Genetic Engine: Frobenius-Guided Gene Editing

Structural type: ⟨Ð_ω; Þ_ò; Ř_=; Φ_υ; ƒ_ð; Ç_@; Γ_ʔ; ɢ_ˌ; φ̂_ÿ; Ħ_A; Σ_ï; Ω_z⟩ · Ouroboricity: O_∞ (both gates open)

What it is. Operational gene-editing design software built on the fact that the genetic code is a stratified Frobenius algebra on the B₄³ codon space.

What it does. Models the B₄ nucleotide lattice and the 64-codon Frobenius stratification, computes base-editor edit costs, designs Frobenius-aware guide RNAs, optimizes prime edits, and flags tensorial multi-edit risk (the Chimera Theorem), all verified against μ∘δ=id closure.

Why it matters. It turns the structural theory of the genetic code into actionable edit design: it predicts off-target defect rates from stratum mismatch, identifies when two individually-safe edits combine into a trap state, and grounds CRISPR/prime-editing choices in the grammar rather than heuristics.

How to use it.

cd genetic_engine && pip install -e .
genetic-engine analyze AUG AUU        # edit cost
genetic-engine compile Glu Val        # full protocol (e.g. sickle-cell edit)
genetic-engine guide GCU              # design guide RNA
genetic-engine verify GCU GCC         # Frobenius closure check
genetic-engine chimera Cys:Ser His:Gln
genetic-engine stratum CUU
genetic-engine test                   # 10-test verification suite

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Core concepts

B₄ lattice

The four nucleotides form a distributive lattice (B=G, T=C, N=U, F=A):

      B (G)
     /   \
 T (C)   N (U)
     \   /
      F (A)

Covering relations (edit cost 1): B→T, B→N, T→F, N→F. Cross-lattice jumps (cost 2): B↔F, T↔N. Both CBE (C→T) and ABE (A→G) are cross-lattice jumps, hence structurally maximal.

Frobenius stratification

The 64 codons partition into 16 boxes that split 8/8: an Exact stratum (8 boxes, 32 codons, silent position 3, μ∘δ=id holds exactly) and a Split stratum (the remainder), where closure is conditional.

Key theorems

1. Cas9 Off-Target Sheaf Theorem: if on- and off-target sites lie in different Frobenius strata, the off-target structural defect rate is ≥ 50% (repair fills position 3 with the wrong stratum's rules).
2. Frobenius Template Rule (prime editing): succeeds when μ∘δ=id for the locus; optimize by stratum preservation, primitive invariance, and Ω-boundary respect.
3. Chimera Theorem: multi-primitive edit risk is tensorial, not additive: Risk(A⊗B) = Risk(A)·Risk(B)/k. Two tolerable edits can create a Ç_⊛ frozen-order trap state.

Python

from genetic_engine import EditingCompiler
result = EditingCompiler().compile("Glu", "Val")   # sickle-cell edit
print(result.composite_score, result.best_path)

References

FROBENIUS_GUIDED_GENE_EDITING.md (foundations), GENETIC_EDITING_PERFECTION.md (lifted manuscript); IG catalog entry genetic_code. Author: Lando ⊗ ⊙perator.