assembly-index

Assembly Index Skill: Molecular Complexity Validation

Status: ✅ Production Ready Trit: -1 (MINUS - validator/constraint) Color: #2626D8 (Blue) Principle: Complexity threshold → Life signature Frame: Assembly pathways with minimal step counting

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Overview

Assembly Index measures molecular complexity by counting the minimum number of joining operations needed to construct a molecule from basic building blocks. Molecules with assembly index > 15 are biosignatures—too complex for random chemistry.

1. Assembly pathway: Shortest construction sequence
2. Copy number threshold: Abundance × complexity = life signal
3. Molecular DAG: Directed acyclic graph of substructures
4. Mass spectrometry integration: MA(m/z) measurement

Core Formula

MA(molecule) = min |steps| to construct from primitives
Life threshold: MA > 15 with copy_number > 1

def assembly_index(molecule: Molecule) -> int:
    """Compute minimum assembly steps via dynamic programming."""
    substructures = enumerate_substructures(molecule)
    dag = build_assembly_dag(substructures)
    return shortest_path_length(dag, source="primitives", target=molecule)

Key Concepts

1. Assembly Pathway Enumeration

class AssemblyPathway:
    def __init__(self, molecule):
        self.mol = molecule
        self.fragments = self.decompose()
    
    def decompose(self) -> list[Fragment]:
        """Find all valid bond-breaking decompositions."""
        return [split for split in self.mol.bonds 
                if split.yields_valid_fragments()]
    
    def minimal_pathway(self) -> list[JoinOperation]:
        """DP over fragment DAG for minimum steps."""
        memo = {}
        return self._dp_assemble(self.mol, memo)

2. Copy Number Amplification

def is_biosignature(molecule, sample) -> bool:
    ma = assembly_index(molecule)
    copies = sample.count(molecule)
    # Life creates copies of complex molecules
    return ma > 15 and copies > 1