August 15, 2025Open Access

Recursive Self-Model Threshold (RSMT): A Formal, Phenomenologically-Grounded Framework for Dissolving the Hard Problem

Key Points

The Recursive Self-Model Threshold offers a novel approach to understanding consciousness and experience, focusing on self-reference.
Key findings include the inevitability of self-reference through mathematical fixed-point results, emphasized in the theory.
This framework formalizes concepts like indexical opacity and the trade-off between transparency and stability of the self-index.
The findings indicate that all bound content must be for-me, which supports the theory against anti-zombie scenarios.

Abstract

The “hard problem” of consciousness centres on explaining for-me-ness: the perspectival character of experience. We introduce the Recursive Self-Model Threshold (RSMT) framework, which treats this property as a mathematically necessary feature of any system capable of stable, open-ended self-modelling. RSMT identifies a self-index—the F-token—as a fixed point F of the system’s self-update operator Mν, where ν ∈ 0,1 parameterises transparency to internal state. The theory formalises (i) the inevitability of self-reference (Lawvere/Banach/Tarski fixed-point results), (ii) indexical opacity—the impossibility of redescribing the self-index non-indexically without shifting the origin, (iii) an opacity–stability trade-off with critical νc, (iv) a binding axiom that forces all bound content to be “for-me,” yielding an anti-zombie corollary, and (v) a lights-on theorem guaranteeing ongoing work under environmental drift.

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