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Suppose that the pullback $f^*|_{\\mathsf{N}^1(X)_\\mathbf{R}}$ of $f$ on the real N\\'eron--Severi space $\\mathsf{N}^1(X)_\\mathbf{R}$ is unipotent and denote the index of the eigenvalue $1$ by $k+1$. We establish the following upper bound for the polynomial volume growth $\\mathrm{plov}(f)$ of $f$: \\[ \\mathrm{plov}(f) \\le (k/2 + 1)d. \\] This inequality is optimal in certain cases. Moreover, we prove that $k\\le 2(d-1)$, extending a result of Dinh--Lin--Oguiso--Zhang for compac"},"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":"2408.15804","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-28T14:01:26Z","cross_cats_sorted":["math.DS","math.RA"],"title_canon_sha256":"d2c76c87e86d9778db65a33434fe637a7db8b4f548fc0bb61f904a69408f0236","abstract_canon_sha256":"f6985bee6be761e0fec6ec2b7d5dfbd8302be2a871bb2351a15643117d76938c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:39.607183Z","signature_b64":"omPB4/j3VP+/M2KcD6ORfz9+cn7K/HleSohfs6W6FtrXQtDXR5tGHkBh3/c+pqJi3CVq7SreVRvCTt4E3SzBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a829090be4ce2c153b68fcf30ef717690c3bd89567df2dd8952e6288ad843b44","last_reissued_at":"2026-05-18T02:44:39.606537Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:39.606537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An upper bound for polynomial volume growth of automorphisms of zero entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.RA"],"primary_cat":"math.AG","authors_text":"Chen Jiang, Fei Hu","submitted_at":"2024-08-28T14:01:26Z","abstract_excerpt":"Let $X$ be a normal projective variety of dimension $d$ over an algebraically closed field and $f$ an automorphism of $X$. 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