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We also show, with no need of the assumption $K_2\\leq K_1$, that if $K_1>0$, or if $Ricci_1>0$ and $K_2\\leq -c$, $c>0$ constant, any map $f:\\Sigma_1\\to \\Sigma_2$ i"},"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":"0804.0783","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-04-04T17:18:40Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"25de7d1702ce716f51553c619e0d253d584a804ecddc046f57e95728ba62a8cb","abstract_canon_sha256":"61d56e527174c3bcef25f66f629ba25b1c213b2b9cefd5dde867c1a5f928adc7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:23.210379Z","signature_b64":"24XS7lm/PzNWgWqZu1oKYpvIchMCBfHeQ2xWrU31Qe5GwL/z297a8ssjZnwkDYPybCMc4YEfoN17hW/504ZHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cae8066605b83fb3f7d631c438700d6b65741dbc3f3708932d68c6a89fe91a5","last_reissued_at":"2026-05-18T04:42:23.209908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:23.209908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mean Curvature Flow of Spacelike Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Guanghan Li, Isabel M.C. 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