TF3: Agency as a Second-Order Fixpoint

A domain-independent definition of the agent and its boundary. Triadic Fixpoint Framework, Volume IV (Core), Version 3.0. An agent is defined as a second-order fixpoint: the stable fixed point of an internal predictive model composed with the world-iteration operator of TF2.5. From this follow four structural pillars: persistent memory, an invariant stability functional, a world-modification channel, and a predictive world model. An entity is an agent only if all four hold, yielding a sharp taxonomy of contemporary systems (frozen model, scaffolded agent, test-time-memory model). Utility is narrowed to selective maintenance rather than psychological goalhood. The four pillars are each instantiated against 2024-2026 AI research. The cosmological extension is published separately as a clearly labelled philosophical companion and is not relied upon here.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-16
DOI
https://doi.org/10.5281/zenodo.20720469
Primary Topic
Embodied and Extended Cognition
Type
preprint
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preprint

TF3: Agency as a Second-Order Fixpoint

Roberto Omezzolli
Zenodo (CERN European Organization for Nuclear Research)
Embodied and Extended Cognition
preprint

TF3: Agency as a Second-Order Fixpoint

Roberto Omezzolli
preprint en

Abstract

A domain-independent definition of the agent and its boundary. Triadic Fixpoint Framework, Volume IV (Core), Version 3.0. An agent is defined as a second-order fixpoint: the stable fixed point of an internal predictive model composed with the world-iteration operator of TF2.5. From this follow four structural pillars: persistent memory, an invariant stability functional, a world-modification channel, and a predictive world model. An entity is an agent only if all four hold, yielding a sharp taxonomy of contemporary systems (frozen model, scaffolded agent, test-time-memory model). Utility is narrowed to selective maintenance rather than psychological goalhood. The four pillars are each instantiated against 2024-2026 AI research. The cosmological extension is published separately as a clearly labelled philosophical companion and is not relied upon here.

Zenodo (CERN European Organization for Nuclear Research)
Embodied and Extended Cognition
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