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

3. Tandem Mass Spectrometry Integration

def ma_from_ms2(spectrum: MS2Spectrum) -> float:
    """Estimate assembly index from fragmentation pattern."""
    fragments = spectrum.peaks
    dag = reconstruct_assembly_dag(fragments)
    return dag.longest_path()

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End-of-Skill Interface

Commands

# Compute assembly index
just assembly-index molecule.sdf

# Validate biosignature threshold
just assembly-validate sample.ms2

# Compare assembly pathways
just assembly-compare mol1.sdf mol2.sdf

Integration with GF(3) Triads

assembly-index (-1) ⊗ turing-chemputer (0) ⊗ crn-topology (+1) = 0 ✓  [Molecular Complexity]

Related Skills

• turing-chemputer (0): Execute chemical synthesis programs
• crn-topology (+1): Generate reaction network topologies
• kolmogorov-compression (-1): Algorithmic complexity baseline

r2con Speaker Resources

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Skill Name: assembly-index Type: Complexity Validator Trit: -1 (MINUS) Color: #2626D8 (Blue)

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 1. Flexibility through Abstraction

Concepts: combinators, compose, parallel-combine, spread-combine, arity

GF(3) Balanced Triad

assembly-index (○) + SDF.Ch1 (+) + [balancer] (−) = 0

Skill Trit: 0 (ERGODIC - coordination)

Secondary Chapters

• Ch4: Pattern Matching
• Ch7: Propagators

Connection Pattern

Combinators compose operations. This skill provides composable abstractions.