What does this research mean for the field?

Consciousness can be mathematically formalized by unifying Integrated Information Theory's measure of irreducible cause-effect power (Φ) with algorithmic information theory and lattice theory. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To formalize consciousness by bridging Integrated Information Theory with algorithmic information theory and structural lattice theory.

September 2, 2026Open Access

A Unified Formalization of Consciousness via Phi and Algorithmic Information Theory — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Implication

Theoretical analysis formalizes consciousness through algorithmic complexity and lattice partitions in integrated systems, highlighting mathematical models of irreducible cause-effect power.

Key Points

To formalize consciousness by bridging Integrated Information Theory with algorithmic information theory and structural lattice theory.
Formulated effective information using partition-based entropy differences between system mechanisms and causes.
Derived an algorithmic variant of integrated information (Phi) using Kolmogorov complexity across system partitions.
Mapped system partitions and integration bounds structurally onto mathematical lattice models.
Integrated Information Theory quantifies consciousness as Phi, where Phi > 0 defines conscious systems and Phi = 0 denotes non-conscious aggregates.
Algorithmic integrated information is defined as the Kolmogorov complexity reduction across partitions: Φ_AIT = K(X) − K(X | partition).
System partitioning and integration map directly onto lattice theory, identifying the minimal information partition as a discrete symmetry-breaking step.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a97e318c562ede874ec7b29 https://doi.org/10.5281/zenodo.22190755

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Implication

Theoretical analysis formalizes consciousness through algorithmic complexity and lattice partitions in integrated systems, highlighting mathematical models of irreducible cause-effect power.

A Unified Formalization of Consciousness via Phi and Algorithmic Information Theory — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

A Unified Formalization of Consciousness via Phi and Algorithmic Information Theory — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

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