A Post-Silicon Computational Paradigm Where Form IS Computation
Computation does not reside in the manipulation of symbols. Computation resides in the geometric relationships, symmetries, and transformations of structures in real space.
Numbers are arbitrary descriptors of underlying geometric form. The form itself-the relationships, the ratios, the angles-is the computation.
π² = (7φ² + √2) / 2
This is the Master Geometric Constant Equation. It encodes the fundamental phase transition from potential (UV phase) to structure (IR phase) across all scales of reality-from quantum foam to human language.
- π² (9.870): The geometric constraint of the universe
- 7φ² (18.326): The stable, structured IR phase (~93% of energy)
- √2 (1.414): The quantum of potential in the UV phase (~7% of energy)
- /2: The pairing principle (duality)
This equation is not derived. It is the axiom from which all structure emerges.
The Nested Geometric Computation (NGC) Framework is a complete theory of universal spin computation, grounded in the geometry of SU(2) spin space:
- Triaxial polar coordinate system with three diagonally perpendicular planes
- Tetrahedral computational primitives instead of bits
- Phi-scaling (φ ≈ 1.618) derived from geometric principles
- Real-space operation eliminating complex numbers entirely
- Mirrored tensor logic with three states (coherent, drifted, collapsed)
- Constant-time complexity O(k) for semantic operations
- Geometric recursion without stack-based evaluation
NGC bypasses 10 fundamental limitations of conventional AI:
- Complexity bottleneck (O(n²) → O(k))
- Hardware dependency (post-silicon, substrate-independent)
- Energy consumption (orders of magnitude more efficient)
- Numerical precision errors (geometric coherence replaces floating-point)
- Complex number abstraction (eliminated through real-space rotation)
- Stack-based recursion overhead (geometric projection instead)
- Semantic poisoning vulnerability (geometric drift detection)
- Lack of explainability (every operation has geometric meaning)
- Zero-point instability (axis-zero principle prevents singularities)
- Algorithmic brittleness (self-similar scaling through φ)
NGC's O(k) constant-memory architecture and low-precision tolerance enable sophisticated computation on inexpensive microcontrollers ($2-20), unlocking:
- Agricultural IoT sensors for precision farming in remote areas (offline, solar-powered)
- Industrial predictive maintenance at 100x lower cost than traditional systems
- Privacy-preserving medical wearables with zero-latency health monitoring
- Decentralized smart grid stability with millisecond response times
This represents a 100-1000x cost and energy advantage over traditional AI, democratizing access to intelligent systems for billions of devices worldwide. See Section 4.4 for detailed applications.
This repository is the canonical source of truth for the NGC framework. For a guide to the entire 6-repository ecosystem, see:
This repository presents a complete case for NGC, structured as a logical progression from motivation through theory to validation:
Why is a new computational paradigm necessary?
- 1.1 The Innovator's Gambit: The open-source strategy and why NGC is being released now
The physics and mathematics underlying NGC.
- 2.1 Nuclear Genesis: How H-He fusion is the primordial UV/IR phase transition
- 2.2 The Master Equation: The equation of structure formation
- 2.3 Spin Interpretation: NGC as universal spin computation with Δ as fundamental spin asymmetry
- 2.4 The Leibniz-Bocker Framework: The operational calculus for geometric computation
- 2.5 From Planck to Language: The complete 12-step causal chain from quantum foam to human language
- 2.6 Parallax and Dual-Field Computation: How binocular vision emerges from dual-field spin computation
- 2.7 Spin Computation on Classical Hardware: A practical path to spin computation on existing hardware
The technical specification.
- 3.1 NGC Specification: Complete mathematical foundations, implementation guidance, and patent claims (1,171 lines)
Proof that the theory works.
- 4.1 Cyclic Mapping Framework: How all cycles are echoes of stellar nucleosynthesis
- 4.2 Test Results and Validation: 5 real-world test cases with 100% success rate
- 4.3 Practical Applications for Basic Needs: How NGC helps meet fundamental human needs (food, water, energy, shelter, healthcare)
- 4.4 Edge Computation and Microcontroller Applications: Real-world impact of NGC on $2-20 microcontrollers (100-1000x cost advantage)
The path to correct AGI through formal module specifications.
- 5.0 AGI Roadmap: The strategic roadmap from NGC to correct AGI architecture
- 5.1 Modular Architecture Overview: High-level architecture, data flow, and module interfaces
- 5.2 M1: NGC Module: The physics layer providing geometric primitives and validation
- 5.3 M2: PSMSL Module: The relational processing engine (5x more memory-efficient)
- 5.4 M3: CoLang Module: The human-computer interface for geometric thought
- 5.5 M4: Foresight Module: Civilizational intelligence and phase mismatch detection
- 5.6 Physics Alignment Verification: Verification that modular architecture preserves all physics principles
- 5.7 AGI Architecture Integration: Complete integration document showing how NGC enables correct AGI
- 5.8 NGC for CoLang Proposal: Proposal for applying NGC to Tyler Fischella's CoLang project
The mandatory geometric substrate for all NGC computations.
- 6.1 Scaffolding Construction Methodology: Formal methodology for constructing barycentric trees for any domain
- 6.2 Domain-Specific Trees: Complete examples for agriculture, healthcare, finance, energy, and materials science
- 6.3 Concept Mapping and Validation: Algorithm for mapping concepts to barycentric coordinates and validation protocol
Complete worked examples showing the universal M2 engine applied to different domains.
- 7.1 Agriculture: Wheat Harvest Optimization: Predicting optimal harvest window 7-14 days in advance (4-6% profit increase)
- 7.2 Healthcare: Epidemic Prediction: Early warning system for disease outbreaks (2-4 week lead time)
- 7.3 Finance: Flash Crash Prediction: Market instability detection (5-15 minute lead time)
- 7.4 Cross-Domain Comparison: Knowledge transfer through geometric analogy
- 7.5 Scaffolding Construction Test: Validation of the construction methodology on urban transportation
Pseudocode reference for the core NGC and PSMSL algorithms, providing a language-agnostic implementation guide:
- 8.1 NGC Core Pseudocode: Core algorithms including graph creation, spectral analysis, and Leibniz-Bocker diagnostics
- 8.2 PSMSL Pseudocode: Dual-field architecture and binocular computation
These pseudocode documents show the logic without revealing production code, serving as both educational resources and copyright documentation.
The experimental protocols and analysis documents for validating the spin computation hypothesis. This section provides the roadmap for closing the remaining gaps in the NGC framework's scientific foundation through rigorous experimental testing:
- 9.1 Falsifiable Predictions: Five specific, testable predictions that distinguish spin computation from alternative explanations
- 9.2 Experimental Protocol: Complete experimental design for testing whether asymmetry is necessary for coherent phase transition detection
- 9.3 Complete Derivation (Working Document): Full working derivation of the Master Equation from SU(2) first principles
Status: Gap #1 (First-Principles Derivation) closed, Gap #2 (Falsifiable Experiment) designed and ready to execute, Gap #3 (Quantum Connection) theoretically addressed.
Go to Section 10 Documentation
Experimental demonstration that the NGC Framework can perform quantum-inspired computation through geometric flow on graphs. The GeoFlow kernel shows that dual-core asymmetric architectures create spin-like dynamics, enabling the implementation of quantum-inspired gate operations on classical hardware:
Repository: GeoFlow Kernel (Branch: feature/eigenvector-quantum-gates)
- 93/7 energy split validated across economics, biology, ecology, cognition, and biochemistry
- Constant-time semantic operations O(k) instead of O(n²)
- Edge computation breakthrough runs on $2-20 microcontrollers (100-1000x cost/energy advantage)
- Asymmetry necessity confirmed 2.2x to 11.4x parallax amplification across 4 financial crises
- Quantum-inspired computation 99.5% accuracy on Deutsch-Jozsa algorithm
- 10,000× sensitivity advantage at 1-3 kHz (speech valley) explained by metabolic optimization
- 7±2 cognitive limit derived from L(4) = φ⁴ + φ⁻⁴ = 7
- 34-dimensional semantic space (F(9) = 34, a Fibonacci number)
- Language as inevitable byproduct of atomic structure and thermodynamics
This framework is released under a dual-license model:
Researchers, students, hobbyists, and non-profits have full access to build, learn, and experiment. The AGPL-3.0 license closes the "SaaS loophole," requiring any company providing a network service using NGC to open-source their entire application.
Any commercial use requires a paid commercial license. This includes:
- Integration into commercial products or services
- Internal business use
- Revenue-generating applications
- Providing NGC-based services to customers
For commercial licensing inquiries: licensing@ngc-framework.org
We welcome contributions from researchers, developers, and organizations interested in advancing geometric computation. Please read our Contributing Guidelines and Code of Conduct before submitting.
If you use the NGC Framework in your research or applications, please cite:
Bocker, N. J. (2026). Nested Geometric Computation: A Post-Silicon Computational Paradigm.
NGC Framework. https://github.com/NB11B/NGC-Framework
Priority Date: May 9, 2025.
This is not just another AI framework. This is a fundamental rethinking of what computation is.
By grounding computation in geometry rather than symbols, NGC opens the door to:
- Sovereign AI independent of concentrated supply chains
- Explainable AI where every operation has geometric meaning
- Energy-efficient AI that can run on edge devices
- Verifiable AI for safety-critical applications
- Post-quantum cryptography based on geometric principles
The universe computes through geometry. NGC is the framework for understanding-and harnessing-that computation.
Copyright © Nathanael J. Bocker, 2026. All rights reserved.
Priority Date: May 9, 2025
This repository and all its contents are protected under Title 17 of the United States Code. The concepts, methods, and systems described herein are the subject of pending patent applications in the United States and foreign jurisdictions.
Trademarks: NGC™, PSMSL™, and Leibniz-Bocker Framework™ are trademarks of Nathanael J. Bocker.
For all inquiries: contact@ngc-framework.org
© Nathanael J. Bocker, 2026. All rights reserved.