{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UGENT3BOH3VRGXRXZPWGEWQOAQ","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":"33961f169dbe91eb505d7c41762bdc235e55f572085f566aed00a7f6d0a17e1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-06T02:35:25Z","title_canon_sha256":"6d6b66223be17c65675f6208f2fba6c8ba92e2c74c7b279887e3536b6d640184"},"schema_version":"1.0","source":{"id":"1404.1541","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1541","created_at":"2026-05-18T02:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1541v2","created_at":"2026-05-18T02:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1541","created_at":"2026-05-18T02:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"UGENT3BOH3VR","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UGENT3BOH3VRGXRX","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UGENT3BO","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:0715e1513a15f5a4a85596b0a93135a4025dea0a6c6bac12f0ee6e5ea9200c1a","target":"graph","created_at":"2026-05-18T02:43:18Z","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 $f\\colon(R,\\mathfrak{m})\\rightarrow S$ be a local homomorphism of Noetherian local rings. Consider two endomorphisms \\textit{of finite length} (i.e., with zero-dimensional closed fibers) $\\varphi\\colon R\\rightarrow R$ and $\\psi\\colon S\\rightarrow S$, satisfying $\\psi\\circ f=f\\circ\\varphi$. Then $\\psi$ induces a finite length endomorphism $\\overline{\\psi}\\colon S/f(\\mathfrak{m})S\\rightarrow S/f(\\mathfrak{m})S$. When $f$ is flat, under the assumption that $S$ is Cohen-Macaulay we prove an additivity formula: $h_{\\mathrm{loc}}(\\psi)=h_{\\mathrm{loc}}(\\varphi)+h_{\\mathrm{loc}}(\\overline{\\psi})$","authors_text":"Mahdi Majidi-Zolbanin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-06T02:35:25Z","title":"On additivity of local entropy under flat extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1541","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":"sha256:1458d899ffab1537f55b0523f68744b7760bc71081f65d96979f6bc0057e5d0c","target":"record","created_at":"2026-05-18T02:43:18Z","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":"33961f169dbe91eb505d7c41762bdc235e55f572085f566aed00a7f6d0a17e1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-06T02:35:25Z","title_canon_sha256":"6d6b66223be17c65675f6208f2fba6c8ba92e2c74c7b279887e3536b6d640184"},"schema_version":"1.0","source":{"id":"1404.1541","kind":"arxiv","version":2}},"canonical_sha256":"a188d9ec2e3eeb135e37cbec625a0e0405f51cdd4aa81568403acb64fb03b75d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a188d9ec2e3eeb135e37cbec625a0e0405f51cdd4aa81568403acb64fb03b75d","first_computed_at":"2026-05-18T02:43:18.927069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:18.927069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hrH114HZOQtcrTvrvTGnnxIPuTVs4BJ+OJzgnxBXrlErFeCsn+YLCwD39/I1+H6o8a6hIvsD+DiHUBXppXxlCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:18.927560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1541","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1458d899ffab1537f55b0523f68744b7760bc71081f65d96979f6bc0057e5d0c","sha256:0715e1513a15f5a4a85596b0a93135a4025dea0a6c6bac12f0ee6e5ea9200c1a"],"state_sha256":"9580763afb15c96303b4ceb02740525e70c3719adb60a75824e3e1ed8c7add48"}