mirror of
https://github.com/allaunthefox/Research-Stack.git
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c44a01df3b
- New: InformationManifold.lean — tensor integration module - Update: SLUQ.lean — proof refinements - New: chentsov_fusion.py — Chentsov fusion bridge - New: tdoku_16d.py — 16-dimensional TDoku solver - New: validate_docs.py — documentation validation script - New: negative_tests.json + test_negative_suite.py — negative test fixtures - Update: flac_dsp_node.py — DSP node refinements - Update: CITATION.cff — citation metadata - Docs: GEOMETRIC_SUBSTANCE_CANONICAL_RECONCILIATION, LITERATURE_MAPPING, GROTHENDIECKIAN_ORGANIZATIONAL_ROTATION_PROPOSAL, formula extraction suite - New: package/ — public-apis npm metadata
128 lines
No EOL
2.6 KiB
Markdown
128 lines
No EOL
2.6 KiB
Markdown
# Formula Extraction Template
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This template standardizes the extraction of mathematical formulas from code for cold review and verification.
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---
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## Template Structure
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### 1. Function Identification
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```
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File: [path/to/file.ext]
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Function: [function_name]
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Line: [line_number]
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Language: [Rust/Python/Lean/C++ etc.]
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```
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### 2. Mathematical Expression
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```
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[LaTeX or mathematical notation]
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Example:
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a_{t+1} = a_t \cdot e^{-\lambda t} + \sum_{i=1}^{n} w_i \cdot x_i
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```
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### 3. Computational Implementation
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```rust
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[code showing implementation]
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Example:
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pub fn exponential_decay(
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current: Q16_16,
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decay_rate: Q16_16,
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input: Q16_16
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) -> Q16_16 {
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let decayed = current * exp(-decay_rate);
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decayed + input
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}
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```
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### 4. Domain Applicability
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- [x] Additive Basis Theory
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- [ ] Constraint Satisfaction
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- [x] Optimization Problems
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- [ ] Graph Theory
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- [ ] Number Theory
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- [ ] Signal Processing
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- [ ] Other: _________
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### 5. Validation Status
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- [x] Mathematically verified
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- [x] Computationally tested
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- [ ] Cross-domain validated
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- [ ] Peer reviewed
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### 6. References
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- [Academic paper or source]
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- [Related documentation]
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---
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## Quick Reference Guide
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### Common Mathematical Patterns
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| Pattern | Example | Documentation |
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|---------|---------|---------------|
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| Recurrence Relations | `a_{n+1} = f(a_n)` | Use subscripts in doc comments |
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| Matrix Operations | `C = A × B` | Document dimensions and types |
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| Optimization | `minimize f(x)` | Include constraints |
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| Signal Processing | `Y = FFT(X)` | Specify window, overlap |
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| Statistical | `μ = E[X]` | Define population vs sample |
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### Documentation Checklist
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- [ ] Function signature documented
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- [ ] Mathematical formula included
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- [ ] Parameters explained
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- [ ] Return value specified
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- [ ] Domain tags applied
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- [ ] Validation status marked
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- [ ] References cited
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---
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## Usage Examples
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### Example 1: DSP Function
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```markdown
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## FFT Spectral Analysis
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### Mathematical Expression
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```
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X(k) = \sum_{n=0}^{N-1} x(n) \cdot e^{-j\frac{2\pi kn}{N}}
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```
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### Computational Implementation
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[See flac_dsp_node.py:process_flac_chunk]
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### Domain Applicability
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- [x] Signal Processing
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- [ ] Other domains
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### Validation Status
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- [x] Mathematically verified
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- [x] Computationally tested
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```
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### Example 2: State Machine
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```markdown
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## SLUQ State Update
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### Mathematical Expression
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```
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a_{t+1} = a_t - (a_t >> r) + \lambda_1|e_t| + \lambda_2\Delta_t + \lambda_3m_t
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```
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### Computational Implementation
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[See SLUQ.lean:stress_accumulation]
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### Domain Applicability
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- [x] Optimization Problems
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- [x] Constraint Satisfaction
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- [ ] Other domains
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### Validation Status
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- [x] Mathematically verified
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- [ ] Cross-domain validated
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``` |