{"paper":{"title":"A complete classification of modular compactifications of the universal Jacobian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"All modular compactifications of the universal Jacobian over the moduli space of curves are parametrized by V-functions on a stability domain of half-vine types.","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Filippo Viviani, Marco Fava, Nicola Pagani","submitted_at":"2026-03-05T18:26:43Z","abstract_excerpt":"This is the third paper in a series, following [FPVa] and [FPVb].\n  We classify all modular compactifications of the universal Jacobian over $\\overline{\\mathcal{M}}_{g,n}$, both as stacks and as their relative good moduli spaces. Our main result gives a combinatorial parametrization of compactified universal Jacobian stacks by $V$-functions on a stability domain $\\mathbb{D}_{g,n}$ of half-vine types (two-components topological types with a chosen side); under this correspondence, fine compactifications are exactly the general $V$-functions.\n  We single out the classical compactified universal "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our main result gives a combinatorial parametrization of compactified universal Jacobian stacks by V-functions on a stability domain D_{g,n} of half-vine types; under this correspondence, fine compactifications are exactly the general V-functions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The classification assumes that every modular compactification arises from a V-function on the given stability domain of half-vine types; if some compactifications exist outside this combinatorial setup, the parametrization would be incomplete.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"All modular compactifications of the universal Jacobian are parametrized by V-functions on a stability domain of half-vine types, with classical numerical polarization cases recovered as special instances.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"All modular compactifications of the universal Jacobian over the moduli space of curves are parametrized by V-functions on a stability domain of half-vine types.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fe7b3bb1aa685b084cabb8718b680f9c52efcd84719c1b4d2ccda04026748091"},"source":{"id":"2603.05455","kind":"arxiv","version":3},"verdict":{"id":"7c88ce41-758c-4dbb-b214-e060d7a2d141","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T15:10:55.598697Z","strongest_claim":"Our main result gives a combinatorial parametrization of compactified universal Jacobian stacks by V-functions on a stability domain D_{g,n} of half-vine types; under this correspondence, fine compactifications are exactly the general V-functions.","one_line_summary":"All modular compactifications of the universal Jacobian are parametrized by V-functions on a stability domain of half-vine types, with classical numerical polarization cases recovered as special instances.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The classification assumes that every modular compactification arises from a V-function on the given stability domain of half-vine types; if some compactifications exist outside this combinatorial setup, the parametrization would be incomplete.","pith_extraction_headline":"All modular compactifications of the universal Jacobian over the moduli space of curves are parametrized by V-functions on a stability domain of half-vine types."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.05455/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":3,"snapshot_sha256":"163670d84638720d31e9f0b94c321ba0cbd47639fedce82addef43345ba9afb8"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}