L1 Paper 6 Longitudinal Goldstone Equivalence

This paper establishes the equivalence between longitudinal gauge modes and Goldstone descriptions as a structural consequence of admissibility and standing preservation, rather than as a dynamical approximation or symmetry argument. The analysis is eliminative: it shows that once chiral consistency, identity persistence, and local admissible interaction are fixed, longitudinal and Goldstone representations cannot remain distinct without introducing redundant or inadmissible structure. The equivalence is classified as representational rather than ontic. Treating longitudinal and Goldstone modes as separate physical entities is shown to either duplicate enforcement, violate closure under composition, or rely on illicit scope transport between representational levels. As a result, their equivalence emerges as a forced bookkeeping identification within any admissible local skin. The paper introduces no new primitives and provides no mechanisms or procedures. Its contribution is boundary-setting: it clarifies why longitudinal–Goldstone equivalence must hold in admissible descriptions, and why attempts to treat it as optional or approximate are structurally unsound.