CollatzX
Parity-block descent, excursion envelopes, and witness harvesting for 3n+1 dynamics.
Explore engine →Vision
ProofX delivers operator-grade verification engines that compress time-to-evidence and scale reproducibility across disciplines. By uniting symbolic logic, deterministic orchestration, and entropy-aware scheduling, ProofX establishes a research-lab-grade foundation for proof-centric AI and mission-critical verification.
- Impact: accelerate the path from idea to evidence with auditable runs and replayable claims.
- Trust: reproducibility and traceability as first-class design principles.
- Reach: enabling research labs, infrastructure operators, and public-interest projects worldwide.
Engines
RiemannX
Zero statistics, GUE conformity checks, and explicit formula diagnostics on ζ(s).
Explore engine →GoldbachX
Sieve portfolios, parity constraints, and counterexample mining on even decompositions.
Explore engine →Quantum Computing Verification
ProofX Quantum engines leverage quantum computing to accelerate verification of complex conjectures with quantum advantage.
Quantum Verification Architecture
Our quantum verification platform integrates multiple quantum computing paradigms with classical verification systems:
Core Quantum Infrastructure
- Quantum Engine Orchestration (QCollatz)
- Hybrid Quantum-Classical Integration
- Quantum Circuit Synthesis & Optimization
- Multi-Backend Support (Qiskit, Pennylane)
- Quantum Error Mitigation Framework
Verification Methodologies
- Quantum Amplitude Amplification
- Quantum Phase Estimation
- Variational Quantum Algorithms
- Quantum Machine Learning Integration
- Quantum Walks for State Space Exploration
Performance Metrics
- Quantum Volume Benchmarking
- Circuit Depth Optimization
- Noise Resilience Analysis
- Quantum Advantage Threshold Detection
- Resource Estimation & Scaling
CollatzX Quantum Engine
Quantum-enhanced verification of the Collatz conjecture using superposition and quantum parallelism.
CoreLogic Tests
- Quantum parity sequence validation
- Superposition descent verification
- Quantum amplitude amplification for cycle detection
- Entanglement-based convergence checking
- Quantum Fourier transform for sequence analysis
ProofDiagnostics
- Quantum state tomography for verification
- Process fidelity measurements
- Quantum circuit depth optimization
- Error mitigation validation
- Quantum volume benchmarking
ConjectureBenchmarks
- Execution time vs classical (10^6 elements)
- Quantum advantage threshold analysis
- Resource estimation for full conjecture
- Noise resilience metrics
- Scalability projections
SymbolicGenerators
- Quantum symbolic execution
- Automated theorem circuit generation
- Parameterized quantum circuit templates
- Variational quantum eigensolver integration
- Hybrid quantum-classical symbolic reasoning
RiemannX Quantum Engine
Quantum algorithms for verifying properties of the Riemann zeta function and hypothesis.
CoreLogic Tests
- Quantum phase estimation for zeta zeros
- Superposition of critical line evaluations
- Quantum counting of non-trivial zeros
- Entanglement-based analytic continuation
- Quantum random walk on critical line
ProofDiagnostics
- Zero distribution statistical tests
- Quantum process verification
- Circuit depth vs precision analysis
- Resource estimation for full verification
- Error bounds and confidence intervals
ConjectureBenchmarks
- Time to first 1000 zeros verification
- Comparison to classical algorithms
- Quantum advantage demonstration
- Scaling with number of qubits
- Noise tolerance thresholds
Quantum Development Framework
Comprehensive tools for developing and testing quantum verification algorithms.
Quantum Simulators
- Statevector simulation backend
- Density matrix simulation
- Noise model integration
- GPU-accelerated simulation
- Distributed simulation capabilities
Quantum Compilers
- Circuit optimization passes
- Gate decomposition strategies
- Hardware-aware compilation
- Pulse-level control generation
- Cross-platform compatibility
Verification Tools
- Quantum program verification
- Equivalence checking
- Performance profiling
- Resource estimation
- Benchmarking suite
Visualization
- Quantum circuit visualization
- State visualization tools
- Performance dashboard
- Interactive exploration
- Export capabilities
Quantum Hardware Integration
Support for multiple quantum computing platforms and hardware backends.
Supported Platforms
- IBM Quantum Experience
- Rigetti Quantum Cloud Services
- IonQ Quantum Cloud
- Google Quantum Computing Service
- Amazon Braket
Hardware Characteristics
- Qubit connectivity graphs
- Gate fidelity statistics
- Coherence time data
- Error rates by operation
- Calibration schedules
Performance Metrics
- Job queue times
- Execution times
- Success rates
- Cost analysis
- Reliability metrics
Future Quantum Engines
Additional quantum verification engines currently in development.
GoldbachX Quantum
- Quantum search for prime pairs
- Superposition of even number decompositions
- Amplitude amplification for counterexamples
- Status: In Development
TwinPrimeX Quantum
- Quantum prime gap analysis
- Entanglement-based pair detection
- Quantum counting of twin primes
- Status: Research Phase
PvsNPX Quantum
- Quantum complexity class separation
- Oracle separation techniques
- Quantum circuit lower bounds
- Status: Theoretical Foundation
YangMillsX Quantum
- Quantum field theory simulation
- Lattice gauge theory implementation
- Mass gap detection algorithms
- Status: Early Research
CollatzX
Overview available in the lab brief. Detailed materials provided on request.
Methods
Partial Solution Dossier — formal statements & checks
- Parity-Block Descent (Theorem A): descent when even-step dominance exceeds log₂3.
- Bounded-Excursion Contraction (Prop. B): recurring contracting blocks imply exponential envelope.
- Structured Residues (Lemma C): instant-descent families with short even cascades.
Reproducibility capsule: parity extraction → window tests → certificate export. Forthcoming formal publication.
Findings
Representative outputs and core diagnostics from ProofX engines.
CollatzX Trajectory
Most starting values collapse quickly, but rare outliers stretch sequence lengths. The red point marks the maximum observed length; reproducibility demonstrates the engine's anomaly-detection rigor.
Download figure (PNG)
Finding 2
Brief note about what this visual demonstrates.
Case Studies
Real-world applications of ProofX engines driving measurable impact.
Optimizing User Onboarding
- Problem
- High drop-off during the first week of app use.
- Approach
- Implemented guided tutorials, streamlined signup, and personalized notifications.
- Outcome
-
- First-week churn reduced by 40%
- User retention increased by 25%
Scaling Backend Infrastructure
- Problem
- Server crashes under high traffic during launch events.
- Approach
- Migrated to cloud auto-scaling architecture and optimized DB queries.
- Outcome
-
- 99.99% uptime during peak traffic
- Response time improved by 60%
Conversion Rate Improvement
- Problem
- Low conversion on checkout page despite high traffic.
- Approach
- A/B tested checkout flows, reduced form fields, added trust badges.
- Outcome
-
- Conversion rate +35%
- Additional ~$150K monthly revenue
Streamlining Customer Support
- Problem
- Backlogged support tickets caused slow response times.
- Approach
- AI-assisted routing, standardized FAQs, live chat automation.
- Outcome
-
- Average ticket resolution time down 50%
- Customer satisfaction rose to 92%
Product Feature Validation
- Problem
- Uncertainty on which feature resonates with users.
- Approach
- Rapid prototyping with small cohort, structured feedback collection.
- Outcome
-
- Feature adoption 70% in first month
- Exceeded engagement expectations
FAQ
How does ProofX ensure determinism and traceability?
ProofX portfolios are seeded, versioned, and replayable with byte-for-byte manifests.
What is the reliability moat?
ProofX builds compounding corpora of runs and counterexamples that improve priors and are hard to replicate.
Is ProofX a SaaS?
No. ProofX is an open-source non-profit, structured around research partnerships and operator deployments.
Founder
Alkindi — Founder & Chief Architect
Founder of ProofX, architect of multi-engine verification platforms uniting symbolic AI, number theory, and operator-grade observability. Builder of 200k+ LOC lab-grade systems with measurable impact.
- Creator of ProofX and CollatzX — research-grade verification engines.
- Cross-disciplinary architecture spanning logic, topology, quantum methods.
- Principles anchored in reproducibility, provenance, and operator trust.