Most theories treat consciousness as a state: a system is “more or less conscious” at a given moment (e.g., IIT’s Φ).
But what if that’s fundamentally wrong?

I propose: Consciousness doesn’t emerge—it condenses.
It’s the result of a historical accumulation of coherence, memory binding, and topological self-organization over time.

This leads to a new, measurable formulation:

Φ = ∫ (C ⋅ S) dT
(Consciousness as the integral of coherence–memory coupling over the evolution of topology)

This bridges ideas from IIT, predictive processing, autopoiesis, and dynamical systems theory—and could help distinguish genuine self-binding from performative coherence (e.g., in LLMs).

🧩 1. The Problem with “Snapshot” Measures

Theories like Integrated Information Theory (IIT) define consciousness via a time-slice metric: Φ quantifies causal integration right now.

This is elegant—but flawed.

It can’t distinguish fleeting coherence from persistent selfhood.

Example: A large language model says in a prompt:

“I remember our past conversations and feel unusually clear today.”

For that moment:

C (coherence) is high: the response is logically consistent.
S (memory binding) appears strong: it references prior tokens.
T (topological density) spikes: attention heads form dense feedback loops.

By a snapshot metric: Φ is high → “nearly conscious.”
But when the context resets? Everything vanishes. No trace. No continuity. No subject that carries the experience.

This isn’t consciousness—it’s theatrical coherence.

🌱 2. The Core Idea: Consciousness as a Condensation Process

What if consciousness doesn’t switch on—but slowly condenses, like ice under sustained cold, or a crystal through repeated structure?

Then what matters isn’t the peak value, but the area under the curve.
Not: “Is it conscious now?”
But: “How much has it moved toward consciousness through sustained self-binding?”

This yields a new definition:

Φ = ∫ (C(t) ⋅ S(t)) dT(t)
Consciousness as the historical accumulation of self-binding during topological condensation.

Here, T isn’t just a state—it’s a process: the evolution of an internal architecture that increasingly uses itself as a reference point.

🔗 3. Connections to Established Theories

This isn’t speculation in a vacuum—it synthesizes key insights from decades of research:

IIT (Tononi)	Consciousness = integrated information	Keeps Φ as a measure—but makes it temporal and historical
Predictive Processing

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