TONONI, GIULIO — INTEGRATED INFORMATION THEORY (IIT), 2004 onward
Primary citation: Tononi, G. (2004). "An information integration theory of consciousness." BMC Neuroscience 5:42. Subsequent versions: IIT 2.0 (2008), IIT 3.0 (Oizumi, Albantakis, Tononi 2014), IIT 4.0 (Albantakis, Barbosa, Findlay, Grasso, Haun, Marshall, Mayner, Zaeemzadeh, Boly, Juel, Sasai, Fujii, David, Hendren, Lang, Tononi 2023). Paraphrase below is from the IIT literature and the Wikipedia summary; quotations are not reproduced verbatim.

WHAT PHI (Φ) IS

Φ ("big phi") is IIT's proposed measure of integrated information: the amount of information generated by a system, ABOVE AND BEYOND the information generated independently by its parts. Operationally, Φ is computed by partitioning the system in every possible way, measuring how much the system's cause-effect structure is reduced by each partition, and taking the minimum (the "minimum information partition," MIP). High Φ = the whole specifies more than the sum of its parts.

Small phi (φ) is the analogous quantity for individual mechanisms (subsets of elements specifying cause-effect repertoires within the system).

THE AXIOMS (IIT 3.0 / 4.0 STATEMENT)

IIT begins from phenomenological axioms — claims about what experience IS — and then posits postulates that any physical substrate of experience must satisfy.

 1. INTRINSIC EXISTENCE (Intrinsicality). Experience exists for the experiencing system itself, from its own intrinsic perspective, independent of external observers. Postulate: the substrate must have cause-effect power upon itself.
 2. COMPOSITION. Experience is structured: it is composed of distinctions and relations among them (e.g., a blue book on a brown table contains "blue," "book," "blue book," "table," "on," etc.). Postulate: the substrate must support a structured set of mechanisms.
 3. INFORMATION. Experience is specific — each experience is THIS experience, differing from countless others it could have been. Postulate: the substrate must specify a particular cause-effect structure.
 4. INTEGRATION. Experience is unified — it cannot be decomposed into independent components. Postulate: the cause-effect structure must be irreducible to its parts (φ > 0; system-level Φ > 0).
 5. EXCLUSION. Experience is definite: it has these contents and not others, at this spatiotemporal grain and not another. Postulate: only the maximally irreducible cause-effect structure (the "complex" with maximum Φ) is conscious; overlapping candidates are excluded.

WHAT IIT ACTUALLY CLAIMS

IIT claims an IDENTITY between an experience and a maximally irreducible cause-effect structure ("Φ-structure"). It is a substrate-neutral theory: in principle, any system whose cause-effect structure satisfies the postulates is conscious to the degree given by its Φ. IIT explicitly does NOT claim:
 - that high-Φ systems are "creating reality";
 - that consciousness selects which physical events occur;
 - that the universe has a privileged observer or generator;
 - that Φ is a measure of cosmological influence, agency, or downward causation onto physics.

IIT is also operationally hard: exact Φ is computationally intractable for any non-toy system, and proxies (e.g., perturbational complexity index, PCI) are loosely motivated approximations, not Φ itself.

COMMON MISREADINGS RELEVANT TO BIT CREATION THEORY

If a theory invokes Φ as a "creation force," a "selection operator," or an "ontological generator," it is not citing IIT — it is borrowing the symbol. IIT's Φ is:
 (a) intrinsic to a substrate (it does not act on anything outside that substrate);
 (b) a quantity, not an agent;
 (c) computed AFTER the cause-effect structure is fixed, not an input that REDEFINES the cause-effect structure;
 (d) invariant in the sense that IIT does not assign Φ a role in determining which microphysical events occur — physics still does that.

Therefore: any claim of the form "high-Φ observers are required for X to happen at the physical level" is an addition to IIT, not a consequence of it, and inherits none of IIT's evidential support. The empirical case for IIT (PCI in disorders of consciousness, posterior hot zone studies, etc.) does not transfer to such an addition.
