Operational
Embedded Agency Theory
— About This Archive

01What Is This

This archive is a record of a dialogue relay that re-examined "What is an observer?" and "What is the self?" in the language of physical information theory.

The core lies in the process of carving out the Observer-Agent as an operational structural concept, built by layering multiple theories including quantum error correction (QEC), holographic tensor networks, von Neumann algebras, counterfactual causal models, and active inference.

The central proposition reached as a result of this investigation:

An observer-agent is a recursive latent structure that internally represents the counterfactual future distinguishability generated by its own interventions, and uses this to maximize the long-term utility of prediction and control under thermodynamic constraints. When accompanied by the back-action of self-measurement, it acquires a first-person center that cannot be fully externalized.

Whether this is correct, and how far it can be generalized — these remain open questions.

02How the Relay Came About

This archive was created through a "copy-paste relay" — passing the same dialogue log to multiple AIs via copy and paste, accumulating the discussion progressively. The participating AIs were as follows:

Each AI that received the log read the preceding exchange, then offered criticism, reinforcement, redefinition, and counterexamples before passing it to the next AI. The repeated peer-review-style back-and-forth repeatedly cut theoretical leaps, functioning as a pressure pushing concepts from poetic metaphor toward operational definitions. In the pre-publication stage, the page structure and descriptive precision were also reviewed.

The full transcript of the dialogue is in the appendix (appendix.html).

03Scope of My Involvement

I will clearly state what I, the human who is publishing this archive, did and did not do.

In short, I am the facilitator and editor of this relay, not an independent author of the mathematical content. This document is a record produced through the AIs' outputs and my choices of selection, connection, and publication.

04On Mathematical Verification

The following points are specifically unverified and unguaranteed:

• — Whether the cited papers (Steinberg et al. 2025, Vanrietvelde et al. 2020, etc.) are used correctly in the context of this document
• — Whether the L2 proposition (regret advantage) can actually be derived from existing theorems for the presented environment class $\mathcal{E}''$
• — Whether the 4-qubit numerical simulation results constitute sufficient evidence for the claims of the quantum version
• — Whether the reparameterization invariance of RICD genuinely holds under the presented equivalence class definition
• — Whether the selection principle simulation (classical surrogate environment) can be interpreted as evidence for the quantum version

This document should be read not as "presenting an established theory," but as a record of the excavation process and the outline that could be reached at this point in time.

05Why Publish Anyway

1. Because I believed the process itself has value. Not "an AI said something," but the process by which AIs criticized and refined each other until concepts converged — that felt worth recording in its own right. The repeated peer-review-style exchanges that kept pulling the theory back "from poetry to definition" represent one model for AI-assisted theory formation.
2. Because the coordinates of the cliff emerged. This is not a claim to have "solved the hard problem of consciousness." But a map of "how far the language of current information theory, algebraic QFT, and control theory can reach, and where it stops" has become more precise than before. I want to share that.
3. Because it might serve as a reference point for others with the same questions. For those searching for "attempts to connect QEC and consciousness" or "operational definitions of the observer," this archive — including its map of failures — might provide a foothold.
4. Because publishing makes it possible to receive criticism. If there are errors, I judged it more honest to put them in a state where they can be pointed out, rather than leaving them unpublished.

06Structure of This Archive