Make the claim precise
Define the computation, its assumptions, and what success would mean. A useful theory tells us what to check.
The ternary research lab
Ternary computation.
From theory to practice.
Urizen is a research lab dedicated to ternary computation and its applications. We work from mathematical foundations to computer architecture, learning, and private, verifiable systems.
Research and products in development. Explore the current scope and public demos below.
A few questions in the margins
- What can three states make possible?
- Can learning shape the program itself?
- What can we actually verify?
01 · Lab philosophy
Theory guides the work.
Evidence changes it.
We study ternary computation across learning, execution, and verification. Intuition suggests a direction; mathematical arguments, decisive experiments, and working software test it.
Make room to be surprised.
Run a decisive test
When the answer is unknown, choose an experiment that can change the next decision. Keep the result and its conditions together.
Let the result change the work
Interpret the evidence, revise the theory or implementation, and repeat. A proof, a passing test, and a product release answer different questions.
Three states. A world of questions.
Let intuition imagine. Let reason build.
Research and development
Ternary foundations.
New ways to compute.
We investigate the mathematics, machines, and learning methods together. PaleFox develops the architecture; SandCat focuses on software inference; Structural Descent studies how executable programs learn.
PaleFox
A programmable ternary computer architecture. The work connects formal machine semantics, finite-cell computation, and hardware implementation.
Defined semantic results are Proved; selected hardware subsets are Implemented + Verified finite + Synthesized. Complete-system FPGA and ASIC execution remain Open.
Hardware research scopeSandCat
A ternary inference engine project for loading and running packed ternary models. Its software focus complements PaleFox’s processor architecture.
Specified. The implementation plan targets Apple Silicon first, then NVIDIA CUDA. Engine implementation has not started; performance and model qualification remain Open.
Inference engine scopeStructural Descent
Learning directly in executable structure. We study local changes to models and programs under explicit objectives, alongside contextual programming and inference.
Defined local-search results are Proved and machine-checked; experiments retain their own finite scope. General runtime refinement and broader model-quality claims remain Open.
Learning research scopeTiamat
Research into coordination around execution receipts: how verified work could support settlement, agent micropayments, and compute credits.
Conjectural / Open. Current evidence comes from deterministic simulations. Consensus security and monetary safety remain open research questions.
Coordination research scope02 · Products
Put the foundations to work.
Nibiru brings ternary execution to private computation. Alongside it, we develop the tools for accountable applications: agent governance, execution, credentials, and evidence routing.
Confidential computation
Nibiru Engine
Run a committed program on encrypted data and check a receipt for its execution.
Explore Nibiru Agent governanceBaobab
Give agent work explicit goals, permissions, budgets, and rules for accepting a result.
Explore Baobab Agent execution and reviewAnansi
Connect a proposed action or code change to its authority, execution evidence, and review.
Explore Anansi Eligibility and credentialsHeimdall
Check a defined eligibility or agent mandate statement while limiting what is disclosed.
Explore Heimdall Model and agent orchestrationEsu
Identify agents within an organization and route signed evidence between tasks.
Explore EsuFrom the research: PaleFox hardware, SandCat inference, and Structural Descent learning.
03 · Nibiru Engine
Keep the inputs private.
Make the execution checkable.
Nibiru connects ternary programs to computation on encrypted data and receipts for a declared execution. We are developing it for compact private decisions and confidential inference, so an operator can compute without reading the inputs.
Compute on encrypted data
Fully homomorphic encryption lets the operator compute on ciphertext. The selected execution profile defines which inputs, state, and program material remain private.
Check the committed execution
A zero-knowledge receipt proves the declared semantic transition over commitments. Its statement defines what a verifier can conclude.
Share the proof work
Multiparty computation supports witness generation when different parties hold private inputs. Each supported mode carries its own assumptions.
Current scope: Implemented + Verified finite for recorded encrypted-execution and receipt profiles. Core bounded-computation theorems are machine-checked in Lean 4. Broader scale, cryptographic binding, and production qualification remain Open.
04 · Agent systems
Baobab
Governed context and controlGive agent work a contract.
Baobab separates what an agent can consider from what it may do. A declared workflow binds the goal, required checks, permitted tools, retry budget, and verifier that can accept progress.
Its SDK records accepted, rejected, and unresolved outcomes, and supports exact continuation and context reduction within defined profiles. When an external action has an uncertain result, that uncertainty remains in the record.
Implemented + Verified finite for recorded serial SDK profiles. The checks establish conformance to a declared policy and verifier. Independent release qualification and control of tools outside those profiles remain Open.
Agent execution and review
Anansi
Evidence for the actionReview what the agent did, and why it was allowed.
Anansi is our code validation and governed execution environment. It brings the proposed change, intent, permissions, required checks, execution evidence, and review decision into one verifiable change case.
Baobab supplies the governance and review rules; Anansi supplies source witnesses, sandbox execution, and records of external actions. Private execution and credential components join through explicit contracts, each with its own verifier.
Implemented + Verified finite for recorded review and execution flows. Recent local private-action tests cover proof admission and recovery after interruption; identity and planning in that campaign use test doubles. Complete integration and independent release qualification remain Open.
Eligibility and credentials
Heimdall
Disclose the required statementCheck eligibility without collecting every underlying detail.
Heimdall develops privacy-preserving credential workflows for people and agents. Its customer-eligibility prototype evaluates encrypted signals against a defined policy. Know-Your-Agent credentials bind an agent presentation to a specified mandate and session.
The verifier checks a particular statement. That statement, the issuer, and the disclosure policy determine what the result means.
Implemented + Verified finite for the standalone package and recorded credential profiles. Regulated KYC sufficiency, revocation, unlinkability, and proof of an agent’s conduct within policy remain Open.
Model and agent orchestration
Esu
Identity and evidence between tasksConnect the work without losing who it belongs to.
Esu is our orchestration track for models and agents. It assigns organization-scoped agent identities from verified Heimdall presentations and routes signed evidence between tasks.
Identity, routing, and authority stay distinct: a signature identifies a registered key; the receiving workflow still checks whether the evidence supports its decision.
The identity core is Implemented + Verified finite. A complete standalone orchestration package remains Open.
05 · Evidence
A claim should come with a way to examine it.
A theorem concerns a mathematical statement. A test concerns the cases it ran. A working prototype concerns a particular implementation. We keep those distinctions visible as the systems develop.
Explore a private run
Nibiru viewer
A guided simulation introduces the flow. A separate retained record exposes the public commitments and receipt of a recorded run.
Open the viewer Explore an agent workflowAnansi demo
Try the proposal simulation, then inspect a declared session specimen, a retained code-review case, and the component status ledger.
Open the demo Understand the limitsRead the current scope
Find the product notes and the meaning of our evidence labels. Contact the lab for a technical discussion of your workload.
Read the documentationThe browser demos are explanatory interfaces and retained exports. They do not run live encrypted workloads or grant an agent authority.
Bring a problem worth making precise.
A ternary workload. A learning problem. A computation that needs privacy.
Tell us what you want to compute, the constraints that matter, and how you would judge the result. Let’s explore what ternary computation can make possible.