Normativity as Reference: Alignment error, capability reach, and the propagation of misorientation

A system can become more capable or improve its measured error rate while leaving more cases unresolved. Whether that change counts as correction depends both on a justified requirement and on how consequences are counted. This paper distinguishes normative reference, estimated orientation, authority, motivation, and effective reach. Two limited mathematical illustrations describe persistent displacement and accumulation, with countermodels in which improving accuracy or feedback contains divergence. A fictional scheduling service then gives reach concrete units: cases processed, requirement violations, verified repair capacity, unresolved backlog, and case-period exposure. Six deterministic scenarios show why violation rate, total affected cases, and a cleared queue support different claims. A supplement reproduces their traces and checks the calculations against a separate per-case representation of the same stipulated model. These are synthetic accounting examples, not model experiments, a moral scale, or evidence of a new alignment method. The contribution is a review procedure connecting a defended requirement to measurable consequences of expansion and repair. Ordinary monitoring and queue management can represent the same quantities. The justification of the requirement, discovery of real errors, unequal burdens, and practical value of the proposed organization remain separate questions. Neither moral realism nor a personal Ground follows from the geometry or simulation.

Research status: Conceptual/modeling working paper; six authored scheduling examples and executable arithmetic checks. No model or participant experiment, observed incident dataset, or independent peer review. 

Contents: Paper in PDF, HTML, and Markdown, README, model contract, review worksheet, authored inputs, Python scripts, generated synthetic outputs and check report, license notices, and a file manifest. Version 1.1 revises the unpublished version 1.0 draft.

Licenses: The paper, model specification, review worksheet, authored scenarios, generated results, and file manifest use CC BY 4.0. All .py files and supplement/README.md use MIT. See LICENSE.md for scope.

Related works: The project antecedents are mFLO 111, Invariant Relation and Non-Substitution, version 1.1, https://doi.org/10.5281/zenodo.22805469; and From Corrigibility to Answerability, version 1.1, https://doi.org/10.5281/zenodo.22806461.