MATHEMATICAL PROOF SYSTEM FOR MINIMUM PAYMENT FEE ACHIEVEMENT WITH CRYPTOGRAPHIC VERIFICATION

PROVISIONAL PATENT APPLICATION

Inventor: Kinan Lemberg
Address: 270 Bolton Rd, Koah, 4881, Australia
Filing Date: June 4, 2025

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of and incorporates by reference the following previously filed applications:
- Cryptographic AI Response Validation System with Mathematical Gate Enforcement (Application No. 63/816,344)
- Real-Time Information Currency Validation (Application No. 63/816,410)
- Immutable Audit Trail System for AI Validation Decisions (Patent Center No. 70694638, Confirmation No. 9234, filed June 3, 2025)
- Multi-Dimensional Risk Assessment System for AI-Generated Business Advice (Patent Center No. 70694573, Confirmation No. 1273, filed June 3, 2025)
- Real-Time Hallucination Detection Method for Streaming AI Responses (Patent Center No. 70696501, Confirmation No. 1825, filed June 2-3, 2025)
- Multi-Model Consensus System for AI Response Validation (filed on or about June 2-3, 2025)
- Dynamic Confidence Scoring System (filed on or about June 2-3, 2025)
- Automated Threshold Adaptation System (filed on or about June 2-3, 2025)
- Privacy-Preserving Validation Protocol (filed on or about June 2-3, 2025)

FIELD OF THE INVENTION

This invention relates to payment processing optimization systems, specifically to mathematical frameworks that prove and cryptographically verify the achievement of minimum possible transaction fees through exhaustive algorithmic analysis and AI-enhanced optimization protocols.

BACKGROUND OF THE INVENTION

Payment processing systems currently charge fees ranging from 1.5% to 3.9% plus fixed amounts per transaction. These fees are set through competitive market forces, historical precedent, and operational cost estimates rather than mathematical optimization. Existing payment routing systems attempt to minimize fees through heuristic approaches, rule-based selection, or simple comparison algorithms, but none provide mathematical proof that the selected fee represents the absolute minimum achievable while maintaining profitability and regulatory compliance.

Current limitations in payment processing optimization include:

1. Heuristic Optimization Without Proof: Existing systems (such as CN115204859A and CN112258173A) select payment channels based on predefined rules or simple comparisons but cannot prove the selected option represents the mathematical minimum.

2. Lack of Cryptographic Verification: No current system provides cryptographic attestation that a computed fee represents the provable minimum across all possible routing options.

3. Incomplete Search Space Analysis: Traditional optimization approaches use shortcuts and approximations rather than exhaustive analysis of all possible payment paths.

4. Static Fee Structures: Current systems cannot dynamically prove minimum fees as market conditions change in real-time.

5. No Integration with Validation Systems: Existing payment processors operate independently of AI validation systems, missing opportunities for enhanced optimization through validated data inputs.

The prior art fails to address the fundamental question: Given all possible payment routing options, regulatory constraints, and operational requirements, what is the mathematically provable minimum fee, and how can this be cryptographically verified?

There exists a critical need for a payment processing system that not only optimizes fees but provides mathematical proof of achieving the absolute minimum possible fee for any given transaction.

SUMMARY OF THE INVENTION

The present invention provides a mathematical proof system for achieving and verifying minimum payment processing fees through exhaustive algorithmic analysis and cryptographic attestation. The system leverages advanced mathematical frameworks, AI-enhanced optimization, and cryptographic verification to guarantee that no lower fee is possible for any given transaction.

The invention comprises:

1. Mathematical Optimization Framework: A comprehensive mathematical model that captures all variables affecting payment processing fees, including routing options, regulatory requirements, currency conversions, and operational constraints.

2. Exhaustive Search Algorithm: An AI-enhanced algorithm that systematically evaluates every possible payment path to identify the absolute minimum fee while maintaining required service levels.

3. Cryptographic Proof Generation: A system for generating cryptographic proofs that attest to the completeness of the search and the optimality of the identified minimum fee.

4. Real-Time Verification Protocol: Dynamic verification mechanisms that continuously validate the minimum fee achievement as market conditions change.

5. AI Integration Layer: Leverages existing AI validation patents to enhance optimization accuracy and provide validated inputs for fee calculation.

The system provides guaranteed minimum fees that are mathematically proven and cryptographically verified, creating a new standard for payment processing transparency and efficiency.

DETAILED DESCRIPTION OF THE INVENTION

System Architecture Overview

The Mathematical Proof of Minimum Fee Achievement system operates as a comprehensive optimization and verification layer within payment processing infrastructure. The system comprises five interconnected components that work together to identify, achieve, and prove minimum possible transaction fees.

Component 1: Mathematical Optimization Framework

The Mathematical Optimization Framework establishes the complete mathematical model for fee calculation across all possible payment paths.

Fee Optimization Function:
The system implements a comprehensive fee function F that captures all cost components:

F(t) = Σ[i=1 to n] (Ci(t) × Wi(t)) + R(t) + O(t) + M(t)

Where:
- t = transaction parameters (amount, currency, origin, destination)
- Ci = cost component i (interchange, processing, currency conversion, etc.)
- Wi = weight factor for component i based on routing path
- R(t) = regulatory compliance costs for transaction t
- O(t) = operational costs including infrastructure and support
- M(t) = minimum acceptable margin for sustainability
- n = total number of cost components

The framework encompasses:

a) Interchange Fee Modeling:
   I(t) = Base_Rate(card_type, merchant_category) × Amount(t) + Fixed_Fee(network)

b) Currency Conversion Optimization:
   C(t) = Spot_Rate(t) × (1 + Spread(volume, pair)) + Hedging_Cost(volatility)

c) Regulatory Compliance Costs:
   R(t) = Σ[j∈jurisdictions] Compliance_Cost(j) × Allocation_Factor(t,j)

d) Multi-Path Routing Options:
   P(t) = {p1, p2, ..., pk} where each pi represents a complete payment path

Component 2: Exhaustive Search Algorithm

The Exhaustive Search Algorithm systematically evaluates every possible payment path to identify the absolute minimum fee.

Algorithm Implementation:

```
function findMinimumFee(transaction):
    paths = generateAllPossiblePaths(transaction)
    minimum_fee = INFINITY
    optimal_path = null
    proof_data = {}
    
    for each path in paths:
        fee = calculateCompleteFee(path, transaction)
        proof_data[path] = {
            fee: fee,
            components: breakdownFeeComponents(fee),
            timestamp: current_time(),
            constraints_satisfied: verifyConstraints(path)
        }
        
        if fee < minimum_fee AND satisfiesAllConstraints(path):
            minimum_fee = fee
            optimal_path = path
    
    return {
        minimum_fee: minimum_fee,
        optimal_path: optimal_path,
        proof: generateCryptographicProof(proof_data),
        guarantee: "No lower fee possible"
    }
```

Path Generation:
The system generates paths considering:
- Direct bank transfers
- Card network routes
- Alternative payment methods
- Cryptocurrency bridges
- Multi-hop combinations

Constraint Verification:
Each path must satisfy:
- Regulatory requirements in all jurisdictions
- Service level agreements (processing time)
- Risk management thresholds
- Liquidity availability
- Technical compatibility

Component 3: Cryptographic Proof Generation

The system generates unforgeable cryptographic proofs of minimum fee achievement.

Proof Structure:
```
MinimumFeeProof = {
    transaction_hash: SHA256(transaction_details),
    search_completeness: MerkleRoot(all_evaluated_paths),
    minimum_fee: optimal_fee_value,
    optimal_path: selected_path_details,
    timestamp: proof_generation_time,
    algorithm_version: system_version,
    signature: RSA_Sign(private_key, proof_data)
}
```

Proof Components:

a) Search Completeness Attestation:
   - Merkle tree of all evaluated paths
   - Cryptographic hash of search algorithm
   - Verification that no paths were skipped

b) Optimality Certificate:
   - Mathematical proof that identified fee is minimum
   - Comparison data for all alternative paths
   - Constraint satisfaction verification

c) Temporal Validity:
   - Timestamp of proof generation
   - Market data snapshot used in calculations
   - Expiration time based on market volatility

Component 4: Real-Time Verification Protocol

The system continuously verifies minimum fee achievement as conditions change.

Continuous Verification Process:

1. Market Monitoring:
   - Real-time exchange rate tracking
   - Regulatory change detection
   - Network fee updates
   - Liquidity pool monitoring

2. Proof Revalidation:
   - Automatic recalculation triggers
   - Incremental proof updates
   - Alert generation for fee changes

3. Historical Proof Chain:
   - Blockchain-style linking of proofs
   - Audit trail of all fee calculations
   - Immutable record of optimizations

Component 5: AI Integration Layer

Leverages existing AI validation patents for enhanced optimization.

AI Enhancement Features:

1. Predictive Optimization:
   - Uses Multi-Model Consensus System for fee prediction
   - Anticipates market movements to lock in lower fees
   - Consensus across multiple prediction models

2. Confidence Scoring:
   - Applies Dynamic Confidence Scoring System to path selection
   - Weighs optimization certainty against potential savings
   - Adjusts risk parameters based on confidence levels

3. Adaptive Learning:
   - Implements Automated Threshold Adaptation System for dynamic optimization
   - Learns from historical patterns to improve future calculations
   - Automatically adjusts algorithm parameters

4. Validation Integration:
   - Uses Cryptographic AI Response Validation System (Application No. 63/816,344) for proof verification
   - Ensures all inputs are validated before optimization
   - Provides additional trust layer for fee calculations

5. Audit Trail Integration:
   - Leverages Immutable Audit Trail System for compliance
   - Creates permanent record of all optimization decisions
   - Enables regulatory verification of fee calculations

Implementation Specifications

Technical Requirements:
- Processing capacity: 10,000+ path evaluations per second
- Proof generation time: <100ms per transaction
- Storage: Distributed ledger for proof records
- Integration: RESTful APIs for payment processor connection

Security Measures:
- Hardware security modules for key management
- Multi-party computation for sensitive calculations
- Zero-knowledge proofs for privacy preservation
- Quantum-resistant cryptographic algorithms

Scalability Architecture:
- Horizontal scaling for path evaluation
- Caching for common transaction patterns
- GPU acceleration for mathematical computations
- Edge computing for regional optimization

ADVANTAGES OVER PRIOR ART

The present invention provides significant advantages over existing payment optimization systems:

1. Mathematical Proof vs. Heuristic Optimization: Unlike existing systems that use approximations, this invention provides mathematical proof of achieving the absolute minimum fee.

2. Cryptographic Verification: The system generates unforgeable proofs that can be independently verified, creating unprecedented transparency in payment processing.

3. Exhaustive Analysis: Rather than shortcuts or sampling, the system evaluates every possible payment path to guarantee optimality.

4. Dynamic Adaptation: Real-time verification ensures the minimum fee is maintained as market conditions change.

5. AI Enhancement: Integration with AI validation systems provides predictive optimization and adaptive learning capabilities.

6. Regulatory Compliance: Built-in compliance verification ensures all optimizations meet regulatory requirements.

INDUSTRIAL APPLICABILITY

The invention has broad applicability across payment processing industries:

1. E-commerce Platforms: Minimize transaction costs for online merchants
2. Financial Institutions: Optimize inter-bank transfers and settlements
3. Cryptocurrency Exchanges: Prove optimal fiat-to-crypto conversion rates
4. International Remittances: Minimize cross-border transfer fees
5. Payment Service Providers: Differentiate services with provably lowest fees

CLAIMS

Claim 1: A mathematical proof system for achieving minimum payment processing fees comprising:
a) a mathematical optimization framework that models all cost components and constraints for payment processing;
b) an exhaustive search algorithm that evaluates every possible payment path to identify the absolute minimum fee;
c) a cryptographic proof generation system that creates verifiable attestations of minimum fee achievement;
d) a real-time verification protocol that continuously validates fee optimality; and
e) an AI integration layer that enhances optimization through predictive modeling and adaptive learning.

Claim 2: The system of claim 1, wherein the mathematical optimization framework comprises:
a) comprehensive fee function capturing all cost components;
b) constraint modeling for regulatory and operational requirements;
c) multi-path routing evaluation across all payment networks; and
d) dynamic parameter adjustment based on real-time market data.

Claim 3: The system of claim 1, wherein the exhaustive search algorithm comprises:
a) systematic generation of all possible payment paths;
b) complete fee calculation for each path including all components;
c) constraint verification ensuring regulatory compliance;
d) proof data collection for cryptographic attestation; and
e) guaranteed identification of the global minimum fee.

Claim 4: The system of claim 1, wherein the cryptographic proof generation comprises:
a) Merkle tree construction of all evaluated paths;
b) digital signature of optimization results;
c) timestamp and version information for temporal validity;
d) zero-knowledge proof options for privacy preservation; and
e) blockchain-compatible proof format for immutable recording.

Claim 5: The system of claim 1, wherein the real-time verification protocol comprises:
a) continuous market data monitoring;
b) automatic proof revalidation triggers;
c) incremental proof updates for efficiency;
d) historical proof chain maintenance; and
e) alert generation for fee optimization opportunities.

Claim 6: The system of claim 1, wherein the AI integration layer comprises:
a) multi-model consensus for fee prediction;
b) dynamic confidence scoring for path selection;
c) adaptive threshold adjustment for optimization parameters;
d) cryptographic validation of all inputs; and
e) machine learning for pattern recognition and improvement.

Claim 7: A method for proving minimum payment processing fee achievement comprising:
a) receiving transaction parameters requiring payment processing;
b) generating all possible payment paths for the transaction;
c) calculating complete fees for each path including all components;
d) identifying the path with absolute minimum fee while satisfying constraints;
e) generating cryptographic proof of the exhaustive search and optimality;
f) executing the transaction using the proven optimal path; and
g) providing the cryptographic proof for independent verification.

Claim 8: The method of claim 7, further comprising:
a) continuously monitoring market conditions affecting fees;
b) automatically recalculating when conditions change materially;
c) updating proofs incrementally for efficiency;
d) maintaining immutable audit trail of all optimizations; and
e) providing real-time fee guarantees to users.

Claim 9: The system of claim 1, wherein the integration with AI validation systems comprises:
a) leveraging the Cryptographic AI Response Validation System (Application No. 63/816,344) for input verification;
b) applying multi-model consensus for robust optimization;
c) using dynamic confidence scoring for decision making;
d) implementing adaptive thresholds for continuous improvement;
e) utilizing the Immutable Audit Trail System for compliance recording; and
f) creating synergistic value through patent portfolio integration.

Claim 10: A computer-readable medium storing instructions that, when executed by a processor, cause the processor to perform the method of claim 7.

ABSTRACT

A mathematical proof system for achieving and verifying minimum payment processing fees through exhaustive algorithmic analysis and cryptographic attestation. The system comprises a mathematical optimization framework modeling all fee components, an exhaustive search algorithm evaluating every possible payment path, cryptographic proof generation for verification, real-time validation protocols, and AI integration for enhanced optimization. Unlike existing heuristic approaches, this system provides mathematical proof that the identified fee represents the absolute minimum possible while satisfying all constraints. The cryptographic proofs enable independent verification and create unprecedented transparency in payment processing. Integration with AI validation systems provides predictive optimization and adaptive learning capabilities. The invention enables payment processors to offer provably minimum fees, creating significant competitive advantages and cost savings for merchants while maintaining regulatory compliance and operational sustainability.