HDT²: Pilot v2 A Follow-On Research Program Derived from HDT² Pilot v1

HDT² (Holistic Data Transformation Theory) introduces a portable, entropy-banded diagnostic framework for assessing reasoning stability in large language models. The methodology centers on the hypothesis that token-level Shannon entropy encodes a cross-model structure—an “uncertainty geometry”—that can be aligned via unsupervised quantile matching. This pilot study establishes both positive and negative evidence: (i) successful entropy-band alignment enabling stable-reasoning detection in compatible models, and (ii) clear empirical boundaries where alignment fails, revealing architectural constraints on portability. This dual evidence grounds ψ* as a scientifically falsifiable substrate for reliability diagnostics and control-theoretic actuation. HDT² Pilot v2 is the formal follow-on to HDT² Pilot v1, extending the work from feasibility testing to the study of epistemic regimes in large language models.Pilot v1 established that token-level Shannon entropy forms stable, measurable geometric patterns within a model and that these patterns can be partitioned into behavioral regimes—stable, ambiguous, and underdetermined. It also showed that entropy geometry is model-dependent, with some models aligning cleanly and others diverging. Pilot v2 builds directly on those findings. Its focus is to characterize these regimes more precisely, examine when regime geometry is shared across models, and explore how regime transitions can serve as control signals for adaptive system behavior. This includes routing, escalation, abstention, hedging, and tool invocation. HDT² Pilot v2 remains exploratory. It raises more questions than it answers. The goal is to map the structure we can measure, identify the structure we do not yet understand, and invite collaborators to help study the dynamics of uncertainty fields in LLMs. The full Pilot v2 technical statement is included in this versioned upload.