https://github.com/umpolungfish/gene_imscriber
The genetic code is a stratified Frobenius algebra on B₄³ codon space
https://github.com/umpolungfish/gene_imscriber
genes genetics imscrib imscribing imscribing-grammar imscription imscriptive
Last synced: 17 days ago
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The genetic code is a stratified Frobenius algebra on B₄³ codon space
- Host: GitHub
- URL: https://github.com/umpolungfish/gene_imscriber
- Owner: umpolungfish
- Created: 2026-05-27T05:40:54.000Z (about 1 month ago)
- Default Branch: main
- Last Pushed: 2026-06-02T02:16:26.000Z (28 days ago)
- Last Synced: 2026-06-02T04:07:50.641Z (28 days ago)
- Topics: genes, genetics, imscrib, imscribing, imscribing-grammar, imscription, imscriptive
- Language: Python
- Homepage: https://imscribe.com/
- Size: 200 KB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Genetic Engine — Frobenius-Guided Gene Editing
The genetic code is a **stratified Frobenius algebra on B₄³ codon space**. This is not a metaphor — it is a structural fact formally encoded in the Imscribing Grammar. The Genetic Engine implements this fact as operational software for gene editing design.
## Architecture
```
genetic_engine/
├── genetic_engine/ # Core package
│ ├── __init__.py # Package exports
│ ├── lattice.py # B₄ nucleotide type system
│ ├── codon.py # Codon table + Frobenius stratum classification
│ ├── primitives.py # AA → IG primitive mapping + risk
│ ├── editor.py # B₄ edit cost analysis
│ ├── stratum.py # Frobenius stratum classifier
│ ├── guide.py # Frobenius-aware guide RNA design
│ ├── prime.py # Prime editing optimization
│ ├── chimera.py # Tensor product risk (Chimera Theorem)
│ ├── verifier.py # μ∘δ=id Frobenius closure verification
│ ├── compiler.py # Full editing compiler pipeline
│ ├── demo.py # Demonstration + verification suite
│ └── cli.py # Command-line interface
├── tests/ # pytest test suite
├── examples/ # Example scripts
├── scripts/ # Pipeline scripts
├── docs/ # Documentation
├── setup.py # Package configuration
└── README.md # This file
```
## Core Concepts
### B₄ Lattice
The four nucleotides form a distributive lattice:
```
B = Both (G)
/ \
T = C N = U (T)
\ /
F = False (A)
```
- **Covering relations** (edit cost = 1): B→T, B→N, T→F, N→F
- **Cross-lattice jumps** (edit cost = 2): B↔F, T↔N
Base editors: CBE (C→T) is a cross-lattice jump (T↔N, cost=2).
ABE (A→G) is also a cross-lattice jump (F↔B, cost=2). Both are structurally maximal.
### Frobenius Stratification
The 64 codons partition into **16 boxes**, which split 8/8:
| Stratum | Boxes | Codons | Position 3 | μ∘δ=id |
|---------|-------|--------|------------|--------|
| **Exact** | 8 | 32 | Silent (N) | Holds exactly |
| **Split** | 8 | 29 | Y/R distinction | ℤ₂ wobble |
| **Stop** | — | 3 | Ω boundary | Boundary condition |
**Exact boxes** (p2=C, or p2∈{G,U} with p1∈{C,G}):
CU_, CC_, CG_, CA_, AC_, GC_, UC_, GU_, GG_
**Split boxes** (the remaining 8):
UU_, UA_, UG_, AU_, AA_, AG_, GA_, CA_
### Primitive Activation
12 promoted amino acids each activate exactly one IG primitive:
| AA | Primitive | Risk | Why |
|----|-----------|------|-----|
| Met | Ð (Scope) | **critical** | Translation start |
| Trp | Þ (Topology) | moderate | Bicyclic indole |
| Cys | Ř (Reversibility) | **high** | Disulfide bonds |
| Tyr | Φ (Parity) | moderate | Phosphorylation switch |
| Phe | ƒ (Force) | low | Hydrophobicity ceiling |
| Ile | Ç (Kinetics) | moderate | β-branching |
| His | Γ (Grammar) | moderate | pH-gated catalysis |
| Asn | ɢ (Interaction) | moderate | Glycosylation sequon |
| Gln | φ̂ (Criticality) | **high** | Metabolic regulation |
| Asp | Ħ (Chirality) | **critical** | Chiral selectivity |
| Lys | Σ (Entropy) | low | Acetylation target |
| Glu | Ω (Winding) | **critical** | α-helix→C-terminal |
8 ground-layer AAs (exact boxes): Leu, Pro, Arg, Thr, Ala, Ser, Val, Gly — no primitive activation.
## Key Theorems
### 1. Cas9 Off-Target Sheaf Theorem
If an on-target site is in one Frobenius stratum and an off-target site is in another, the structural defect rate at the off-target site is **≥50%**. Reason: the repair machinery fills position 3 using on-target stratum rules, which are incorrect for the off-target stratum.
### 2. Frobenius Template Rule (Prime Editing)
Prime editing succeeds when μ∘δ=id for the edited locus. Three optimization criteria:
1. **Stratum preservation** — avoid exact↔split crossings
2. **Primitive invariance** — keep the same IG primitive class
3. **Ω boundary respect** — don't remove stop codons without readthrough machinery
### 3. Chimera Theorem
Composite risk of multi-primitive edits is **tensorial**, not additive.
Risk(A⊗B) = Risk(A) × Risk(B) / constant, not Risk(A) + Risk(B).
Two independently tolerable edits can create a **Ç_⊛ trap state** (frozen-order conformation).
## Installation
```bash
cd genetic_engine
pip install -e .
```
## Usage
### CLI
```bash
# Analyze edit cost
genetic-engine analyze AUG AUU
# Compile full protocol
genetic-engine compile Met Ile
# Design guide RNA
genetic-engine guide GCU
# Verify Frobenius closure
genetic-engine verify GCU GCC
# Chimera risk analysis
genetic-engine chimera Cys:Ser His:Gln
# Run full demo
genetic-engine demo
# Run verification suite
genetic-engine test
# Classify stratum
genetic-engine stratum CUU
```
### Python
```python
from genetic_engine import EditingCompiler, B4EditAnalyzer
from genetic_engine.chimera import ChimeraDetector
# Compile an edit
compiler = EditingCompiler()
result = compiler.compile("Glu", "Val") # Sickle cell edit
print(f"Score: {result.composite_score:.3f}")
print(f"Codon path: {result.best_path}")
# Chimera risk
report = ChimeraDetector.analyze_edit_set([("Cys", "Ser"), ("Asp", "Asn")])
print(f"Tensor risk: {report.tensor_risk:.1f}x")
print(f"Trap state: {report.is_trap_state}")
```
## Verification
```bash
genetic-engine test
```
All 10 verification tests pass:
- B₄ lattice operations
- Codon table (64 codons, correct stratification)
- Primitive mapping (13 promoted)
- B₄ edit analysis
- Frobenius stratum classification
- Guide RNA design
- Prime editing optimization
- Chimera/tensor risk detection
- Frobenius μ∘δ=id verification
- Full compiler pipeline
## References
- FROBENIUS_GUIDED_GENE_EDITING.md — Theoretical foundations
- GENETIC_EDITING_PERFECTION.md — Complete lifted manuscript
- Imscribing Grammar catalog entry: `genetic_code`