The Center of the Algebra Is Where the Physics Lives: Categorical Defects, Boundary Completions, and Information-Theoretic Saturation in Recent hep-th and math.CT Preprints

Version 2 — revised in response to an external structural review and an automated critique pass. See "Response to Review" appendix in the PDF for the change log.

Across the late-May/early-June 2026 hep-th, math.CT, math.QA, and math-ph preprint corpus, a single structural move keeps surfacing in independently motivated work: the *center* (or commutant) of a region's observable algebra is no longer treated as kinematic bookkeeping but is upgraded to a categorical object that *carries* the non-perturbative or structural content of the theory. We argue this is a coherent heuristic reading of five independent constructions, not a derivation from a shared formal structure. Boundary gravitons in (2+1)d gravity have an irreducible non-trivial center that must be completed by monodromy data, and gauging that nonlocal data filters the partition function down to wormhole physics [corpus:arxiv:2605.28748v1]. Defect Hilbert spaces of $BF$+Chern-Simons theory are recovered as \*-representations of a $C^*$-algebra built from a Fell line bundle over a conjugation groupoid, with the Verlinde formula appearing as a convolution eigenvalue [corpus:arxiv:2605.28485v1]. Maxwell theory on ALE spaces fails to produce scalar partition functions and instead produces vector-valued boundary states; turning on 1-form symmetry backgrounds promotes these to sections of a line bundle over the Cartan torus [corpus:arxiv:2605.26224v1]. Hodge loci in Calabi-Yau sigma models are detected by the *existence* of a non-trivial category of topological defects, with Complex Multiplication appearing at points where this category embeds finite products of number fields [corpus:arxiv:2605.30418v1]. The cohesive $\infty$-topos $\mathbf{H}_{\mathbb{Q}}$ built from finite-dimensional $C^*$-algebras has a quantum modality given by precomposition with the center functor, identified with decoherence [corpus:arxiv:2606.02269v1]. We propose three falsification paths: (i) a region whose center is categorically trivial but which nonetheless requires wormhole-type completion; (ii) a sigma model with non-trivial $TDL$ category and no Hodge endomorphism; (iii) a system whose Krylov complexity reconstructs operator dynamics without reference to any centrally-acting algebra.

Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename.

Cited arXiv preprints: 2605.26224v1, 2605.26617v1, 2605.26829v1, 2605.27198v1, 2605.27568v1, 2605.27770v1, 2605.28485v1, 2605.28681v1, 2605.28748v1, 2605.29923v1, 2605.30354v1, 2605.30418v1, 2605.30970v1, 2605.31181v1, 2606.02269v1