PUBLISHED2026-02
The Fine-Structure Constant from Discrete Hodge Theory
Sayed Amir Karim
This paper derives the electromagnetic fine-structure constant α⁻¹ = 137.0359 (0.79 ppm deviation) from the nilpotency condition d²=0 via discrete Hodge theory. The derivation uses a self-dual triangulation (K₄), the Pell equation from circulant criticality at z=4, and the Koide phase δ=2/9. No free parameters are fitted; all values emerge from mathematical structure.
Mathematical PhysicsView Details →
PUBLISHED2026-02
The Pell Equation from Circulant Criticality (z=4)
Sayed Amir Karim
A mathematical note isolating the number-theoretic step used in the AQEA chain: how criticality of the z×z circulant at z=4 forces the amplitude A²=2, introducing the quadratic field Q(√2). The Pell equation x²−2y²=1 then uniquely selects (N,d)=(3,2), producing the stability parameter δ=d/N²=2/9.
Mathematical TheoryView Details →
PUBLISHED2026-01
AQEA: Technical Report — Domain-Adaptive Semantic Compression of Embeddings
Sayed Amir Karim
Technical report introducing AQEA compression achieving up to 320×+ compression with ≤97% quality retention across four modalities (Video, Text, Audio, Protein). Features steerable 'Lenses' (~35KB) for domain adaptation without retraining the underlying embedding model. Validated with ground-truth human labels [GT-H].
Information TheoryView Details →
PUBLISHED2026-01
Addressing the Semantic Twins Problem in Legal RAG: A Lens Steering Approach
Sayed Amir Karim
Working paper addressing the 'semantic twins' problem in legal RAG systems, where documents with identical embeddings carry opposite legal weight. The Lens steering approach achieves Hard-Negative@10 (HN@10) reduction from ~56% to 0.000, demonstrating complete resolution of the semantic collision problem.
Ethics & SecurityView Details →
PUBLISHED2026-01
Ground-Truth-Aware Metric Terminology for Vector Retrieval
Sayed Amir Karim
A proposal for disambiguating evaluation in embedding-based systems through terminology standards. Introduces notation requiring explicit ground-truth encoding: [GT-H] for human labels, [GT-S] for synthetic, [GT-M] for model-generated. Argues that metrics like Spearman correlation, Recall@k, and nDCG are meaningless without ground-truth specification.
Semantic SystemsView Details →
PUBLISHED2025-01
Multi-Layer Network Theory Resolves the Semantic Compression Problem
Sayed Amir Karim
Semantic similarity systems face a fundamental trade-off between domain expertise and multilingual capability. This work presents a novel three-layer semantic approach that integrates domain-specific, cross-linguistic, and cross-domain embeddings, achieving 15% higher correlation than existing methods.
Network TheoryView Details →
CONFIDENTIAL2024-12
AQEA Universal Addressing: 4-Byte Knowledge Representation
Sayed Amir Karim
Introduction of the AQEA Universal Addressing system, demonstrating how any concept in any language can be represented using just 4 bytes (AA:QQ:EE:A2 format). This breakthrough enables unprecedented compression and retrieval performance through natural information organization patterns.
Information TheoryView Details →
CONFIDENTIAL2024-11
Harmonic Hierarchies in Knowledge Graph Construction
Sayed Amir Karim
Application of golden ratio-based harmonic structures in building self-organizing knowledge graphs. This approach enables cycle-safe navigation through complex conceptual spaces while maintaining mathematical elegance.
Graph TheoryView Details →
CONFIDENTIAL2024-10
Ethical Constraints in Distributed Systems: RuleCore™ Architecture
Sayed Amir Karim
Introduction of RuleCore™, an immutable ethics enforcement layer that operates across distributed systems without central authority. The system uses cryptographic consensus to ensure ethical compliance that cannot be overridden.
Ethics & SecurityView Details →
CONFIDENTIAL2024-09
Phi Metrics: Measuring Information Integration in Complex Systems
Sayed Amir Karim
A mathematical framework for quantifying the degree of information integration in complex adaptive systems. Based on Integrated Information Theory, this metric provides objective measurement of system consciousness levels.
Complexity ScienceView Details →
CONFIDENTIAL2024-08
Adversarial Robustness in Multi-Layer Networks
Sayed Amir Karim
Analysis of adversarial attack resistance in multi-layer network architectures. Demonstrates provable robustness guarantees with explicit Lipschitz constants.
SecurityView Details →
CONFIDENTIAL2024-07
Universal Approximation in Semantic Spaces
Sayed Amir Karim
Proof of universal approximation capabilities in multi-dimensional semantic spaces with optimal convergence rates. Establishes theoretical foundation for arbitrary concept representation.
Mathematical TheoryView Details →
CONFIDENTIAL2024-06
Production Optimization for Quantum-Entangled Systems
Sayed Amir Karim
Optimization strategies for production deployment of quantum-entangled information systems. Addresses scalability, latency, and resource allocation in distributed environments.
System OptimizationView Details →
CONFIDENTIAL2024-05
Cross-Domain Semantic Bridging Theory
Sayed Amir Karim
Novel approach to connecting disparate knowledge domains through semantic bridging layers. Enables unprecedented cross-disciplinary knowledge transfer.
Semantic SystemsView Details →
CONFIDENTIAL2024-04
Swarm Intelligence Integration Framework
Sayed Amir Karim
Framework for integrating swarm intelligence patterns into multi-layer network architectures. Enables emergent behavior while maintaining deterministic guarantees.
Distributed IntelligenceView Details →