Pi Squared Docs

Welcome to the Pi Squared Docs. On this page, we provide a soft landing for you to understand who we are, our products, and technologies.

What is Pi Squared?

In one sentence, Pi Squared (Pi2) is a verifiability-first platform that unites all languages, apps, and ecosystems through fast, verifiable, and cross-chain computation & settlement.

Whether you're building AI agents, DeFi protocols, or distributed apps, Pi Squared gives you the cryptographic backbone to execute and verify anything, across any chain, in any language, without relying on centralized intermediaries or unprovable logic.

You can think of Pi Squared as the "verifiability stack" that lets Web3 work the way Web2 developers expect software to work — fast, interoperable, and reliable — but with trust baked in.

Our Mission

At Pi Squared, we aim to bring verifiability, correctness, and performance to Web3 via our infrastructure, technologies, and products.

Verifiability

Today's Web3 world is suffering from the fragmentation of users and liquidity. That fragmentation has caused inefficiencies in this ecosystem and has resulted in poor user experience, incompatible technologies, innovation stagnation, and growth limitations.

At Pi Squared, we see verifiability as a promising solution to the issue of fragmentation in Web3. Computation and information are produced and verified once and become usable everywhere.

Pi Squared's Verifiable Settlement Layer (VSL) brings scalable, affordable, and customizable verifiability to all Web3 protocols, applications, and users, enabling them to freely communicate with each other at minimal costs.

Correctness

As Web3 applications and developers embrace more programming languages, virtual machines (VMs), and instruction set architectures (ISAs), the need for higher-level safety and correctness also arises.

Pi Squared responds to that increasing need via a semantics-based approach that consists of two cornerstones: the K framework and Proof of Proof. They bring the highest level of safety and correctness guarantees to all programming languages, VMs, and ISAs.

Compilers and interpreters are automatically derived from their formal mathematical definitions, and all execution traces are justified by formal mathematical proofs.

We allow no compromise at Pi Squared when it comes to safety and correctness!

Performance

In Web3, a perfect, slow solution is as good as a totally useless solution.

At Pi Squared, we view performance as a lifeline, and we put performance as top priority. We work on optimizations at all levels, from system-wise and methodological architecture designs to code and circuits fine tuning.

The Verifiable Settlement Layer (VSL) is powered by a novel generic consensus protocol that settles payments and transactions at a speed that no blockchain can compete.

The K framework incorporates decade-long engineering innovations in its core pattern matching algorithms that brings the speed of auto-derived execution tools to the same level as hand-written execution tools. Proof of Proof adopts a two-phase proof generation process that enables mathematical-level shortcuts and optimizations in addition to the great advancements in the zero-knowledge (ZK) area.

At Pi Squared, no feature is achieved by sacrificing performance.

Why the name "Pi Squared"?

Pi Squared means Proof of Proof, which stands for zero-knowledge proof of mathematical proof. It is one of our earliest, signature, and unique technologies.

Our Technologies

We pursue our missions by delivering three technologies.

Verifiable Settlement Layer (VSL)

This is our infrastructure-level decentralized network that offers scalable, affordable, and customizable verifiability to all Web3 protocols, applications, and users.

Exchange of assets, value, data, information, and services among various participants is connected via VSL claims, which encode anything verifiable or provable.

VSL claims are submitted to a set of homogeneous and permissionless VSL validators for validation, after which they are settled on the VSL network for good.

VSL allows fast, simple, and secure access to the settled claims on all ecosystems, platforms, and blockchains.

K Framework

This is our open-source semantics-based framework for formalizing programming languages using their rigorous mathematical definitions, from which fast and correct-by-construction execution tools can be automatically derived, eliminating the need to trust the correctness of any interpreters, compilers, or transpilers.

Proof of Proof

This is our signature technology for verifiable computing for all programming languages, virtual machines, and instruction set architectures, bringing mathematical, cryptographic, and/or zero-knowledge (ZK) safety and correctness to Web3 applications.

These technologies bring verifiability, correctness, and performance to Web3.

Next Steps

What are you waiting for? Don't let us tell you all about it. Explore our docs and see for yourself!

Verifiable Settlement Layer

K Framework

Proof of Proof