Selective Transcription: A Principle for Classical Observability of Quantum Structure Under Noise

This archive contains version 1.1 of the third paper in a coherent three-paper research trilogy examining how quantum structure is reflected—or fails to be reflected—in classical measurement statistics obtained from noisy quantum systems. The paper introduces the Principle of Selective Transcription, which explains when quantum structural properties can be classically observable under noise. Classical observability is formalised as a pipeline-relative, operational notion, determined by the combined action of the noise channel, the measurement basis, and the classical feature used to summarise outcomes. Compatibility with this transcription pipeline is identified as a necessary condition for robust classical observability. On this basis, the paper introduces a taxonomy of transcribability, classifying quantum structure as robustly transcribable, fragilely transcribable, or intrinsically invisible relative to a given pipeline. The framework explains why different classical features fail in a consistent and predictable order as noise increases, and why this ordering can reverse under changes of measurement basis. The work synthesises and explains the empirical results of the first two papers in the trilogy, accounting for conditional survival of structure, feature-dependent collapse, basis-dependent blindness, and regimes of fundamental diagnostic invisibility. The framework is illustrated by a minimal analytical example (a two-qubit Bell state) and supported by a targeted numerical confirmation demonstrating basis-dependent reversal of feature collapse ordering. This paper serves as the conceptual capstone of the trilogy. It does not propose new reconstruction methods, learning algorithms, or universal noise theorems. Instead, it provides an explanatory framework clarifying the scope and limits of classical access to quantum structure in noisy systems. Version note: Version 1.1 incorporates clarified definitions, softened necessity-only claims, expanded contextual positioning, and minor stylistic corrections following detailed internal and external review.