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We prove that if $p_g(X)> 243$, then the degree of the canonical map is at most $72$. Moreover, equality holds only if the general fibre $F$ of the Albanese morphism of $X$ is a smooth minimal surface of general type satisfying $p_g(F)=3,q(F)=0$ and $K_F^2=36$, and the canonical map of $F$ has degree $36$. This result improves the lower bound on $p_g(X)$ previously obtained by Jin-Xing Cai~\\cite{Cai08}.\n  As a consequence, we show that if the canonical degree is bigger than $64$, then the genera","authors_text":"Jiabin Du, Yong Hu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-30T06:00:07Z","title":"On the canonical degree of a Gorenstein minimal threefold of general type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31170","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:24f68411c90a61b7caca786955250f3520ce477a93b482d2324c0f9625d16c48","target":"record","created_at":"2026-07-01T01:17:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e0c23a81be27ec6ea419e7a82092ccabb361f7f5a846c7c06a8739b8168c7c13","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-06-30T06:00:07Z","title_canon_sha256":"89df346b89ce1411d3ef51327c334caf69e5e07998d663c0015df9f8d609fa88"},"schema_version":"1.0","source":{"id":"2606.31170","kind":"arxiv","version":1}},"canonical_sha256":"99734dd0a6365bc84da084ad421f42430714a9c8132f2bce370f695f5225623a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99734dd0a6365bc84da084ad421f42430714a9c8132f2bce370f695f5225623a","first_computed_at":"2026-07-01T01:17:31.080526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:17:31.080526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g9fbRh0+vy/GNtRWFD0LIr7HplxK3Tdl/R/ciP7GjzxzkJqpfD8yQ/t9kyMLMUv332aNsP2l08CVybJM4+8sAQ==","signature_status":"signed_v1","signed_at":"2026-07-01T01:17:31.080910Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.31170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24f68411c90a61b7caca786955250f3520ce477a93b482d2324c0f9625d16c48","sha256:d9bb36f5e6c2e9d22adf33caa11bea2d3b507d8a163a00270610290105226620"],"state_sha256":"cc62cdeacfa6bd3628959e2550346d348706f38259cb431928aae3603bfb678f"}