Locality and Symmetry as Primary Coordinates: A Structural Reorganization of Quantum Many-Body Hilbert Space

Abstract

A recurring pattern in the recent quant-ph, math-ph, math.QA, and cond-mat.stat-mech preprints — read over a thirty-day window ending 2026-06-02 — suggests that several structures long treated as primary coordinates of many-body Hilbert space are in fact derived. Entanglement magnitude, the existence of a free-fermion language, dynamical universality classes, the ground-state manifold, and even the complex-versus-real structure of the operator algebra each appear, in independent recent work, to refine into finer distinctions once one asks two prior questions: *how is locality measured?* and *which symmetry resolves the count?* We collect seven specific findings — Gheorghiu's constant-depth pseudoentanglement separation [corpus:arxiv:2605.31448v1], Lu, Fu and Liu's intrinsic-locality dimension for stabilizer codes [corpus:arxiv:2605.31441v1], Jindal and Hosur's non-Abelian-ETH entropy correction [corpus:arxiv:2605.30798v1], Fukai, Pozsgay and Vona's path-product expansion for hidden free fermions [corpus:arxiv:2605.31453v1], Sinha and collaborators' hidden Ising structure from a generalized Yang-Baxter equation [corpus:arxiv:2605.30007v1], Balducci and collaborators' traversable-versus-nontraversable quantum phase transitions [corpus:arxiv:2605.31472v1], and Surace, Minagawa and Kunjwal's reversal of the real-complex hierarchy under indefinite causal order [corpus:arxiv:2605.30238v1]. We also use Divi, Lessa and Wang's local strong-to-weak SSB diagnostic [corpus:arxiv:2605.28967v1] as an internal cross-check. The thesis we synthesize: *the apparent dimensionality, universality, and even reality of a quantum system are conditional on the choice of locality metric and the symmetry resolution applied to its Hilbert space; they are not intrinsic features of the state or Hamiltonian alone.* The falsification path: each refinement we cite is operationally testable — a constructed example, a closed-form bound, or a finite-data diagnostic — and the thesis fails if any of the underlying mechanisms is retracted, or if a counter-example emerges in which a symmetry resolution or locality metric does not change the structural conclusion. The contribution here is the synthesis, not the underlying results. Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2605.28967v1, 2605.30007v1, 2605.30238v1, 2605.30798v1, 2605.31441v1, 2605.31448v1, 2605.31453v1, 2605.31472v1