{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DL5BZJZ2MWNL6GVGOH4BCWDVK4","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":"fed2d8892cbb1ebb625ec324a74cf5d611289850752aad12b59acb0a7bbb3e99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-12T07:22:27Z","title_canon_sha256":"48c8455f8a487bec7c25405150df1a0a877f15ffcc5c36a3708b7f8c5ded3903"},"schema_version":"1.0","source":{"id":"1504.02939","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02939","created_at":"2026-05-18T01:37:13Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02939v2","created_at":"2026-05-18T01:37:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02939","created_at":"2026-05-18T01:37:13Z"},{"alias_kind":"pith_short_12","alias_value":"DL5BZJZ2MWNL","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DL5BZJZ2MWNL6GVG","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DL5BZJZ2","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:2483ddea0fdd942d9b9d8366d394ccde081e37ccd108546082ea4e6a0d537ac2","target":"graph","created_at":"2026-05-18T01:37:13Z","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 paper is the second part of a work devoted to the study of elliptic systems involving multiple Hardy-Sobolev critical exponents: $$\\begin{cases} -\\Delta u-\\lambda \\frac{|u|^{2^*(s_1)-2}u}{|x|^{s_1}}=\\kappa\\alpha \\frac{1}{|x|^{s_2}}|u|^{\\alpha-2}u|v|^\\beta\\quad &\\hbox{in}\\;\\Omega,\\\\ -\\Delta v-\\mu \\frac{|v|^{2^*(s_1)-2}v}{|x|^{s_1}}=\\kappa\\beta \\frac{1}{|x|^{s_2}}|u|^{\\alpha}|v|^{\\beta-2}v\\quad &\\hbox{in}\\;\\Omega,\\\\ \\kappa>0,(u,v)\\in \\mathscr{D}:=D_{0}^{1,2}(\\Omega)\\times D_{0}^{1,2}(\\Omega), \\end{cases}$$ where $s_1\\neq s_2\\in (0,2), \\alpha>1,\\beta>1, \\lambda>0,\\mu>0,\\kappa>0, \\alpha+\\beta","authors_text":"Wenming Zou, Xuexiu Zhong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-12T07:22:27Z","title":"On Elliptic Systems involving critical Hardy-Sobolev exponents (Part II)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02939","kind":"arxiv","version":2},"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:e22fa508c5a2fc1922c07c2e44f96d3a5ce0aefe14f6480f74539b8b886990e1","target":"record","created_at":"2026-05-18T01:37:13Z","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":"fed2d8892cbb1ebb625ec324a74cf5d611289850752aad12b59acb0a7bbb3e99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-12T07:22:27Z","title_canon_sha256":"48c8455f8a487bec7c25405150df1a0a877f15ffcc5c36a3708b7f8c5ded3903"},"schema_version":"1.0","source":{"id":"1504.02939","kind":"arxiv","version":2}},"canonical_sha256":"1afa1ca73a659abf1aa671f81158755727583397b32dedbcf2cfb218b5267240","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1afa1ca73a659abf1aa671f81158755727583397b32dedbcf2cfb218b5267240","first_computed_at":"2026-05-18T01:37:13.401872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:13.401872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ldbtG8+Q+tdlffohUTYA0EbtoShohDk+NB/NRT5p3xifkPQQXqER4MDSZhWmLb1yP51SfMBnsGnEuB4oePh4AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:13.402481Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02939","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e22fa508c5a2fc1922c07c2e44f96d3a5ce0aefe14f6480f74539b8b886990e1","sha256:2483ddea0fdd942d9b9d8366d394ccde081e37ccd108546082ea4e6a0d537ac2"],"state_sha256":"f145ff2917a71275820648926ea65f7f879579f40c7c2d85225251cae89d10a4"}