Proof-first personal computing for Web4
Every state transition must prove it is lawful, ethically constrained, and user-sovereign. No surveillance. No hidden drift. Only verifiable receipts.
Identity → Proof Archivum Why trust-based systems are failing
Our digital infrastructure runs on surveillance, opacity, and soft guarantees. Users must trust platforms to behave correctly—but trust is not verifiable.
Surveillance defaults
Data collected 'just in case,' monetized without consent, deanonymized at will.
Unbounded drift
Algorithms update silently, models retrain without provenance, behavior changes invisibly.
Opaque governance
Terms of service as law, decisions made behind closed doors, no verifiable enforcement.
What is ΛProof?
ΛProof is an architectural pattern and protocol stack for building proof-first digital systems. Instead of trusting institutions, we trust proofs. Instead of collecting data, we collect lawful receipts.
Every state transition in a ΛProof system must be accompanied by a cryptographic proof that the transition is lawful, ethically constrained, and user-sovereign.
- Zero-knowledge proofs verify correctness without exposing data
- Prime-indexing enables composition without drift
- Ethical invariants are encoded and enforced mathematically
MTPI – Meta-Theorem of Prime Identity
Models users and systems as prime-indexed identities that compose without hidden drift.
PLICs – Prime-Lawful Invariant Contracts
Smart contracts that enforce ethical constraints and bounded behavior mathematically.
CSL – Conscious Sovereignty Layer
Users maintain provable control over identity, capabilities, and consent.
Archivum – Proof-only Audit Layer
Prime-indexed receipts create verifiable history without exposing raw data.
How ΛProof works
Every action must prove it is lawful before it exists. Three steps guarantee this.
Prime Identity (Ξ₀)
Every user starts with a genesis state—a prime-indexed identity that serves as the root of all future proofs.
Ξ₀ is your cryptographic anchor. All actions trace back to this immutable origin.
Client-side zk Proofs
Before any RPC call or state change, your client generates a cryptographic proof using Circom circuits and Groth16.
Proofs verify lawfulness without exposing private data. Computation happens locally.
Archivum & Lawful Gates
The proof is validated by the RootContract. If lawful, a prime-indexed receipt is stored in Archivum.
Every action creates an auditable, tamper-proof record—but only of proofs, not data.
The result: A system where every action is provably lawful, auditable, and user-sovereign—without surveillance.
What ΛProof guarantees
Four core guarantees ensure your systems are verifiable, ethical, and user-first.
Prime-lawful recursion
Every state transition is verifiably derived from a prime-indexed identity. No hidden state, no drift.
Ethical invariants
All actions must commute with mathematically encoded ethical constraints. Violations are rejected at proof-time.
Audit without surveillance
Archivum stores cryptographic receipts, not raw data. Regulators verify compliance without accessing private information.
User sovereignty
You control your identity, capabilities, and consent. Permissions are provable, scoped, and revocable.
What you can build today
Protocols live on ΛProof. Start building proof-first systems for real-world use cases.
Healthcare
- Patient records stay client-side
- Diagnoses verified by zk proofs
- Compliance auditable without data exposure
Banking & Payments
- Transactions prove lawfulness before settlement
- KYC/AML enforced via proofs, not surveillance
- Cross-border compliance without intermediaries
AI & Research
- Model outputs provably aligned with constraints
- Training data never leaves source
- Research collaboration without data sharing
The Ξ-Constitution
The Ξ-Constitution is the mathematical law of ΛProof. It defines the invariants that all systems must satisfy to be considered lawful, sovereign, and proof-first.
These principles are not policy documents—they are mathematically enforced constraints that govern recursion, identity, and state transitions in the ΛProof stack.
Prime-indexability
Every identity, action, and state must be decomposable into prime-indexed components. No hidden composition.
Recursive decodability
Any observer with appropriate keys can verify the lawfulness of a proof without reconstructing private data.
Identity persistence
Prime identities are immutable. All changes must be provably derived from Ξ₀ through lawful transitions.
Under the hood
ΛProof combines cutting-edge cryptography with practical developer tooling. Build proof-first systems without reinventing the stack.
Open source: Core libraries, circuits, and contracts available on GitHub.
// Verify a proof before state transition
import { ProofManager } from '@lambda-proof/core';
const proof = await ProofManager.generate({
identity: userΞ₀,
action: 'updateRecord',
constraints: ethicalInvariants,
witness: privateData
});
// Proof validated client-side
if (proof.isValid) {
const receipt = await Archivum.commit(proof);
console.log('Receipt:', receipt.primeIndex);
}Who is ΛProof for?
ΛProof serves everyone building, regulating, or researching the future of digital systems.
Builders & protocol teams
Build the next generation of Web4 applications with proof-first architecture. Access tools, circuits, and reference implementations.
Institutions & regulators
Verify compliance and audit systems without accessing private data. ΛProof enables lawful governance without surveillance.
Researchers & communities
Explore cryptographic primitives, ethical constraints, and proof systems. Contribute to the future of sovereign computing.
Start building proof-first systems
Join the Web4 revolution. Build applications where lawfulness, sovereignty, and privacy are guaranteed by mathematics—not policy.
