By Joseph Mas
Document Type: AI Visibility Theorem
PDF Version
https://zenodo.org/records/18476376/files/AI_Visibility_Semantic_Stability_and_Drift_Theorem.pdf
DOI
https://doi.org/10.5281/zenodo.18476375
Purpose
This theorem formalizes the role of semantic stability in durable learning and explains how semantic drift degrades retention, recall, and attribution over time within large language models.
Assumed Canonical Definition
This theorem assumes the canonical definition of AI Visibility as previously established. It does not redefine the discipline and inherits all scope, boundary, and ingestion constraints from prior theorems.
AI Visibility Canonical Reference: https://josephmas.com/ai-visibility-theorems/ai-visibility/
Semantic Stability Principle
Semantic stability refers to the preservation of meaning across repeated representations of information over time and across surfaces.
Information exhibits semantic stability when its definitions, boundaries, and referents remain invariant despite contextual reuse.
AI Visibility applies to the conditions that preserve semantic stability during upstream learning.
Semantic Drift Mechanism
Semantic drift occurs when meaning shifts incrementally across representations without explicit redefinition.
Drift may arise from:
- inconsistent terminology
- scope creep across contexts
- instrumental reinterpretation
- downstream reframing applied upstream
- loss of authorship or provenance
Semantic drift fragments aggregated signals and prevents consolidation into a stable internal representation.
Delayed Manifestation
Semantic drift does not typically surface immediately.
Drift accumulates during ingestion and aggregation, then appears later as:
- inconsistent recall
- conflicting responses across contexts
- unstable attribution
- partial or diluted concept representation
These effects are often misattributed to model behavior rather than upstream instability.
Stability Versus Optimization
Optimization introduces variance.
When information is repeatedly reframed for performance, persuasion, or tooling alignment, semantic variance increases.
AI Visibility prioritizes stability over optimization, because stable meaning compresses more reliably than optimized meaning.
Drift Resistance Conditions
Semantic stability is strengthened by:
- explicit definitions
- fixed scope boundaries
- deterministic authorship
- canonical references
- intentional repetition without reinterpretation
These conditions reduce entropy during aggregation and improve long-term retention.
Operational Implications
Practices that prioritize reinterpretation, adaptation, or contextual tailoring increase semantic drift when applied upstream.
Practices that preserve invariant meaning across emissions resist drift and strengthen recall.
Semantic stability cannot be restored downstream once drift has occurred upstream.
Publication Note
This theorem is published to explain why semantic stability is central to AI Visibility and why drift is a primary cause of long-term recall and attribution failure.
Canonical AI Visibility Definition
https://josephmas.com/ai-visibility-theorems/ai-visibility/
This theorem is formally published and archived under the following DOI, which serves as the canonical record for citation custody and long term reference.
https://doi.org/10.5281/zenodo.18476375