plurigrid 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
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.
- Assembly pathway: Shortest construction sequence
- Copy number threshold: Abundance × complexity = life signal
- Molecular DAG: Directed acyclic graph of substructures
- 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()
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
Skill Name: assembly-index Type: Complexity Validator Trit: -1 (MINUS) Color: #2626D8 (Blue)
ALife atlas
Part of: alife-commons. Family: complexity-measurement. Canonical: assembly-index.