RESEARCH
Prime Radiant's research is organized around a small number of recurring questions rather than individual technologies or application domains.
Across financial systems, physical infrastructure, autonomous agents and quantum computation, the objective remains the same: to find mathematical representations that expose useful structure in complex information and decision spaces.
The research develops along three closely connected directions.
STRUCTURING HIGH-DIMENSIONAL COMPLEXITY
Finding representations that make otherwise intractable spaces computationally accessible.
Many important optimization problems are difficult not simply because they contain many variables, but because meaningful solutions occupy only a small and highly structured part of an enormous space of possibilities.
This research explores how graph structure, physical constraints, hierarchical decomposition and tensor networks can be used to identify and represent the parts of those spaces that matter.
The work ranges from general mathematical frameworks to concrete problems in financial settlement, adversarial allocation, autonomous systems and large physical networks.
FOUNDATIONAL FRAMEWORKS
A Rigorous Graph-Theoretic Formulation of High-Dimensional Combinatorial Optimization
A general mathematical framework for high-dimensional decision spaces constrained by underlying physical or topological relationships.
The research develops a four-stage skeleton extraction process designed to identify feasible regions before expensive optimization begins, and applies the framework across power grids, satellite tasking, protein packing, data-center allocation, quantum error correction and adversarial drone swarms.
A Generic Tensor Network Framework for Constrained Combinatorial Optimization
A general tensor-network architecture for representing enormous constrained decision spaces without explicitly constructing them.
Global constraints are transformed into local tensor operations, allowing feasibility structure to survive successive stages of compression. The framework is developed with applications to cryptocurrency arbitrage and systemic settlement optimization at scales of 104–105 variables.
APPLICATIONS & EXTENSIONS
Explicit LSMC Restructuring of Trade Settlement Optimization
Large-scale trade settlement is reformulated as a sequential logical and tensor-network problem, replacing explicit enumeration of settlement combinations with a compressed representation of the relationships that generate and constrain them.
The resulting architecture provides exact representation of the underlying settlement logic while creating a bridge toward hybrid quantum optimization.
Blueprint: LSMC-Skeleton Solver for Systemic Settlement Optimization
Extends the settlement architecture toward systemic networks of approximately 100,000 transactions by replacing a linear tensor representation with a tree tensor network designed to reflect the hierarchical topology of the banking system.
QUANTUM-NATIVE COMPUTATION
Useful classical mathematics today. Quantum-ready representations for tomorrow.
Quantum computation is treated here not as a separate application area, but as a computational direction.
The research asks which mathematical representations naturally cross the classical–quantum boundary, where genuine quantum advantage can arise, and where state preparation, data loading, measurement or hardware constraints eliminate it.
The objective is not to attach quantum algorithms to conventionally formulated problems after the fact. It is to develop representations that can be investigated and implemented classically today while remaining structurally compatible with quantum computation as the technology matures.
FOUNDATIONS
A Unified Mathematical Model of Quantum Monte Carlo
A common mathematical model spanning quantum Monte Carlo architectures from amplitude estimation to variational and diffusion approaches.
The framework reduces apparently different methods to a common ratio-form estimand and identifies the architectural choices and cost conditions determining whether quantum transposition produces genuine computational advantage.
Quantum Monte Carlo in Application
A systematic application of the unified framework across sixteen domains, ranging from derivatives and credit risk to electronic structure and nuclear physics.
Each application is evaluated not simply for theoretical speedup but for the practical bottlenecks—particularly loading, sampling and hardware requirements—that determine whether quantum advantage survives implementation.
Exponential Quantum Advantage via Quantum Oracle Sketching
An investigation of whether massive classical information can be transformed directly into compact quantum representations without reproducing the classical memory bottleneck quantum computation is intended to overcome.
The proposed architecture combines Quantum Oracle Sketching, block encoding and quantum singular value transformation with classical-shadow extraction to construct and interrogate functional quantum representations without explicit storage of the ambient high-dimensional object.
A Unified Framework for Quantum Tensor Network Algorithms in High-Dimensional Graph Analysis
A broader mathematical framework connecting high-dimensional graphs, tensor-network representations and quantum computation, developed across cryptocurrency arbitrage, electricity markets, banking settlement and decentralized transaction routing.
QUANTUM-READY APPLICATIONS
A hybrid architecture addressing a concrete insurance problem: understanding portfolio-level risk across thousands of interacting factors when the combinations that matter most occur in the extreme tails.
The research combines classical dependence modelling, tail-aware dimensional restructuring, quantum-compatible distribution representation and quantum amplitude estimation of rare outcomes.
Quantum Accelerated Arbitrage Discovery
A quantum architecture for discovering positive-ROI arbitrage cycles across multiple cryptocurrency exchanges.
The constrained cycle space is encoded as a Hamiltonian, allowing quantum minimum-finding methods to search for optimal cycles while retaining closure, transfer, DEX and other structural requirements of executable arbitrage.
Mathematical Foundations and Quantum Enhancements for Trade Settlement Optimization
A quantum-classical settlement framework combining multi-objective variational optimization, adaptive constraint handling and hierarchical spectral decomposition, with explicit analysis of near-term and fault-tolerant implementations.
A Three-Stage Quantum Architecture for Tensor Train Q-Function Induction
A quantum-classical architecture for path-dependent real-option valuation that identifies distinct quantum insertion points in simulation, tensor training and final expectation estimation rather than treating the entire problem as a single candidate for quantum acceleration.
INTELLIGENT DECISION & COORDINATION SYSTEMS
Finding structure when decisions, information and incentives interact.
Complexity does not arise only from dimensionality.
In many systems, the structure itself evolves because decisions interact with future states, other agents, incomplete information or physical networks.
This research combines game theory, financial engineering, machine learning and structured optimization to investigate environments in which actions themselves help determine the states and opportunities that follow.
DYNAMIC DECISIONS
A Rigorous Mathematical Analysis of the Precision Dilemma in the Longstaff-Schwartz Method
A mathematical decomposition of the limitations of conventional high-dimensional real-option valuation into three interacting sources: approximation error from dimensionality, backward-propagation error through time, and maximization bias across competing decisions.
A Quantum-Native, Static Tensor Train Architecture for Path-Dependent Real Option Valuation
A static tensor representation of a high-dimensional path-dependent decision policy, replacing repeated sequential regression while preserving the feedback between previous decisions and future states.
The architecture uses DMRG-style tensor training and is designed from the outset to remain naturally compatible with quantum circuit implementation.
RECONSTRUCTING ECONOMIC INFORMATION
LLM-Guided Hedge Portfolio Construction in Prediction Markets
A framework for transforming an economic risk expressed in natural language into an executable portfolio of prediction-market contracts.
LLM reasoning identifies causal and semantic relationships, probabilistic inconsistencies are reconciled into a coherent joint distribution, and financial optimization transforms the resulting structure into minimum-variance or CVaR-based hedge positions.
PRISM: Probabilistic Risk Inversion via Structured Market Hedging (not Prime Radiant research)
A systematic prediction-market hedging framework using semantic structure and historical resolution data to discover combinations of apparently distinct contracts with useful portfolio-level hedging properties.
In empirical testing across 300 resolved markets, the framework reduced return variance by 31.3% and improved maximum drawdown by 26.9 percentage points while preserving risk-adjusted performance.
STRATEGIC & MULTI-AGENT COORDINATION
Complex multi-agent systems introduce a different form of computational difficulty: the solution depends not only on the size of the decision space, but on the simultaneous actions, constraints and objectives of other agents.
This research explores how game-theoretic structure, tensor representations and hierarchical decomposition can be combined to coordinate large populations of interacting agents under resource constraints, uncertainty and adversarial response.
Hierarchical Tensor Network Formalization of Combinatorial Drone Swarm Defensive Strategies
A tensor-network formulation of swarm coordination in which large spaces of defensive strategies are reduced through resource-feasibility constraints, saturation structure and symmetry.
The architecture combines hierarchical partitioning, TT-Cross approximation and dynamic-programming extraction, with a multi-scenario extension for coordination under uncertainty.
Tensor-Train Approximation under Scenario Uncertainty for Robust Weapon–Target Assignment: The WTA-HDAE Algorithm
A tensor-train approach to coordinated resource allocation under uncertainty, exploiting exact structural separability to make large combinatorial assignment spaces computationally accessible.
The framework incorporates multiple scenarios and extends naturally from expected performance toward mean-variance and CVaR-based robust coordination.
Tensor-Train Approximation under Scenario Uncertainty for Robust Weapon–Target Assignment: The WTA-HDAE Algorithm With Stackelberg Equilibrium
Extends the coordination problem from optimization under uncertainty to strategic interaction.
The Defender commits to an allocation while the Attacker responds strategically, transforming the tensor architecture into a Bayesian Stackelberg framework and introducing Unified Scenario Tensorization for large adversarial strategy spaces.
Pareto-Optimal State Manipulation for Black-Box AI Agent Coordination via Incentive-Aligned LSMC-MUB-VQE Optimization
A game-theoretic framework for coordinating independently acting black-box AI agents through minimal changes to their perceived states, while preserving individual rationality and targeting Pareto-efficient collective outcomes.
The architecture combines constrained Nash bargaining, structured tensor representations and quantum-native optimization to transform decentralized agent behavior into a tractable coordination problem.