{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:OR4ACX4CNPZ5GDEF43TSHZ27L7","short_pith_number":"pith:OR4ACX4C","schema_version":"1.0","canonical_sha256":"7478015f826bf3d30c85e6e723e75f5fde765abe22a9dcb73725ea87d78095a9","source":{"kind":"arxiv","id":"math/0601410","version":1},"attestation_state":"computed","paper":{"title":"Compactness results and applications to some \"zero mass\" elliptic problems","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Pomponio, Antonio Azzollini","submitted_at":"2006-01-17T11:02:34Z","abstract_excerpt":"In this paper we present some compactness results, showing how they can be applied in dealing with \"zero mass\" problems by a variational approach. In particular we use our results in two different situations: we look for complex valued solutions of a very classical elliptic equation, and we study an elliptic problem on an axially symmetric unbounded domain."},"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":"math/0601410","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-01-17T11:02:34Z","cross_cats_sorted":[],"title_canon_sha256":"a1ade9b0bb268fda0d628f47600e31055fc242bcd7ff10b475d96a6894a9935f","abstract_canon_sha256":"ae6d1e76735a54e5129a9dbd0679cefc898c2cb6903b237e9aea45b2cd3f8a37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:52:49.656740Z","signature_b64":"RTrMJC2BF3aJq35FA6Vimo3LMJ7iOQxon4A5KjAIhMkHmA0wI6hD/M1vMRTj2Ik4Sd7MPLLBDzEgc7GZHQdoCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7478015f826bf3d30c85e6e723e75f5fde765abe22a9dcb73725ea87d78095a9","last_reissued_at":"2026-07-04T14:52:49.656298Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:52:49.656298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compactness results and applications to some \"zero mass\" elliptic problems","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Pomponio, Antonio Azzollini","submitted_at":"2006-01-17T11:02:34Z","abstract_excerpt":"In this paper we present some compactness results, showing how they can be applied in dealing with \"zero mass\" problems by a variational approach. In particular we use our results in two different situations: we look for complex valued solutions of a very classical elliptic equation, and we study an elliptic problem on an axially symmetric unbounded domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601410","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0601410/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0601410","created_at":"2026-07-04T14:52:49.656369+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0601410v1","created_at":"2026-07-04T14:52:49.656369+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601410","created_at":"2026-07-04T14:52:49.656369+00:00"},{"alias_kind":"pith_short_12","alias_value":"OR4ACX4CNPZ5","created_at":"2026-07-04T14:52:49.656369+00:00"},{"alias_kind":"pith_short_16","alias_value":"OR4ACX4CNPZ5GDEF","created_at":"2026-07-04T14:52:49.656369+00:00"},{"alias_kind":"pith_short_8","alias_value":"OR4ACX4C","created_at":"2026-07-04T14:52:49.656369+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.03220","citing_title":"Holomorphic Structure and Quantum Critical Points in Supersymmetric Lifshitz Field Theories","ref_index":49,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OR4ACX4CNPZ5GDEF43TSHZ27L7","json":"https://pith.science/pith/OR4ACX4CNPZ5GDEF43TSHZ27L7.json","graph_json":"https://pith.science/api/pith-number/OR4ACX4CNPZ5GDEF43TSHZ27L7/graph.json","events_json":"https://pith.science/api/pith-number/OR4ACX4CNPZ5GDEF43TSHZ27L7/events.json","paper":"https://pith.science/paper/OR4ACX4C"},"agent_actions":{"view_html":"https://pith.science/pith/OR4ACX4CNPZ5GDEF43TSHZ27L7","download_json":"https://pith.science/pith/OR4ACX4CNPZ5GDEF43TSHZ27L7.json","view_paper":"https://pith.science/paper/OR4ACX4C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0601410&json=true","fetch_graph":"https://pith.science/api/pith-number/OR4ACX4CNPZ5GDEF43TSHZ27L7/graph.json","fetch_events":"https://pith.science/api/pith-number/OR4ACX4CNPZ5GDEF43TSHZ27L7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OR4ACX4CNPZ5GDEF43TSHZ27L7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OR4ACX4CNPZ5GDEF43TSHZ27L7/action/storage_attestation","attest_author":"https://pith.science/pith/OR4ACX4CNPZ5GDEF43TSHZ27L7/action/author_attestation","sign_citation":"https://pith.science/pith/OR4ACX4CNPZ5GDEF43TSHZ27L7/action/citation_signature","submit_replication":"https://pith.science/pith/OR4ACX4CNPZ5GDEF43TSHZ27L7/action/replication_record"}},"created_at":"2026-07-04T14:52:49.656369+00:00","updated_at":"2026-07-04T14:52:49.656369+00:00"}