Canonicalizing the Wrong Thing: Quotient-Aligned Gauge Fixing for Semantic Representations

Abstract

This preprint studies when prediction-equivalent representations are interchangeable under a declared downstream interface. It formalizes quotient-aligned representative selection, shows that factor-balance invariants can fail to distinguish operationally different coordinates, and reports local conservation-law audits in specified factorized settings. Structural and neural experiments compare interface-matched gauge fixing with canonicalizers that optimize different criteria. Under stated linear-model assumptions, an interface-angle residual characterizes the excess error of restricted one-module adaptation; frozen vision features and GPT-2 XL editing provide diagnostics beyond that exact setting. This upload provides a public, non-anonymous rendering of the complete manuscript from the frozen v12 supplement, together with an optional manuscript-source archive. The scientific text is unchanged by this formatting conversion. Separate later revisions of Sections 1-3 and subsequent abstract edits have not been merged into this upload. The first public version was deposited on August 9, 2026, at https://doi.org/10.5281/zenodo.21858138; that earlier date applies to the contents of that earlier version. Version 2 adds an AI usage statement to both documents; see the footnote on the first page.