.

Application Interoperability

USL supports validating cross-chain communication with minimal trust requirements. This cross-communication can include token bridging, atomic cross-chain swaps and transfers, cross-chain aggregator services, and oracles. Applications that integrate with USL automatically benefit from its security and validation services. Additionally, USL promotes interoperability between upper-layer application modules and networks, such as AppChains.

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