{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QHJTHS5PBKKBPON7DJEJC6WAMC","short_pith_number":"pith:QHJTHS5P","canonical_record":{"source":{"id":"1705.08047","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2017-05-23T00:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"a9b81dc7a35b401aca0c97ec0d45dd049b360c5842cd8089e8fef49bdab52035","abstract_canon_sha256":"8a632b6346446e9d9166bd72e4d3c92559701256f2c8e27e6855cffa07d340c2"},"schema_version":"1.0"},"canonical_sha256":"81d333cbaf0a9417b9bf1a48917ac060b6479da22205d8b3f5dd5a04bc074bf5","source":{"kind":"arxiv","id":"1705.08047","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08047","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08047v4","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08047","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"pith_short_12","alias_value":"QHJTHS5PBKKB","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHJTHS5PBKKBPON7","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHJTHS5P","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QHJTHS5PBKKBPON7DJEJC6WAMC","target":"record","payload":{"canonical_record":{"source":{"id":"1705.08047","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2017-05-23T00:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"a9b81dc7a35b401aca0c97ec0d45dd049b360c5842cd8089e8fef49bdab52035","abstract_canon_sha256":"8a632b6346446e9d9166bd72e4d3c92559701256f2c8e27e6855cffa07d340c2"},"schema_version":"1.0"},"canonical_sha256":"81d333cbaf0a9417b9bf1a48917ac060b6479da22205d8b3f5dd5a04bc074bf5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:37.682455Z","signature_b64":"9laxQhjQhRioVEGLoorONy9XlxVpDc/Fmrmqtpr0oVlmKCuDU64k3Nelz9KYRxY/jctlusbkoRqB2ESSHIJQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81d333cbaf0a9417b9bf1a48917ac060b6479da22205d8b3f5dd5a04bc074bf5","last_reissued_at":"2026-05-18T00:15:37.681871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:37.681871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.08047","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Nu37rJqbe+wfn8QNFrDTaAwwZ7FZJA1YWV5GH5mmCx3Ubshu8wgBU7o6gYojSxKumL2IqoBuG4Lbsldx6eBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:37:45.848123Z"},"content_sha256":"22ac85419619e749bbc65841595be019b8eecbbfee2d6c0c0d912bfb701befd5","schema_version":"1.0","event_id":"sha256:22ac85419619e749bbc65841595be019b8eecbbfee2d6c0c0d912bfb701befd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QHJTHS5PBKKBPON7DJEJC6WAMC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On nonhomogeneous elliptic equations with the Hardy-Leray potentials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Quaas, Feng Zhou, Huyuan Chen","submitted_at":"2017-05-23T00:26:05Z","abstract_excerpt":"In this paper, we present some suitable distributional identities of the solutions for nonhomogeneous elliptic equations involving the Hardy-Leray potentials and study qualitative properties of the solutions to the corresponding nonhomogeneous problems by the distributional identities. We address some applications on the nonexistence of some nonhomogeneous problems with the Hardy-Leray potentials and the nonexistence principle eigenvalue with some indefinite potentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08047","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uoPwRTEzFbLIT3/Qm3dGC0W48VLjVEWXWBL9NeDj3VAIWs1KA5Ffcz7HlOGaAtvPMEjSCfoUxqvcyz4HNXsyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T23:37:45.848748Z"},"content_sha256":"e6a367de1e82aa13c7afbb93bfad3e0a2aa406d7a681598956a30dfc62592838","schema_version":"1.0","event_id":"sha256:e6a367de1e82aa13c7afbb93bfad3e0a2aa406d7a681598956a30dfc62592838"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHJTHS5PBKKBPON7DJEJC6WAMC/bundle.json","state_url":"https://pith.science/pith/QHJTHS5PBKKBPON7DJEJC6WAMC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHJTHS5PBKKBPON7DJEJC6WAMC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T23:37:45Z","links":{"resolver":"https://pith.science/pith/QHJTHS5PBKKBPON7DJEJC6WAMC","bundle":"https://pith.science/pith/QHJTHS5PBKKBPON7DJEJC6WAMC/bundle.json","state":"https://pith.science/pith/QHJTHS5PBKKBPON7DJEJC6WAMC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHJTHS5PBKKBPON7DJEJC6WAMC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QHJTHS5PBKKBPON7DJEJC6WAMC","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":"8a632b6346446e9d9166bd72e4d3c92559701256f2c8e27e6855cffa07d340c2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2017-05-23T00:26:05Z","title_canon_sha256":"a9b81dc7a35b401aca0c97ec0d45dd049b360c5842cd8089e8fef49bdab52035"},"schema_version":"1.0","source":{"id":"1705.08047","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08047","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08047v4","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08047","created_at":"2026-05-18T00:15:37Z"},{"alias_kind":"pith_short_12","alias_value":"QHJTHS5PBKKB","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHJTHS5PBKKBPON7","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHJTHS5P","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:e6a367de1e82aa13c7afbb93bfad3e0a2aa406d7a681598956a30dfc62592838","target":"graph","created_at":"2026-05-18T00:15:37Z","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 present some suitable distributional identities of the solutions for nonhomogeneous elliptic equations involving the Hardy-Leray potentials and study qualitative properties of the solutions to the corresponding nonhomogeneous problems by the distributional identities. We address some applications on the nonexistence of some nonhomogeneous problems with the Hardy-Leray potentials and the nonexistence principle eigenvalue with some indefinite potentials.","authors_text":"Alexander Quaas, Feng Zhou, Huyuan Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2017-05-23T00:26:05Z","title":"On nonhomogeneous elliptic equations with the Hardy-Leray potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08047","kind":"arxiv","version":4},"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":"sha256:22ac85419619e749bbc65841595be019b8eecbbfee2d6c0c0d912bfb701befd5","target":"record","created_at":"2026-05-18T00:15:37Z","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":"8a632b6346446e9d9166bd72e4d3c92559701256f2c8e27e6855cffa07d340c2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2017-05-23T00:26:05Z","title_canon_sha256":"a9b81dc7a35b401aca0c97ec0d45dd049b360c5842cd8089e8fef49bdab52035"},"schema_version":"1.0","source":{"id":"1705.08047","kind":"arxiv","version":4}},"canonical_sha256":"81d333cbaf0a9417b9bf1a48917ac060b6479da22205d8b3f5dd5a04bc074bf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81d333cbaf0a9417b9bf1a48917ac060b6479da22205d8b3f5dd5a04bc074bf5","first_computed_at":"2026-05-18T00:15:37.681871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:37.681871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9laxQhjQhRioVEGLoorONy9XlxVpDc/Fmrmqtpr0oVlmKCuDU64k3Nelz9KYRxY/jctlusbkoRqB2ESSHIJQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:37.682455Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08047","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22ac85419619e749bbc65841595be019b8eecbbfee2d6c0c0d912bfb701befd5","sha256:e6a367de1e82aa13c7afbb93bfad3e0a2aa406d7a681598956a30dfc62592838"],"state_sha256":"3b144ce375eb4a049d170e21f718d9c8c7161b75791559a79030189fd7b9fc51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tE2/UUYhbvdaEBjg5BTFRUzb98gCMZpu4hrIugWB+vbQOxSxSjE5oZiUF3sGH1w5DAan8wq9+gXnMccmJeX4CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T23:37:45.852036Z","bundle_sha256":"ae72cf1ff6c5abc09e95f47e2cfd72ffb372992ba161013745be8f2126c3c3a9"}}