Pi Squared Docs

Welcome to the Pi Squared Docs. This is your starting point to explore FastSet, the new settlement protocol built for the scale of AI, digital assets, and decentralized applications.

What is Pi Squared?

Pi Squared (Pi²) is building FastSet, a next-generation verifiable settlement protocol designed to power high-frequency, high-scale applications without the overhead of blockchains.

FastSet combines cryptographic trust with real-time performance, allowing millions of claims to be processed in parallel, without requiring global ordering or consensus.

From decentralized payments and verifiable computation to AI-native value flows, FastSet offers a fast, flexible, and verifiable foundation for modern decentralized systems.

Want to test FastSet in action? Head to our Developer Docs for a complete wallet implementation guide.

Our Mission

At Pi Squared, our mission is to unlock a new era of verifiable, speed, and decentralized infrastructure, without the bottlenecks of traditional blockchains.

FastSet enables this by rethinking settlement from the ground up:

Massively Parallel

In traditional blockchains, every transaction must be added to a single global ledger in a fixed order, which means all validators must agree on the same sequence before anything is considered final. This is slow and inherently sequential.

FastSet breaks this bottleneck by eliminating total order. Instead of trying to globally coordinate every claim, FastSet assumes most claims are weakly independent—that is, they don’t conflict and can be processed in any order.

Because of this, validators don’t need to communicate with each other or reach consensus. Each one processes incoming claims locally and concurrently, settling them as soon as they’ve been validated. This architecture enables massive parallelism, allowing FastSet to scale naturally with application demand.

Verifiability

Removing global coordination doesn’t mean sacrificing trust. In FastSet, every settled claim is backed by a cryptographic certificate, which is a compact proof that a quorum of validators has independently verified the claim.

This means:

• Validators don’t need to reach consensus or sync state.

• Clients and third parties can trust the result of a claim without having to trust any single validator.

• Every update to state is provable and auditable using digital signatures and well-defined validation rules.

The result is a system that maintains the security guarantees of decentralized networks, but with none of the consensus overhead.

Ecosystem-Agnostic

Most blockchain platforms lock developers into ecosystem-specific languages (e.g., Solidity for Ethereum, Move for Aptos) or VMs. If you want to prove computation or settle claims across ecosystems, you're forced to rewrite logic from scratch.

FastSet changes that.

Thanks to our K Framework and Proof of Proof technology, developers can write application logic in any language be it, Python, Rust, C++, JavaScript, Go, etc. and generate formal proofs of execution without having to adapt to a new VM or contract platform.

This opens the door to:

• Reusing code you already trust.

• Writing smarter, safer applications in languages you’re familiar with.

• Interoperating across chains and systems without being locked in.

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.

FastSet

FastSet is our decentralized settlement protocol that achieves real-time performance without consensus overhead. It is inspired by blockchains but designed to avoid global bottlenecks by settling claims in parallel.

Each claim represents a verifiable intent like a payment, a proof, or a computation result and is independently validated by a quorum of nodes. No total ordering, no mining, and no coordination rounds required.

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.

Together, these technologies enable high-throughput, provable, and programmable infrastructure that works across chains, ecosystems, and execution environments.

Next Steps

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

FastSet

K Framework

Proof of Proof