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 (May 1, 2026) introduces langualgebra as a candidate notational refinement for the framework's language-math formulas. Langualgebra proposes that variable slots in productive language formulas — the operators that govern transformation, composition, and inference at the linguistic level — be written using numerals rather than letters or descriptive words, on the grounds that numerals occupy a more isolated region of LLM token space and do not collide with the lexical roles of letter-variables embedded in language. V4 adds Section 9, which defines langualgebra, positions it against prior art (de Bruijn 1972; Montague semantics; Grammatical Framework; the McCoy/Linzen syntactic-transformation literature; Symbol Tuning; Procedural Pretraining), states the empirical hypothesis, specifies an experimental protocol for testing it, and gives explicit falsification conditions. Langualgebra is presented as a candidate, not a declared standard: until controlled training experiments are run, the framework's existing formulas continue to use the conventions established in Sections 1–8. Sections 1–8 are substantively unchanged. V4 was prepared in dialogue with Claude (Anthropic), with bounded prior-art review conducted in the same session.