Identify the global cognitive-hierarchy mixture depth for human convention profiles

Determine the cognitive-hierarchy depth parameter that best reproduces the full human convention-gap profile as a mixture of the five off-belief-learning level profiles, or establish why no such finite depth is identifiable when human-specific categories exceed every available agent level.

Background

The paper fits human category gaps as a mixture of the five off-belief-learning profiles, with a single parameter controlling the distribution over reasoning levels. The global fit places the depth parameter at the edge of the search grid rather than yielding an interior estimate.

The authors attribute this failure of identification to categories in which human gaps exceed all five agent profiles, so no mixture of the available levels can reproduce those observations. The question therefore remains unresolved for the full profile, although depth can be estimated on the subset of conventions shared by humans and agents.

References

What mixture of levels best reproduces the human profile? is the parametric question, and its depth parameter is unidentified globally because these categories exceed the entire basis: no mixture of levels reaches them, so the fit pushes \tau to the grid edge and the flags fire.

— What and Where in Identifying and Quantifying Conventions in Humans and AI Agents  (2610.20205 - Fukushima et al., 14 Oct 2026) in Appendix, Section “Depth of reasoning,” subsection “What is and is not identified”