{"paper":{"title":"Divisorial Persistence and Asymptotic Homology of Analytic Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Nivaldo Grulha","submitted_at":"2026-07-07T18:33:45Z","abstract_excerpt":"We introduce \\emph{Divisorial Asymptotic Homology} (DAH) for analytic pairs $(X,\\mathcal I)$, a homological theory governed by the asymptotic concentration of Hausdorff measure inside shrinking sublevel sets of the intrinsic analytic energy $K_{\\mathcal I}=\\sum_j|f_j|^2$. DAH defines a covariant functor to the category of persistent graded abelian groups and distinguishes three layers of asymptotic information: the real log canonical threshold, the intrinsic divisorial spectrum, and the homological spectrum, the latter governing persistence and recording the asymptotic concentration rates real"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06717","kind":"arxiv","version":1},"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/2607.06717/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"}