{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4TCBBGPPMSHIRSX3KIB6QYVADG","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":"d82c48f3de6e552281f6202bf584144437ee322f095c6d3e9af83a7ec0796f5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-26T11:00:38Z","title_canon_sha256":"f4c9d034dd777f7fe02ebf69d56325136e259511c18c79a5bfa851b7b965382b"},"schema_version":"1.0","source":{"id":"1605.08226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08226","created_at":"2026-05-18T00:49:32Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08226v2","created_at":"2026-05-18T00:49:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08226","created_at":"2026-05-18T00:49:32Z"},{"alias_kind":"pith_short_12","alias_value":"4TCBBGPPMSHI","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4TCBBGPPMSHIRSX3","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4TCBBGPP","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:246cbac0ae49e50feebd34bd817d3ed0b0ff51d72a53b4011ba4411633e5b305","target":"graph","created_at":"2026-05-18T00:49:32Z","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":"Given a finite morphism $\\varphi:Y\\to X$ of quasi-smooth Berkovich curves over a complete, algebraically closed field $k$ of characteristic $0$, we prove a Riemann-Hurwitz formula relating their Euler-Poincar\\'e characteristics (calculated using De Rham cohomology of their overconvergent structure sheaf). The main tools are $p$-adic Runge's theorem together with valuation polygons of analytic functions. Using the results obtained, we provide another point of view on Riemann-Hurwitz formula for finite morphisms of curves over algebraically closed fields of positive characteristic.","authors_text":"Velibor Bojkovi\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-26T11:00:38Z","title":"Riemann-Hurwitz formula for finite morphisms of $p$-adic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08226","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":"sha256:71b1f68218a56e6f8c22f571130fa20b4d95f219396dc72f511909818bb891e9","target":"record","created_at":"2026-05-18T00:49:32Z","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":"d82c48f3de6e552281f6202bf584144437ee322f095c6d3e9af83a7ec0796f5b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-26T11:00:38Z","title_canon_sha256":"f4c9d034dd777f7fe02ebf69d56325136e259511c18c79a5bfa851b7b965382b"},"schema_version":"1.0","source":{"id":"1605.08226","kind":"arxiv","version":2}},"canonical_sha256":"e4c41099ef648e88cafb5203e862a019835d87ddea6150e8ee945a1169531a30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4c41099ef648e88cafb5203e862a019835d87ddea6150e8ee945a1169531a30","first_computed_at":"2026-05-18T00:49:32.534041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:32.534041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6ikJ6LmfHWVLPscEpVMJQ3k/mnDkcmkD9UH+TNbMGumPptWD7MDrX0CYhMi32sDMDme0KVPdYlnKLg8W6hsMBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:32.534690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71b1f68218a56e6f8c22f571130fa20b4d95f219396dc72f511909818bb891e9","sha256:246cbac0ae49e50feebd34bd817d3ed0b0ff51d72a53b4011ba4411633e5b305"],"state_sha256":"cea389fd95bd520a05b2fd3e8ebc9e82512b0c5458f145f90026f3a454868ebe"}