Platforms Built on Proof

Every system validated through rigorous mathematics before implementation. From quantum execution to biological intelligence.

The Mathematical Foundation

🧮

AIDF Master Calculus

59 Formal Mathematical Proofs

Sequent Calculus
Operational Semantics
Category Theory
KKT Optimization
↓

Platform Layers Built on AIDF

⚛
Quantum Layer

LEF execution framework

Built on AIDF operational semantics

⚗
Chemistry Layer

LQL compositional bonding

Built on AIDF category theory

🧬
Biology Layer

AIOS cognitive systems

Built on AIDF master calculus

TAI Platform

Tutelarius Auxilium Intellectus
Conversational AI with mathematically-proven memory systems.

Holographic Memory: H(x,t) = ∫∫∫ M(ξ,τ) K(x-ξ, t-τ) dξdτ

Mathematical Guarantees:

  • Proven recall accuracy through holographic equations
  • Deterministic context retrieval
  • Traceable memory operations
  • Multi-model orchestration via AIUCP
Explore TAI Mathematics →
🧠

Holographic Memory

Unlike traditional vector databases, TAI's memory system uses holographic principles where every piece contains the whole, enabling perfect recall even with partial information.

⚡

Intent to Execution

LATTICE transforms high-level intent into quantum-inspired execution patterns, with mathematical guarantees at every transformation layer.

LATTICE Framework

Complete AI Operating System
From quantum execution to biological intelligence patterns.

Composition: L(f∘g) = L(f) ⊗ L(g) + B(f,g)

Core Components:

  • LQL - Lattice Query Language for compositional AI
  • LEF - Execution framework with quantum parallelism
  • COE/CNS - Cognitive orchestration & nervous system
  • Mathematical Proofs - Every operation validated
Explore LATTICE Theory →

AIDF Governance

AI Development Framework
Ethical AI through mathematical design and provable compliance.

Traceability: T(req → impl) = ∏ᵢ P(stepᵢ | stepᵢ₋₁)

Framework Guarantees:

  • Mathematical proof of compliance
  • Traceable from requirements to deployment
  • Ethical constraints as equations
  • Auditable decision paths
Explore AIDF Framework →
⚖️

Ethical by Design

AIDF doesn't just document compliance—it proves it mathematically. Every ethical constraint becomes an equation, every governance rule a mathematical boundary.

Platform Capabilities

CapabilityTAILATTICEAIDF
Mathematical Proofs✓✓✓
Holographic Memory✓○-
Quantum Execution○✓-
Compositional Calculus○✓○
Ethical Constraints○○✓
Traceability✓✓✓

✓ Full Support   ○ Integration Available   - Not Applicable

Ready to Build with Mathematical Certainty?

Our platforms aren't just tools—they're mathematically proven systems that guarantee behavior from intent to execution.

Schedule a Technical ReviewRead Our Proofs