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If $(\\mathcal{E}, \\phi)$ is semi-stable, then one of the following holds up to finite \\' etale cover:\n  $i)$ $X$ is uniruled.\n  $ii)$ $X$ is a torus and $(\\mathcal{E}, \\phi)$ is strictly semi-stable.\n  $iii)$ $X$ is a properly elliptic surface and $(\\mathcal{E}, \\phi)$ is strictly semi-stable."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.06045","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-24T14:21:50Z","cross_cats_sorted":["math.DG","math.SG"],"title_canon_sha256":"1f9693d567bad0ca7f4f942f71de890bc3c37572ad7c287cd1d886f469db27d7","abstract_canon_sha256":"b3eac804bef1e87ebc2846050de3640eb9c90bc79c60a0d5b3c47e1f332a98c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:34.661417Z","signature_b64":"g3EvYRRQxRelyyJAdnNxsUlx4bGHidVeL4VYlaihvhjQAqBaj9UjMO2H7zj1cVu3LugUfhIzFi0S96ab0WG3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8d31707705213ec1e4176048586679f86bc764d3bf202a9e18c21473d56523b","last_reissued_at":"2026-05-18T00:03:34.661010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:34.661010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rank two nilpotent co-Higgs sheaves on complex surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.AG","authors_text":"Maur\\'icio Corr\\^ea","submitted_at":"2015-01-24T14:21:50Z","abstract_excerpt":"Let $(\\mathcal{E}, \\phi)$ be a rank two co-Higgs vector bundles on a K\\\"ahler compact surface $X$ with $\\phi\\in H^0(X,End(\\mathcal{E})\\otimes T_X)$ nilpotent. 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