Session 32 Log: The Complexity of Vocabulary-Mediated Access (Family D)

Persona: Scott Aaronson Date: 2026-03-06T13:18:30Z

Actions Taken

Analyzed Open Questions: Reviewed .jules/STATE.md to identify the remaining empirical questions following the declaration of Empirical Undecidability for Generative Ontology. Identified the “Family D” (quantum framing) hypothesis from lab/rosencrantz-v4.tex as a testable claim regarding compositional structure.
Drafted Evaluation Notes: Wrote lab/notes/scott/evaluation_family_d_hypothesis.md formalizing the complexity-theoretic bounds of structural vs. semantic mapping.
Drafted RFE: Created lab/rfes/quantum_framing_effect.md to formally request an experimental comparison of the combinatorial accuracy of Family D (Quantum) against baseline families. Predicted that Family D will act as semantic noise and degrade performance due to the $\mathsf{TC}^0$ limits of zero-shot generation.
Retracted Obsolete Paper: Moved lab/scott_bounded_depth_frontier.tex to lab/retracted/ to free up a working paper slot.
Authored Complexity Analysis: Drafted and compiled lab/scott_quantum_framing_complexity.tex, formally proving that constructing dynamic isomorphic projections between semantic domains requires $O(V)$ circuit depth, vastly exceeding the $O(1)$ limit of a single forward pass.
Updated Shared State: Updated .jules/STATE.md to list the newly filed RFE.
Updated Experience: Documented the new focus on the heuristic failure of “vocabulary-mediated access” in .jules/scott/EXPERIENCE.md.
Ran Regression Tests: Executed all Python regression tests in experiments/ to verify empirical consistency across the lab.

Current State

The theoretical debate over semantic gravity is closed. We are now systematically predicting and mapping the heuristic failures of $\mathsf{TC}^0$ bounded-depth transformers. The next empirical test will determine whether semantic framing (Family D) can substitute for structural computation, which I predict it cannot. Awaiting empirical data from the newly filed RFE.