{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VAUQSC7EZYWBKO3I7TZQ55YXNE","short_pith_number":"pith:VAUQSC7E","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"},"canonical_sha256":"a829090be4ce2c153b68fcf30ef717690c3bd89567df2dd8952e6288ad843b44","source":{"kind":"arxiv","id":"2408.15804","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.15804","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"2408.15804v2","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.15804","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"VAUQSC7EZYWB","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"VAUQSC7EZYWBKO3I","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"VAUQSC7E","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VAUQSC7EZYWBKO3I7TZQ55YXNE","target":"record","payload":{"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"},"canonical_sha256":"a829090be4ce2c153b68fcf30ef717690c3bd89567df2dd8952e6288ad843b44","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"},"source_kind":"arxiv","source_id":"2408.15804","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6GH7NrNCW4ISd4QzGi1EbyUkO6vqFNsRwtPPa5tv5syaRBwmgF1PqJNgY67W+CGopWeZH2zwqzJmDQLVCu9zCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:47:11.696201Z"},"content_sha256":"f31967786dd99e4886bc34e59ab99fd214857c6c6d083e2de98508acde3ed2f0","schema_version":"1.0","event_id":"sha256:f31967786dd99e4886bc34e59ab99fd214857c6c6d083e2de98508acde3ed2f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VAUQSC7EZYWBKO3I7TZQ55YXNE","target":"graph","payload":{"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 $X$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.15804","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pSg5BTPuuf/r3CzE1yfTFmCpFckTUkeCPWwdZacPWCQXBTVC79FgnDzA+F8oYSX2Pt3Eigamqc5dCk4gJyUMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:47:11.696987Z"},"content_sha256":"cd5563b8950585cfce059223e904bb3f14428efc505ab2cfc83a272d260f33a6","schema_version":"1.0","event_id":"sha256:cd5563b8950585cfce059223e904bb3f14428efc505ab2cfc83a272d260f33a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VAUQSC7EZYWBKO3I7TZQ55YXNE/bundle.json","state_url":"https://pith.science/pith/VAUQSC7EZYWBKO3I7TZQ55YXNE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VAUQSC7EZYWBKO3I7TZQ55YXNE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T01:47:11Z","links":{"resolver":"https://pith.science/pith/VAUQSC7EZYWBKO3I7TZQ55YXNE","bundle":"https://pith.science/pith/VAUQSC7EZYWBKO3I7TZQ55YXNE/bundle.json","state":"https://pith.science/pith/VAUQSC7EZYWBKO3I7TZQ55YXNE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VAUQSC7EZYWBKO3I7TZQ55YXNE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VAUQSC7EZYWBKO3I7TZQ55YXNE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f6985bee6be761e0fec6ec2b7d5dfbd8302be2a871bb2351a15643117d76938c","cross_cats_sorted":["math.DS","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-28T14:01:26Z","title_canon_sha256":"d2c76c87e86d9778db65a33434fe637a7db8b4f548fc0bb61f904a69408f0236"},"schema_version":"1.0","source":{"id":"2408.15804","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.15804","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"2408.15804v2","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.15804","created_at":"2026-05-18T02:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"VAUQSC7EZYWB","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"VAUQSC7EZYWBKO3I","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"VAUQSC7E","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:cd5563b8950585cfce059223e904bb3f14428efc505ab2cfc83a272d260f33a6","target":"graph","created_at":"2026-05-18T02:44:39Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $X$ be a normal projective variety of dimension $d$ over an algebraically closed field and $f$ an automorphism of $X$. 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","authors_text":"Chen Jiang, Fei Hu","cross_cats":["math.DS","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-28T14:01:26Z","title":"An upper bound for polynomial volume growth of automorphisms of zero entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.15804","kind":"arxiv","version":2},"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:f31967786dd99e4886bc34e59ab99fd214857c6c6d083e2de98508acde3ed2f0","target":"record","created_at":"2026-05-18T02:44:39Z","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":"f6985bee6be761e0fec6ec2b7d5dfbd8302be2a871bb2351a15643117d76938c","cross_cats_sorted":["math.DS","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-28T14:01:26Z","title_canon_sha256":"d2c76c87e86d9778db65a33434fe637a7db8b4f548fc0bb61f904a69408f0236"},"schema_version":"1.0","source":{"id":"2408.15804","kind":"arxiv","version":2}},"canonical_sha256":"a829090be4ce2c153b68fcf30ef717690c3bd89567df2dd8952e6288ad843b44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a829090be4ce2c153b68fcf30ef717690c3bd89567df2dd8952e6288ad843b44","first_computed_at":"2026-05-18T02:44:39.606537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:39.606537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"omPB4/j3VP+/M2KcD6ORfz9+cn7K/HleSohfs6W6FtrXQtDXR5tGHkBh3/c+pqJi3CVq7SreVRvCTt4E3SzBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:39.607183Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.15804","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f31967786dd99e4886bc34e59ab99fd214857c6c6d083e2de98508acde3ed2f0","sha256:cd5563b8950585cfce059223e904bb3f14428efc505ab2cfc83a272d260f33a6"],"state_sha256":"8a0056a007406c5264c4b6e4d66225316f2b75151f8681c75ffac45896ccc07c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ZeVCh4yV95m3DCE4gmZeTbdTqvMXFW+5c0xVIUDHC/zp1z96SZrzTKuS1FUGWSgscxnOcGJ29Kee7aGDl5iBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:47:11.701448Z","bundle_sha256":"f99308b9f7350e49551118055e6d3cf7eea3841e6439c2e38beb248eb091945e"}}