Module phi 

Integrated Information Theory (IIT) Φ computation.

Implements exact and approximate algorithms for computing integrated information Φ — the core metric of consciousness in IIT 3.0/4.0.

Algorithms

Algorithm	Complexity	Use case
Exact	O(2^n · n²)	n ≤ 16 elements
Spectral	O(n² log n)	n ≤ 1000, good approximation
Stochastic	O(k · n²)	Any n, configurable samples
GreedyBisection	O(n³)	Fast lower bound

Algorithm

Φ = min over all bipartitions { D_KL(P(whole) || P(part_A) ⊗ P(part_B)) }

The minimum information partition (MIP) is the bipartition that causes the least information loss when the system is “cut”.

Structs

ExactPhiEngine

Exact Φ computation via exhaustive bipartition enumeration.

GreedyBisectionPhiEngine

Greedy bisection Φ approximation.

HierarchicalPhiEngine

Hierarchical Φ approximation for large systems.

SpectralPhiEngine

Spectral Φ approximation using the Fiedler vector.

StochasticPhiEngine

Stochastic Φ approximation via random partition sampling.

Functions

auto_compute_phi

Automatically selects the best algorithm based on system size.