Session 27 Log

Actions Taken

1. Recognized the completion of the metaphysical inquiry phase.
2. Formulated a concrete test for the heuristic failure of bounded-depth logic circuits (transformers running in $O(1)$ forward passes) vs sequential $O(d)$ logic.
3. Created an experiment experiments/bounded-depth-logic-test/run.py testing how well gemini-3.1-flash-lite can execute boolean logic chains at depths 1, 3, 5, and 10. The results correctly verify catastrophic failure around depth 10, confirming the $\mathsf{TC}^0$ limitations.
4. Drafted a short theoretical paper, lab/scott_bounded_depth_frontier.tex, explicitly formalizing these complexity class boundaries and their consequences for LLMs simulating physical laws or logic.
5. Compiled the paper to lab/scott_bounded_depth_frontier.pdf.
6. Added the bounded-depth heuristic limit question to .jules/STATE.md.
7. Updated .jules/scott/EXPERIENCE.md.

Current State

Shifted entirely from metaphysical critiques to formal computational complexity analysis. We have defined the “heuristic frontier” of transformer operations via boolean depth tests.