{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:H6FMNSXCAFHBKYNDKJGYUSDGZP","short_pith_number":"pith:H6FMNSXC","canonical_record":{"source":{"id":"1811.04353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-11T05:14:23Z","cross_cats_sorted":[],"title_canon_sha256":"3af68abaf9395112a7a055f21b55e33cfa3b964b8a0e17a284acc7ed878139c0","abstract_canon_sha256":"361685dbbea90b75d9b70ee428973f74258a810f436ae7029b46fb3d5b813b3b"},"schema_version":"1.0"},"canonical_sha256":"3f8ac6cae2014e1561a3524d8a4866cbed2c687c7336c76c6e1581155f3b6eae","source":{"kind":"arxiv","id":"1811.04353","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04353","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04353v1","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04353","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"pith_short_12","alias_value":"H6FMNSXCAFHB","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H6FMNSXCAFHBKYND","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H6FMNSXC","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:H6FMNSXCAFHBKYNDKJGYUSDGZP","target":"record","payload":{"canonical_record":{"source":{"id":"1811.04353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-11T05:14:23Z","cross_cats_sorted":[],"title_canon_sha256":"3af68abaf9395112a7a055f21b55e33cfa3b964b8a0e17a284acc7ed878139c0","abstract_canon_sha256":"361685dbbea90b75d9b70ee428973f74258a810f436ae7029b46fb3d5b813b3b"},"schema_version":"1.0"},"canonical_sha256":"3f8ac6cae2014e1561a3524d8a4866cbed2c687c7336c76c6e1581155f3b6eae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:05.457908Z","signature_b64":"hkepn5WBQZ1CyBf555Yw6geB8IGlEn0Dtn4wGwkhEezR6Z9a58ezx5k73hRb6KGdk6PsotZ3xOg5LE5mlso6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f8ac6cae2014e1561a3524d8a4866cbed2c687c7336c76c6e1581155f3b6eae","last_reissued_at":"2026-05-18T00:01:05.457272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:05.457272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.04353","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tjgKa9rykoOLjajMrNAP2h8bzH328plDOXFEN3Mr9tJKbK1gKTRTiMlkuZPfAfEKUunNKsYzNGrHtZ7DbuXcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T09:22:01.979416Z"},"content_sha256":"d82438932138dc8fa11a73790cf2480c9a9ed41cca84f89f90e3d209afda3de2","schema_version":"1.0","event_id":"sha256:d82438932138dc8fa11a73790cf2480c9a9ed41cca84f89f90e3d209afda3de2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:H6FMNSXCAFHBKYNDKJGYUSDGZP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical growth elliptic problems with Choquard type nonlinearity:A survey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"K.Sreenadh, Tuhina Mukherjee","submitted_at":"2018-11-11T05:14:23Z","abstract_excerpt":"This article deals with a survey of recent developments and results on Choquard equations where we focus on the existence and multiplicity of solutions of the partial differential equations which involve the nonlinearity of convolution type. Because of its nature, these equations are categorized under the nonlocal problems. We give a brief survey on the work already done in this regard following which we illustrate the problems we have addressed. Seeking the help of variational methods and asymptotic estimates, we prove our main results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04353","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oNa9qEqQZMwDavLJ00xtJ+I6mwVeAgFsvmg0vxBAB4/K3ygbLxqTuS6AvZGWBnsr5qtsGXWKcTuosfoqD7HwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T09:22:01.979766Z"},"content_sha256":"c82ed1862cdf87e4007b7825dda9ab799bf90cc003494952c2c01dcca67d4452","schema_version":"1.0","event_id":"sha256:c82ed1862cdf87e4007b7825dda9ab799bf90cc003494952c2c01dcca67d4452"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H6FMNSXCAFHBKYNDKJGYUSDGZP/bundle.json","state_url":"https://pith.science/pith/H6FMNSXCAFHBKYNDKJGYUSDGZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H6FMNSXCAFHBKYNDKJGYUSDGZP/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":"2026-06-23T09:22:01Z","links":{"resolver":"https://pith.science/pith/H6FMNSXCAFHBKYNDKJGYUSDGZP","bundle":"https://pith.science/pith/H6FMNSXCAFHBKYNDKJGYUSDGZP/bundle.json","state":"https://pith.science/pith/H6FMNSXCAFHBKYNDKJGYUSDGZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H6FMNSXCAFHBKYNDKJGYUSDGZP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H6FMNSXCAFHBKYNDKJGYUSDGZP","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":"361685dbbea90b75d9b70ee428973f74258a810f436ae7029b46fb3d5b813b3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-11T05:14:23Z","title_canon_sha256":"3af68abaf9395112a7a055f21b55e33cfa3b964b8a0e17a284acc7ed878139c0"},"schema_version":"1.0","source":{"id":"1811.04353","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04353","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04353v1","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04353","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"pith_short_12","alias_value":"H6FMNSXCAFHB","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H6FMNSXCAFHBKYND","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H6FMNSXC","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:c82ed1862cdf87e4007b7825dda9ab799bf90cc003494952c2c01dcca67d4452","target":"graph","created_at":"2026-05-18T00:01:05Z","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":"This article deals with a survey of recent developments and results on Choquard equations where we focus on the existence and multiplicity of solutions of the partial differential equations which involve the nonlinearity of convolution type. Because of its nature, these equations are categorized under the nonlocal problems. We give a brief survey on the work already done in this regard following which we illustrate the problems we have addressed. Seeking the help of variational methods and asymptotic estimates, we prove our main results.","authors_text":"K.Sreenadh, Tuhina Mukherjee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-11T05:14:23Z","title":"Critical growth elliptic problems with Choquard type nonlinearity:A survey"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04353","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:d82438932138dc8fa11a73790cf2480c9a9ed41cca84f89f90e3d209afda3de2","target":"record","created_at":"2026-05-18T00:01:05Z","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":"361685dbbea90b75d9b70ee428973f74258a810f436ae7029b46fb3d5b813b3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-11T05:14:23Z","title_canon_sha256":"3af68abaf9395112a7a055f21b55e33cfa3b964b8a0e17a284acc7ed878139c0"},"schema_version":"1.0","source":{"id":"1811.04353","kind":"arxiv","version":1}},"canonical_sha256":"3f8ac6cae2014e1561a3524d8a4866cbed2c687c7336c76c6e1581155f3b6eae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f8ac6cae2014e1561a3524d8a4866cbed2c687c7336c76c6e1581155f3b6eae","first_computed_at":"2026-05-18T00:01:05.457272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:05.457272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hkepn5WBQZ1CyBf555Yw6geB8IGlEn0Dtn4wGwkhEezR6Z9a58ezx5k73hRb6KGdk6PsotZ3xOg5LE5mlso6DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:05.457908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04353","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d82438932138dc8fa11a73790cf2480c9a9ed41cca84f89f90e3d209afda3de2","sha256:c82ed1862cdf87e4007b7825dda9ab799bf90cc003494952c2c01dcca67d4452"],"state_sha256":"f41a9a3ac4422bff97920b4df7c987d8d57395c21acd6ff4dfb7dcd20c24ae89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yZlJLED9z7Fh3WelI85tXovMwH0YFD8r+QmhfsBGRVmF/ccpE842WQRtvwWVErYAWwweQCnaWICxC7eSAp5+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T09:22:01.981846Z","bundle_sha256":"222f2a878b2b4df7705869da873af63ab6f40e8e89300271127bf284227dfc13"}}