{"paper":{"title":"The Space of augmented stability conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Antonios-Alexandros Robotis, Daniel Halpern-Leistner","submitted_at":"2025-01-01T03:13:31Z","abstract_excerpt":"Given a triangulated category $\\mathcal{C}$, we construct a partial compactification, denoted $\\mathcal{A}\\mathrm{Stab}(\\mathcal{C})$, of the quotient of its stability manifold by $\\mathbb{C}$. The purpose of $\\mathcal{A}\\mathrm{Stab}(\\mathcal{C})$ is to shed light on the structure of semiorthogonal decompositions of $\\mathcal{C}$. A point of $\\mathcal{A}\\mathrm{Stab}(\\mathcal{C})$, called an augmented stability condition on $\\mathcal{C}$, consists of a newly introduced homological structure called a multiscale decomposition, along with stability conditions on subquotient categories of $\\mathc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.00710","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.00710/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}