A Working Language-Math Framework for Detecting Drift and Vacuum in AI-Affected Definitions

This working framework proposes a compact language-math notation for identifying drift and vacuum in definitions affected by the advent of AI. It introduces a reusable structure for distinguishing a general concept or class/label, a specific instance of that concept, an AI-collaborative class/label, and a specific AI-collaborative instance. The framework is designed to clarify when existing definitions no longer fully hold, when human-only assumptions persist unnoticed, and when new labels are required for outputs achieved through or within human collaboration with AI. Pattern in DRIFT:The formula does not just detect drift. It reveals the directionality of drift — how different concepts deform under AI conditions and what kind of conceptual failure is occurring. Pattern in VACUUM:The formula reveals that vacuums are not just missing words. They are structural absences — places where language cannot extend because its underlying assumptions prevent it. The vacuum is not an accident of vocabulary. It is a boundary condition of the human self-concept. Other frameworks ask: What can AI do?This framework asks: What happens to our words when AI does what it does? It reveals that: 1. Drift is not always gradual. Sometimes it is abrupt — a word's meaning can shift or collapse quickly under new conditions. 2. Vacuums grow. As AI capability expands, the space of what cannot be cleanly named also expands. 3. Drift and vacuum interact. When systems resist updating definitions, unresolved cases accumulate outside the language. 4. Some concepts may be unextendable. Certain terms resist incorporation into AI-collaborative forms without losing coherence. This is an early-stage working framework (v0.2). It is intended as a diagnostic tool for examining how language, classification, and meaning evolve under human-AI collaboration.An accompanying worked example applies the framework to INVENTION / INVENTIONAIVersion 3 (April 27, 2026) adds Section 7 (Conceptual Lineage), Section 8 (Positioning and Bounded Novelty), and Appendix A (Bounded Prior-Art Review and Positioning Notes), plus a front-loaded terminology discipline block and a status note. Sections 1–6 are substantively unchanged except for an acknowledgment note at 1.4 citing Bratman's joint-action lineage. v3 was prepared in dialogue with Claude (Anthropic) and ChatGPT (OpenAI), with bounded prior-art review and merge review conducted in the same session. Version 4.4 (May 2, 2026) clarifies Formula 001 as the framework’s foundational class-instance / AI-involvement formula, separates the primary type-preservation hypothesis from the downstream training-ergonomics conjecture, fixes the letter baseline, sharpens falsification conditions, and clarifies the status of numeral notation as provisionally adopted and empirically testable.