{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HWEFJLXPMYPAQW2XCA4UQ2ZTCG","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":"bfb263d6d474c411b589771045f3825cd9a4332584bcab9d5909a54db5a3bc2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-03T08:47:52Z","title_canon_sha256":"d0b6fc58b2697a56c9f46e29637795aa4973d69b0a14f3baa1c5424dd88d7814"},"schema_version":"1.0","source":{"id":"1905.02026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.02026","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"arxiv_version","alias_value":"1905.02026v1","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02026","created_at":"2026-05-17T23:46:56Z"},{"alias_kind":"pith_short_12","alias_value":"HWEFJLXPMYPA","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HWEFJLXPMYPAQW2X","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HWEFJLXP","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:fe7f0f2413fc2106d0e92534408e7d92070a682ea6c17d3ca361ce6a6f4d7d12","target":"graph","created_at":"2026-05-17T23:46:56Z","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":"In this paper we prove a kind of rotational symmetry for solutions of semilinear elliptic systems in some bounded cylindrical domains. The symmetry theorems obtained hold for low-Morse index solutions whenever the nonlinearities satisfy some convexity assumptions. These results extend and improve those obtained in \\cite{DaPaSys, DaGlPa1, Pa, PaWe}.","authors_text":"Filomena Pacella, Lucio Damascelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-03T08:47:52Z","title":"Sectional symmetry of solutions of elliptic systems in cylindrical domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02026","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:fa6251e0136f7a2d901f537bb1508feadab3799112efb7a74e5b87c68d44bffe","target":"record","created_at":"2026-05-17T23:46:56Z","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":"bfb263d6d474c411b589771045f3825cd9a4332584bcab9d5909a54db5a3bc2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-03T08:47:52Z","title_canon_sha256":"d0b6fc58b2697a56c9f46e29637795aa4973d69b0a14f3baa1c5424dd88d7814"},"schema_version":"1.0","source":{"id":"1905.02026","kind":"arxiv","version":1}},"canonical_sha256":"3d8854aeef661e085b571039486b3311b4458fc65e06e733ab22d848ba81759d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d8854aeef661e085b571039486b3311b4458fc65e06e733ab22d848ba81759d","first_computed_at":"2026-05-17T23:46:56.628010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:56.628010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sOm2uakjOq9+ot6jAUOjLoPB2YM1tsBCDdF4yzjcHsIofNFfEen3P6QcEuEmGHpTwnuPD1OFb0k+QSAO70u+Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:56.628761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.02026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa6251e0136f7a2d901f537bb1508feadab3799112efb7a74e5b87c68d44bffe","sha256:fe7f0f2413fc2106d0e92534408e7d92070a682ea6c17d3ca361ce6a6f4d7d12"],"state_sha256":"bedf0e1e7b7077a22d96292a2e3c6b0e40cbbc5bd5ff5421c465db0b9563e139"}