{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FFMKLZZBBSAOL3EFWTHPZ5AZ5N","short_pith_number":"pith:FFMKLZZB","schema_version":"1.0","canonical_sha256":"2958a5e7210c80e5ec85b4cefcf419eb66bc837761d7b721531555cc81f2cb57","source":{"kind":"arxiv","id":"1609.01512","version":1},"attestation_state":"computed","paper":{"title":"On a singular Liouville-type equation and the Alexandrov isoperimetric inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniele Bartolucci, Daniele Castorina","submitted_at":"2016-09-06T12:12:23Z","abstract_excerpt":"We obtain a generalized version of an inequality, first derived by C. Bandle in the analytic setting, for weak subsolutions of a singular Liouville-type equation. As an application we obtain a new proof of the Alexandrov isoperimetric inequality on singular abstract surfaces. Interestingly enough, motivated by this geometric problem, we obtain a seemingly new characterization of local metrics on Alexandrov's surfaces of bounded curvature. At least to our knowledge, the characterization of the equality case in the isoperimetric inequality in such a weak framework is new as well."},"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":"1609.01512","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-06T12:12:23Z","cross_cats_sorted":[],"title_canon_sha256":"1729b6080f94a2e5b2273a563f9141595b87ace0fd224edaf9afcac740960aac","abstract_canon_sha256":"32406f4308989d8ff6808b282a7dfe84effca9f730b1352964debfceb8a4bd05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:07.061257Z","signature_b64":"/v1IuY3Dt9NDPJKhDhKTC0oc9Rta19Gv4yG/ebadexsuO6Rwe8JQzS0FlqPG/e6n6ULZmd4tyjT0YRJzflRBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2958a5e7210c80e5ec85b4cefcf419eb66bc837761d7b721531555cc81f2cb57","last_reissued_at":"2026-05-18T00:39:07.060637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:07.060637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a singular Liouville-type equation and the Alexandrov isoperimetric inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniele Bartolucci, Daniele Castorina","submitted_at":"2016-09-06T12:12:23Z","abstract_excerpt":"We obtain a generalized version of an inequality, first derived by C. Bandle in the analytic setting, for weak subsolutions of a singular Liouville-type equation. As an application we obtain a new proof of the Alexandrov isoperimetric inequality on singular abstract surfaces. Interestingly enough, motivated by this geometric problem, we obtain a seemingly new characterization of local metrics on Alexandrov's surfaces of bounded curvature. At least to our knowledge, the characterization of the equality case in the isoperimetric inequality in such a weak framework is new as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01512","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.01512","created_at":"2026-05-18T00:39:07.060745+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.01512v1","created_at":"2026-05-18T00:39:07.060745+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01512","created_at":"2026-05-18T00:39:07.060745+00:00"},{"alias_kind":"pith_short_12","alias_value":"FFMKLZZBBSAO","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FFMKLZZBBSAOL3EF","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FFMKLZZB","created_at":"2026-05-18T12:30:15.759754+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FFMKLZZBBSAOL3EFWTHPZ5AZ5N","json":"https://pith.science/pith/FFMKLZZBBSAOL3EFWTHPZ5AZ5N.json","graph_json":"https://pith.science/api/pith-number/FFMKLZZBBSAOL3EFWTHPZ5AZ5N/graph.json","events_json":"https://pith.science/api/pith-number/FFMKLZZBBSAOL3EFWTHPZ5AZ5N/events.json","paper":"https://pith.science/paper/FFMKLZZB"},"agent_actions":{"view_html":"https://pith.science/pith/FFMKLZZBBSAOL3EFWTHPZ5AZ5N","download_json":"https://pith.science/pith/FFMKLZZBBSAOL3EFWTHPZ5AZ5N.json","view_paper":"https://pith.science/paper/FFMKLZZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.01512&json=true","fetch_graph":"https://pith.science/api/pith-number/FFMKLZZBBSAOL3EFWTHPZ5AZ5N/graph.json","fetch_events":"https://pith.science/api/pith-number/FFMKLZZBBSAOL3EFWTHPZ5AZ5N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FFMKLZZBBSAOL3EFWTHPZ5AZ5N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FFMKLZZBBSAOL3EFWTHPZ5AZ5N/action/storage_attestation","attest_author":"https://pith.science/pith/FFMKLZZBBSAOL3EFWTHPZ5AZ5N/action/author_attestation","sign_citation":"https://pith.science/pith/FFMKLZZBBSAOL3EFWTHPZ5AZ5N/action/citation_signature","submit_replication":"https://pith.science/pith/FFMKLZZBBSAOL3EFWTHPZ5AZ5N/action/replication_record"}},"created_at":"2026-05-18T00:39:07.060745+00:00","updated_at":"2026-05-18T00:39:07.060745+00:00"}