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Core Concepts
Fundamental Principles
🎯 Single Source of Truth
Lean 4 is the authoritative source of truth for all formal claims. Every mathematical statement, algorithm, and system invariant must be expressible and verifiable in Lean 4.
🔢 Fixed-Point Arithmetic
All computation uses Q16.16 fixed-point arithmetic with Q0.64 scalars as the universal interface. This ensures deterministic behavior across all computational substrates.
📊 Receipt-Bounded Transformations
Every transformation must generate a receipt that proves:
- What changed
- What survived
- What was lost
- What it cost
- At what scale
- What receipt proves it
System Architecture
🏗️ Layer Model (USTSM)
The Universal Substrate Topological State Machine consists of 7 layers:
| Layer | Name | Domain | Status |
|---|---|---|---|
| L0 | Primordial | Pure math, fixed-point arithmetic | ✅ Implemented |
| L1 | Geometric | Shape-aware topology | 🟡 Partial |
| L2 | Biological | Genetic codes, spiking neurons | 🟡 Speculative |
| L3 | Thermodynamic | Energy-aware quality | 🟡 Speculative |
| L4 | Security | Attack-aware gating | 🟡 Partial |
| L5 | Semantic | Meaning-aware filtering | 🟡 Partial |
| L6 | Meta | Self-aware adaptation | 🟡 Partial |
🔄 Transformation Pipeline
Lean Formal Proof → Receipt Generation → Hardware Extraction → Validation
Key Components
📐 Mathematical Foundations
- Q16.16 Fixed-Point Arithmetic - Core number system
- Braid Fields - Topological data structures
- PIST/DIAT Shell - Computational framework
- SSMS_nD - n-dimensional state machine
🔐 Security & Safety
- AngrySphinx - Exponential proof of work
- FAMM - Frustration-avoiding memory management
- ASIC Topology - Attack-aware system design
🧬 Biological Computing
- Genetic Code Tables - 30+ genetic code implementations
- Spiking Dynamics - Izhikevich neuron models
- Genomic Compression - DNA-based data compression
⚡ Hardware Extraction
- FPGA Implementation - Field-programmable gate arrays
- ASIC Design - Application-specific integrated circuits
- Hardware Receipts - Physical validation receipts
Research Methodology
🎯 Attack Plans
Structured research initiatives that follow the pattern:
- Assessment - Current state analysis
- Implementation - Formal proof development
- Verification - Receipt generation and validation
📊 Milestones
Time-bound objectives with clear success criteria:
- Burgers 4-Theorem Attack Plan - Active milestone
- Eigensolid Convergence - Core compression theorem
- Receipt Invertibility - Bijective encoding theorem
🔍 Conjectures
Research hypotheses requiring formal proof:
- Sidon Field Conjectures - Combinatorial optimization
- Mass Number Admissibility - Number theory constraints
- Hyperfluid Density Profiles - Physical modeling
Quality Assurance
✅ Formal Verification
- Lean Compilation - All code must compile without errors
- Proof Checking - All theorems must have valid proofs
- Type Safety - Strong typing prevents runtime errors
🧾 Receipt Validation
- Schema Compliance - Receipts must follow defined schemas
- Hash Verification - Cryptographic integrity checks
- Reproducibility - Results must be reproducible
🔬 Experimental Validation
- Numerical Testing - Computational experiments
- Hardware Testing - Physical implementation validation
- Cross-Validation - Multiple verification methods
Terminology
📚 Glossary
- Sidon Label - Address from a set with unique pairwise sums
- BraidStorm - 8-strand braid topology for compression
- Eigensolid - Converged, stable state of braid crossing loop
- Yang-Baxter - Braid relation defining order invariance
- GCL - Genetic Code Language
- AVM - Adaptive Virtual Machine
- TSM - Topological S3C Manifold
🏷️ Tag System
#layer-L0through#layer-L6- Layer classification#formal-proof- Lean formal proofs#receipt- Receipt documents#attack-plan- Research attack plans#milestone- Project milestones#conjecture- Research conjectures
Related Concepts
🔗 Cross-References
- Formal Methods - Mathematical verification techniques
- Topology - Mathematical study of shapes and spaces
- Information Theory - Quantitative information analysis
- Quantum Computing - Quantum mechanical computation
- Neural Networks - Machine learning architectures
📖 External Resources
#core-concepts #research-stack #formal-methods