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

cd genetic_engine
pip install -e .

Usage

CLI

# 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

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

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