S =
ΓA + ΓB
ΛA × ΛB

THE STABILITY EQUATION

Every collapse has a structure. Every structure has a threshold.

We build instruments for structural risk.

  • Deterministic engine: not what will happen, but what cannot survive.
  • Domain-agnostic: one equation, fifteen industry adapters.
  • Validated: 180,320+ simulation runs, reproduced canonical game theory.
  • EU-based. Production-grade. Pre-seed stage.

KAIROS

Deterministic Simulation Engine

Λ Lambda — Agency / Pressure

The force an entity exerts on a system. In finance, this is leverage. In AI, model capability. In geopolitics, military pressure. Lambda measures how hard an actor pushes against the boundaries of stability.

Γ Gamma — Buffer / Friction

The structural resistance that keeps systems intact. Capital reserves in banking, alignment constraints in AI, treaty frameworks in defense. Gamma is what stands between pressure and collapse.

When Lambda exceeds Gamma, the system crosses an irreversible threshold. KAIROS calculates exactly where that threshold lies.

Domain Λ Lambda Γ Gamma
Finance Leverage Ratio Capital Reserve
AI Safety Model Capability Alignment Constraint
Defense Force Projection Treaty Framework
Supply Chain Supplier Concentration Inventory Buffer
Geopolitics Military Pressure Diplomatic Channel

KAIROS // Rosetta

15 Domain Adapters

The stability equation is domain-agnostic — it describes the relationship between pressure and resistance in any system. Rosetta is the translation layer that maps Lambda and Gamma to the native language of each industry. The same math that detects a banking crisis can identify an AI alignment failure or a supply chain collapse.

One equation. Fifteen languages.

Finance
Λ Leverage Ratio Γ Capital Reserve
Bank stress testing
AI Safety
Λ Model Capability Γ Alignment Constraint
LLM containment bounds
Defense
Λ Force Projection Γ Treaty Framework
Escalation thresholds
Supply Chain
Λ Supplier Concentration Γ Inventory Buffer
Single-source risk
Geopolitics
Λ Military Pressure Γ Diplomatic Channel
Deterrence stability
Insurance
Λ Claim Frequency Γ Reserve Ratio
Catastrophe modeling
Cyber
Λ Attack Surface Γ Defense Depth
Zero-day exposure
Energy
Λ Demand Spike Γ Grid Capacity
Blackout cascades
Climate
Λ Emission Rate Γ Carbon Sink
Tipping point analysis
Pharma
Λ Trial Complexity Γ Regulatory Gate
Approval probability
Real Estate
Λ Speculative Demand Γ Lending Standard
Bubble detection
Trade
Λ Tariff Pressure Γ Trade Agreement
Decoupling risk
Labor
Λ Automation Rate Γ Retraining Capacity
Displacement waves
Biotech
Λ Research Velocity Γ Ethics Framework
Dual-use risk
Space
Λ Orbital Density Γ Debris Mitigation
Kessler threshold

KAIROS // Agon

5 Simulation Products

Current strategy games use arbitrary stability points and scripted collapse events. KAIROS replaces them with mathematically grounded dynamics — real stability thresholds, emergent instability, and replayable traces of futures narrowly averted.

64 ticks/s · 120 simultaneous agents · 32μs decode overhead

WarRoom Defense Military wargaming and operational training
CrisisDesk Finance / Supply Chain Corporate crisis simulation and stress testing
DiplomacyEngine Geopolitics Foreign policy and negotiation training
AlignmentLab AI Safety Multi-agent alignment scenario training
EcoSim Climate Climate policy negotiation and impact modeling

Ananke // Spindle

Validated Research

180,320+ simulation runs
2,112 parameter configs
8/8 Axelrod dynamics
1,620+ tests passing

Axelrod Cooperation Dynamics

Reproduced all 8 iterated prisoner's dilemma dynamics from first principles — no domain calibration required.

Financial Crisis Reconstruction

Predicted collapse structure of the financial crisis before any domain-specific calibration was applied.

Paperclip Maximizer Experiment

Constrained agents outperform pure maximizers across all metrics. Cliff's delta = 1.0 (maximum effect size).

Tragedy of the Commons Simulation

Sharp phase transition at f*=0.50 depletion threshold. Institutional rescue mechanisms validated.

First Principles


Ananke

Ἀνάγκη — Necessity

In Greek cosmology, Ananke is the force that even gods cannot override — the structural constraint that holds the cosmos in order. Her spindle turns the celestial spheres; her laws admit no exception.

In the equation, she is Gamma (Γ) — the institutional constraint, the reserve ratio, the treaty framework, the alignment boundary. The thing that holds.

Kairos

Καιρός — The Opportune Moment

Not chronos — sequential, measurable time — but the critical instant when conditions converge and the window for action opens or closes. The ancient Greeks carved him with a razor's edge: once passed, he cannot be seized again.

In the equation, Kairos is the moment Λ/Γ → 1 — when pressure meets the limit of what structure can bear. The engine exists to find that moment before it finds you.

Request Early Access to KAIROS

KAIROS is currently in pre-release. We're onboarding select partners across finance, defense, AI safety, and adjacent domains. Submit your details and we'll reach out with next steps.

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2. Intellectual Property

All content, software, research, and materials on this site are the property of AnankeLabs. The KAIROS engine, Rosetta adapter layer, Spindle simulation framework, and Serious Gaming SDK are proprietary technologies. No license is granted except as explicitly stated in a signed agreement.

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