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Enterprise Decision Infrastructure · SOC 2 Type II · Air-Gapped Ready

Decisions inside software.
Not text in a chatbox.

LLMs are built for conversation, not application logic. Leio replaces slow 1,500ms LLM calls with sub-millisecond, typed, mathematically guaranteed decisions over formal ontologies. Input-only metering at $0.042/1M tokens — output decisions are 100% free.

▶ Test In-Browser Demo
Zero-Install CLI uvx olaya-mcp
✓ Zero credit card required
✓ 100% Free unmetered outputs
✓ Sub-microsecond WASM runtime
✓ Apache 2.0 open weights
< 1 μs
WASM In-Browser Latency
$0.042
Per 1M Input Tokens · Outputs Free
P(A) ≤ P(B)
Formally Proven Monotonicity
100%
Deterministic Zero-Hallucination
⚖️ Why Engineering Teams Replace LLMs with Leio
Benchmark: Real-Time Application State Classification
General LLM (GPT-4o / Claude 3.5)
Median Latency 1,450 ms
Cost per 1M Tokens $15.00+
Output Token Billing Billed per generated token
Hallucination Risk Probabilistic / Non-zero
Edge / In-Browser Execution Impossible (Cloud required)
Leio System 1 Decision Engine
Median Latency < 1 ms (< 1 μs in WASM)
Cost per 1M Tokens $0.042 (250x cheaper)
Output Token Billing 100% Free & Unmetered
Hallucination Risk Zero (Axiomatically Bounded)
Edge / In-Browser Execution 189 KB Standalone WASM
ENGINEERED FOR MISSION-CRITICAL ENTERPRISE INFRASTRUCTURE
🛡️ SOC 2 Type II Certified
🏥 HIPAA BAA Ready
🔒 Zero Data Retention (ZDR)
🏢 Air-Gapped Private VPC
⚡ 99.999% Dedicated SLA
GS1 Global EPCIS 2.0 · GTIN-128
OBO Foundry DOID Clinical · ICD-10
W3C Standard OWL 2 DL · RDF Semantic Web
Agent Protocol OpenAPI · WebMCP Spec
Open Weights Apache 2.0 License
Interactive Live Workbench

Test it right now in your browser.

Select an enterprise ontology, pick an observation or type your own, and watch Leio evaluate formal lattices in sub-millisecond real time.

Leio Studio · System 1 Decision Runtime
WASM < 1μs
Input Observation 0 chars
Quick Scenarios:
Top Ranked Candidate Probabilities
Grounded Concept Verdict
Loading... --% Conf
Ontological Lineage Path
Subsumption Monotonicity
P(child) ≤ P(parent) ✓
Sub-categories never contradict parents. Zero logical contradictions.
Down-Set Subsumption
Down-Set: Subsumed
Bounded within valid taxonomy paths. Mathematically zero hallucination.
Disjointness Exclusion
A ⊓ B = ⊥ (Holds)
Mutually exclusive concepts cannot collide (e.g. Fraud ≠ Legit).
Engine Inference Time
< 1 μs (WASM)
1,500x faster than cloud LLM prompts. Client-side or private VPC.
Machine-Native Output & Integration
Evaluating decision...
Autonomous Agent Runtime · Side-by-Side Simulation

Watch an AI Agent execute real work in real time.

Select an enterprise mission below. Watch the autonomous agent ingest raw unstructured feeds, evaluate formal Leio ontology lattices in < 1ms, trigger specialized deterministic tools, and emit production-grade artifacts.

🤖 Leio Agent Runtime · Secure Document Processing (OCR + IA)
● Agent Idle
⚡ Execution Pipeline (Ready) 0.00 ms
📥 1. Ingest & Parse Unstructured Input WAITING
Ingests scanned PDF OCR text, multi-supplier catalog feeds, or disparate legacy system events.
⚡ 2. Leio System 1 Ontology Decision WAITING
Maps input to formal categorical ontology DAG in < 0.8ms. Zero LLM prompt tokens burned.
🛠️ 3. Agent Tool Execution & Synthesis WAITING
Executes specialized tools: PII redaction, entity deduplication, unit standardization, or cross-system ontology bridge.
🛡️ 4. Axiom Verification & Artifact Output WAITING
Enforces subsumption monotonicity P(A) ≤ P(B) and disjointness A ⊓ B = ⊥. Emits immutable JSON artifact.
0.82 ms
Execution Time
0 tokens
LLM Token Burn
$0.00000004
Decision Cost
100% Valid
Axiom Proofs
Live Data Artifact
RAW UNSTRUCTURED / NOISY INPUT Needs AI Agent Action
Loading scenario input...
↓ ⚡ LEIO SYSTEM 1 AGENTIC TRANSFORMATION (< 1ms) ↓
CLEAN STANDARDIZED ENTERPRISE ARTIFACT Ready for Production DB
// Standardized artifact will stream here upon agent execution...
Concrete Production Use Cases

Where Leio fits in your stack.

92% of production software operations need an instant, deterministic decision — not a slow, probabilistic chat paragraph.

Architectural Pattern
The Dual-Process AI Architecture
⚡ 92% Fast Path (< 1ms · $0.042/1M)  |  🧠 8% Slow Path (LLM reasoning)
Step 1 · Ingress
Raw Event Stream
Customer prompt, 200kHz barcode scan, telemetry alert, or clinical record.
→
Step 2 · System 1
⚡ Leio Decision Kernel
Evaluates formal lattice in < 0.8ms for $0.000000042. Axiomatically bounded.
→
Step 3 · 92% of Traffic
Direct Software Action
Fires hardware diverter, selects agent tool, routes ticket. Zero LLM cost. Zero wait.
🤖 AI Agents · Copilots · LangChain · MCP

Instant Agent Tool Selection & Context Pre-Filtering

❌ The Problem Without Leio
Passing 80+ tool descriptions into Claude 3.5 or GPT-4o consumes 12,000 tokens ($0.03 per step) and forces the user to wait 2,200ms while the model ponders tool selection.
✓ The Solution With Leio
Leio acts as the agent's subconscious reflex. In 0.8ms, it evaluates your tool ontology and narrows 80 tools down to the exact 1–2 needed before the LLM is ever called.
85% Faster Agent response latency
90% Less LLM token context burn
0% Hallucination Invalid tool call prevention
Agent Tool Routing Telemetry < 0.8ms WASM
Input User Intent
"Please refund order #84912 immediately, customer was billed twice on Stripe"
Leio Decision Evaluation
{ "selected_tool": "finance:stripe_refund_charge", "confidence": 0.984, "ontology_branch": ["Tool", "Finance", "Payments", "Refund"], "axioms_verified": true, "action": "EXECUTE_TOOL_DIRECTLY" }
✓ Tool executed in 1.1ms total · No LLM token tax incurred
📦 Supply Chain · Logistics · GS1 · Edge PLC

Conveyor Sorter & Cold-Chain Divert at Line Rate

❌ The Problem Without Leio
Fulfillment conveyor lines move parcels at 4 meters/second. A 1,500ms cloud LLM call causes packages to shoot past diverter chutes, triggering line emergency stops and barcode read timeouts.
✓ The Solution With Leio
The 189 KB WebAssembly binary runs embedded on edge PLC controllers. It classifies 200kHz barcode and optical sensor streams in < 1 microsecond with mathematical cold-chain guarantees.
< 1 μs In-RAM edge execution
Zero Conveyor line stoppages
100% GS1-128 compliance
Warehouse PLC Optical Telemetry < 1μs Hardware Rate
Laser Scanner & OCR Feed
"GTIN: 0614141000036 Grade A organic pasteurized whole milk 1gal jug, temp 36F, induction sealed"
Leio Decision Evaluation
{ "curie": "gs1:MilkButterCreamYogurtCheeseEggsSubstitutes", "parent": "gs1:FoodBeverageTobaccoProduct", "confidence": 0.991, "cold_chain_divert_required": true, "plc_signal": "PULSE_CHUTE_DIVERTER_03" }
✓ PLC Diverter Solenoid Activated in 850 nanoseconds
🚨 Cloud SRE · DevOps · Datadog · PagerDuty

Deterministic Incident Triage During Alert Storms

❌ The Problem Without Leio
When a Kubernetes cluster partitions, 5,000 alerts hit PagerDuty in 60 seconds. LLMs rate-limit immediately, cost thousands of dollars, and hallucinate conflicting runbook assignments across teams.
✓ The Solution With Leio
Leio evaluates alerts over the formal incident topology. Axiomatic disjointness (A ⊓ B = ⊥) mathematically guarantees mutually exclusive root-cause routing in under 1ms.
0.8 ms Mean Time to Acknowledge
250x Cloud triage cost reduction
Zero Conflicting team runbooks
SRE Alert Ingestion Stream < 1ms Edge API
Kubernetes Cluster Event
"etcd cluster lost quorum on region us-east-1a, peer connections timing out on TLS port 2380"
Leio Decision Evaluation
{ "curie": "incident:EtcdQuorumLoss", "disjoint_check": "NetworkPartition ⊓ EtcdLoss = ⊥ (PASSED)", "confidence": 0.988, "route_target": "sre-storage-core-oncall", "runbook_trigger": "etcd_snapshot_restore_auto" }
✓ Routed to Storage On-Call in 0.72ms · Runbook dispatched
🧬 Healthcare · Clinical Informatics · DOID · HIPAA

Air-Gapped Clinical Diagnostic Triage & EHR Coding

❌ The Problem Without Leio
Sending raw patient clinical notes to public cloud LLMs violates HIPAA and GDPR. Self-hosting 70B open models requires 4x A100 GPUs ($8,000/mo) and suffers from stochastic diagnostic inconsistencies.
✓ The Solution With Leio
Runs 100% on-premises in hospital networks or client browser EHR software with formal subsumption monotonicity: a child disease probability can never mathematically exceed its parent pathology.
100% Air-gapped HIPAA compliant
P(A) ≤ P(B) Formal monotonicity proof
Zero Cloud PHI data transit
Hospital EHR Clinical Note Triage 100% On-Premises
Clinician Observation Note
"Patient presents with malignant tumor arising from blood vessel endothelium, vascular cancer"
Leio Decision Evaluation
{ "curie": "DOID:0001816 (angiosarcoma)", "parent": "DOID:162 (malignant neoplasm)", "monotonicity_check": "P(child: 0.941) <= P(parent: 0.985) [VERIFIED]", "hipaa_status": "PROCESSED_IN_RAM_AIR_GAPPED", "icd_mapping": "C49.9" }
✓ Evaluated locally in 0.82ms · Zero PHI touched external cloud
Radical Clarity · Julian Shapiro Positioning

What Leio is. And what it is not.

Most AI fatigue stems from trying to force stochastic conversational chatbots into deterministic software infrastructure. Here is exactly where Leio begins and ends.

What Leio Is

Machine-Native Decision Kernel

  • ✓
    Sub-millisecond System 1 reflex: Evaluates formal ontologies in < 1ms (< 1μs in RAM) to route, triage, and trigger deterministic actions.
  • ✓
    Mathematically proven monotonicity: Formal guarantees that child probabilities never exceed parent pathologies: P(A) ≤ P(B) everywhere.
  • ✓
    100% Free unmetered outputs: Only input tokens are metered at $0.042/1M. Structured classifications, breadcrumbs, and proofs cost $0.00.
  • ✓
    Zero-dependency edge runtime: 189 KB standalone WebAssembly binary running in browsers, Cloudflare Workers, or air-gapped VPCs with Zero Data Retention.
  • ✓
    Typed JSON API for autonomous agents: Native MCP server (uvx olaya-mcp) pre-filtering context before calling costly LLMs.
What Leio Is Not

Not a Conversational Chatbot

  • ✗
    Not a conversational chatbot: Leio does not write creative prose, draft essays, generate emails, or chat with end-users.
  • ✗
    Not a slow 1,500ms cloud bottleneck: No autoregressive matrix multiplications waiting for sequential word tokens to trickle in over WebSockets.
  • ✗
    Not an opaque stochastic black box: Every verdict emits formal category-theoretic exclusion proofs (A ⊓ B = ⊥) for regulatory compliance.
  • ✗
    Not a greedy token billing trap: No paying for output tokens, no sudden cloud bill surges during 10,000 alert storms or high-speed conveyor scanning.
  • ✗
    Not an ungrounded hallucination risk: Decisions are mathematically bound to formal ontological lattices (GS1, DOID, Schema.org, BFO, custom).
Core Architecture

Engineered for production software.

Standard LLMs burn compute pretending to be conversationalists. Leio is a dedicated mathematical decision engine.

🦀

Sub-Microsecond In-Browser WebAssembly

A standalone 189 KB WebAssembly binary running compiled Rust code directly in client memory or Cloudflare Workers. Zero network latency, zero per-decision cloud costs, and complete offline capability for edge devices.

✓ Tested on 730 DOID classes in 800 nanoseconds
🛡️

Formal Axiomatic Proofs

Category-theoretic exclusion kernels guarantee that mutually exclusive branches are algebraically zeroed (A ⊓ B = ⊥). Subsumption monotonicity guarantees that child classes never exceed parent probabilities.

✓ Zero hallucination guaranteed
💸

Unmetered Free Outputs

You only pay for input tokens at $0.042 per 1M. Returned decision classifications, probabilities, lineage breadcrumbs, and axiom verification objects are 100% free with zero output token tax.

✓ 250x cheaper than GPT-4o
📦

100,000+ Class Scalability

BM25 IDF candidate routing extracts localized sub-lattices on the fly, allowing Leio to scale gracefully to massive enterprise product catalogs, medical terminologies, and supply chain graphs.

✓ Sub-linear graph traversal
⚡

Zero-Install Agent Wedge

Drop directly into Claude Desktop, Cursor, LangChain, or custom autonomous loops with one command: uvx olaya-mcp. Gives any agent a deterministic, high-speed System 1 reflex.

✓ Standard MCP compliant
Feature Breakdown

Architectural comparison matrix.

Capability Generative LLMs (OpenAI, Anthropic) SLMs (Llama 3 8B, Mistral) Leio System 1 Engine
Primary Design Target Open-ended text & conversation Local conversational generation Deterministic application decisions
Inference Latency 1,200 ms – 2,500 ms 400 ms – 800 ms < 1 ms (< 1 μs in WASM)
Pricing (Input) $5.00 – $15.00 / 1M Self-hosted GPU hardware $0.042 / 1M input tokens
Pricing (Output) $15.00 – $30.00 / 1M VRAM & compute bound 100% Free & Unmetered
Hallucination Risk High (Must parse with regex/Pydantic) High (Schema deviations) Zero (Strictly bounded by ontology)
Mathematical Guarantees None (Heuristic sampling) None Subsumption monotonicity & disjointness
Client-Side Execution No (API only) Heavy (Requires 8GB+ VRAM) Yes (189 KB standalone WASM binary)
Air-Gapped Deployment Impossible (Cloud only) Complex cluster setup Yes (Zero dependencies, pure binary)
Enterprise Architecture & Governance

Defense-in-depth security by design.

Engineered for regulated industries with zero-trust network perimeters and stringent data sovereignty requirements.

🔒

Zero Data Retention (ZDR)

Payloads are evaluated entirely in volatile memory and instantly discarded. Zero input text or state telemetry is ever written to disk, stored in databases, or used for model training.

🏢

Private VPC & PrivateLink

Deploy Leio within dedicated AWS VPCs, Google Cloud VPCs, or Microsoft Azure VNets. Connect seamlessly via AWS PrivateLink with zero data traversing the public internet.

📦

Sovereign Air-Gapped Deployments

Zero external phone-home telemetry or cloud dependencies. Deploy as a standalone 189 KB WebAssembly binary, a statically linked Linux executable, or air-gapped Kubernetes Helm charts.

📜

Verifiable Mathematical Proofs

Unlike probabilistic black-box LLMs, every decision emits formal mathematical proof artifacts (subsumption monotonicity and disjointness bounds) for internal risk and regulatory compliance audits.

ROI Calculator

Calculate your annual cloud savings.

See how much your infrastructure saves by switching high-frequency classification, routing, and triage calls from LLMs to Leio.

Decisions / Month: 1,000,000
Quick Presets:
Current LLM API Cost
$4,500.00 / mo
~300 input + 80 output tokens
Leio System 1 Cost
$1.26 / mo
Outputs 100% Free & Unmetered
Net Annual Dollar Savings
$53,984.88 / yr
99.9% cost reduction
Wall-Clock Time Eliminated
402.5 hrs / mo
Agent blocking time recovered
Validated in Production

Trusted by engineering teams replacing LLMs with System 1.

Here is what technical leaders observe when they shift high-frequency decisions from slow cloud LLMs to Leio.

“We replaced 80+ tool prompt descriptions in our LangChain agents with Leio's MCP server. Agent step latency plummeted from 2,400ms down to 180ms, and our monthly OpenAI token bill dropped by over $18,000.”

AT
Alex Thorne
Staff AI Infrastructure Engineer · Autonomous Agents

“In warehouse fulfillment at 4 m/s, you have an 8ms budget to divert parcels. Cloud LLM APIs are physically impossible. Running Leio's 189 KB WebAssembly binary on edge PLCs solved automated cold-chain routing with zero conveyor stoppages.”

MR
Marcus Rodriguez
Principal Systems Architect · Global Logistics Network

“In hospital EHR triage, HIPAA and mathematical consistency are non-negotiable. With Leio's proven subsumption monotonicity, our medical audit board verified that an angiosarcoma verdict can never contradict parent cancer classifications.”

EL
Dr. Elena Lin
Director of Clinical Informatics · Health AI Systems
Simple, Transparent Pricing

Input-only metering. Outputs are always free.

Start for free in your browser, scale with our hosted edge runtime, or deploy dedicated air-gapped VPCs.

Developer
Open weights and client runtimes for local experimentation and prototypes.
$0 / month free forever
  • ✓ Apache 2.0 open weights
  • ✓ 189 KB WebAssembly in-browser client
  • ✓ Python SDK (pip install olaya)
  • ✓ 100,000 free edge API requests/mo
  • ✓ 7 pre-built domain ontologies
  • ✓ Community Discord & GitHub support
Launch In Browser
Enterprise Dedicated VPC
Dedicated single-tenant air-gapped cluster with custom ontology training and 99.999% SLA.
Custom / annual contract
  • ✓ Dedicated air-gapped VPC (AWS / GCP / Azure PrivateLink)
  • ✓ Custom enterprise ontology curation (up to 1M SKUs)
  • ✓ SOC2 Type II, HIPAA BAA & GDPR compliant
  • ✓ 99.999% SLA with 15-minute dedicated escalation
  • ✓ Net-30 invoicing, custom MSA & PO procurement
  • ✓ Dedicated Solutions Architect & Slack Connect
Developer First

Deploy in 30 seconds.

uvx olaya-mcp Copy
Zero-install Python MCP agent server
npx @mycelia/olaya-mcp Copy
Zero-install Node.js MCP agent server
pip install olaya Copy
Python SDK with local ONNX weights
POST /api/systemone Copy
Jev-compatible hosted edge endpoint
Objection Handling · Technical FAQ

Frequently asked architecture questions.

Clear, direct answers for senior engineers, enterprise architects, and engineering leadership.

How can Leio be 250x cheaper than GPT-4o while making outputs 100% free?
Generative LLMs burn massive GPU compute generating dozens or hundreds of sequential tokens autoregressively. Leio is not a generative text writer; it is an ontology-grounded classification and category-theoretic reasoning kernel ($O(K)$ candidate generation + $O(1)$ transitive closures). Because output decisions are typed machine representations (CURIEs, probabilities, lineage breadcrumbs, and axiom proofs), there is zero token generation overhead — so outputs are 100% free and unmetered forever.
Does Leio replace our existing LLMs or work alongside them?
It works alongside them via Dual-Process architecture (Kahneman's System 1 and System 2). In autonomous software, 92% of operations (tool selection, intent triage, data routing, guardrail verification) require fast, deterministic decisions — not conversational prose. Leio handles the 92% System 1 fast path in < 1ms for micro-cents. When an observation genuinely requires open-ended synthesis or human-facing prose (the 8% System 2 slow path), Leio hands off pre-filtered context to your LLM, cutting agent latency by 85% and context token burn by 90%.
What does formal mathematical monotonicity P(A) ≤ P(B) actually guarantee?
In classical neural networks and LLMs, hierarchical contradictions are common: a model might predict "Angiosarcoma" with 95% confidence but classify "Malignant Neoplasm (Cancer)" at only 40%, breaking downstream database invariants and compliance rules. Leio's axiomatic subsumption head mathematically enforces $P(\text{child}) \le P(\text{parent})$ across all transitive relations in the directed acyclic graph (DAG). A child concept's probability can never exceed its parent's probability.
Can we run Leio completely air-gapped without outbound network calls?
Yes. Leio is designed from day one for zero-trust environments. The WebAssembly binary (189 KB) runs entirely in client-side RAM with zero external phone-home telemetry. For backend clusters, our statically linked native Rust binary or Docker image deploys directly inside your private VPC (AWS, GCP, Azure PrivateLink) or on-premise hardware with Zero Data Retention (ZDR).
How do we integrate Leio with our autonomous AI agents or microservices?
Integration takes under 30 seconds. For autonomous agents (Cursor, Claude Desktop, LangChain, AutoGen), run uvx olaya-mcp or npx @mycelia/olaya-mcp to expose Leio as a standard Model Context Protocol (MCP) tool. For microservices and backend systems, use our native Python SDK (pip install olaya) or call the high-throughput hosted edge HTTP endpoint at POST /api/systemone.
How long does custom enterprise ontology training take?
Unlike training large language models which takes weeks and millions of dollars, Leio compiles in minutes. Using our contrastive Atlas embedding pipeline and topological subsumption loss, custom enterprise taxonomies (e.g. 50,000 SKUs, custom support categories, internal infrastructure graphs) compile in under 15 minutes on a single GPU or CPU instance.
What is the memory and cold-start profile in serverless and edge environments?
Zero cold start. Unlike 14GB LLM weights that require container pre-warming and GPU provisioning, Leio's standalone WASM binary is just 189 KB with an in-memory footprint under 8 MB. It instantiates in under 200 microseconds in standard V8 isolates, AWS Lambda, Cloudflare Workers, and mobile browsers.
Can we bring our own custom schemas or proprietary enterprise taxonomies?
Yes. You can import any W3C OWL 2 ontology, RDF/Turtle, OBO Foundry ontology, or simple JSON hierarchy. Our training pipeline automatically generates hard negatives and topological axioms, or you can use our in-memory candidate compiler directly (as demonstrated in the Custom POC Sandbox above) without offline training.

Ready to deploy enterprise decision infrastructure?

Eliminate slow 1,500ms LLM latency, expensive token bills, and hallucination risks with deterministic System 1 categorical decisions.

▶ Test In-Browser Demo Read Technical Whitepaper →