{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:CQ46P3SVFUVBTCPB3SRRMRDXZN","short_pith_number":"pith:CQ46P3SV","canonical_record":{"source":{"id":"0904.4611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-29T13:49:03Z","cross_cats_sorted":[],"title_canon_sha256":"d8f14ded83fe35a5e0fddfdac648838ab35ef52dcdef1229e37fac22871aaca6","abstract_canon_sha256":"5cc0ced8ebef3ec156731db0b32b326301d74eee55fbae02a54b9d0a588f11bb"},"schema_version":"1.0"},"canonical_sha256":"1439e7ee552d2a1989e1dca3164477cb523ea6bbf527c3adc38361e20828c914","source":{"kind":"arxiv","id":"0904.4611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4611","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4611v1","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4611","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"pith_short_12","alias_value":"CQ46P3SVFUVB","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"CQ46P3SVFUVBTCPB","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"CQ46P3SV","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:CQ46P3SVFUVBTCPB3SRRMRDXZN","target":"record","payload":{"canonical_record":{"source":{"id":"0904.4611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-29T13:49:03Z","cross_cats_sorted":[],"title_canon_sha256":"d8f14ded83fe35a5e0fddfdac648838ab35ef52dcdef1229e37fac22871aaca6","abstract_canon_sha256":"5cc0ced8ebef3ec156731db0b32b326301d74eee55fbae02a54b9d0a588f11bb"},"schema_version":"1.0"},"canonical_sha256":"1439e7ee552d2a1989e1dca3164477cb523ea6bbf527c3adc38361e20828c914","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:49.943069Z","signature_b64":"wmr4Dx1x7eT4/Zmdw3ZpXzpGUWHLQrQ5WA4cX5Jbsuq7GChMCo547Vi0IMzovAnCXXwbDH5vUsCCfZ0hb85HAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1439e7ee552d2a1989e1dca3164477cb523ea6bbf527c3adc38361e20828c914","last_reissued_at":"2026-05-18T02:27:49.942635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:49.942635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.4611","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":"2026-05-18T02:27:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jfqgh3TJHJili+eHSiCyyXl2eU7Dpfey3jXkkIerHjRUNTU2EIPjn/SJwqxCrQJKUrKmb1hx5QGdXV/J7oZjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T10:59:02.584660Z"},"content_sha256":"5ab5843dc740a987007cf338c567a3984dec17dc7a0c5d9bbbb9bd326a1641bc","schema_version":"1.0","event_id":"sha256:5ab5843dc740a987007cf338c567a3984dec17dc7a0c5d9bbbb9bd326a1641bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:CQ46P3SVFUVBTCPB3SRRMRDXZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bound states for a stationary nonlinear Schrodinger-Poisson system with sign-changing potential in $R^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huan-Song Zhou, Yongsheng Jiang","submitted_at":"2009-04-29T13:49:03Z","abstract_excerpt":"We study the following Schr\\\"odinger-Poisson system (P_\\lambda){ll}\n  -\\Delta u + V(x)u+\\lambda \\phi (x) u =Q(x)u^{p}, x\\in \\mathbb{R}^3 \\\\\n  -\\Delta\\phi = u^2, \\lim\\limits_{|x|\\to +\\infty}\\phi(x)=0, u>0, where $\\lambda\\geqslant0$ is a parameter, $1 < p < +\\infty$, $V(x)$ and $Q(x)$ are sign-changing or non-positive functions in $ L^{\\infty}(\\mathbb{R}^3)$. When $V(x)\\equiv Q(x)\\equiv1$, D.Ruiz \\cite{RuizD-JFA} proved that ($P_\\lambda$) with $p\\in(2,5)$ has always a positive radial solution, but ($P_\\lambda$) with $p\\in(1,2]$ has solution only if $\\lambda>0$ small enough and no any nontrivial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4611","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":"2026-05-18T02:27:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5NDMR74/cvSJXUbjZbCMHffYzRHc/LTGwHXuVNCuK6RteQiSuX9KIsIK0CTisH+0tNvUSaOvmNIf3QBs1q/MCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T10:59:02.585230Z"},"content_sha256":"0318bcdc7ac0a69000439537166052709769e409869800be288da25e60fc674b","schema_version":"1.0","event_id":"sha256:0318bcdc7ac0a69000439537166052709769e409869800be288da25e60fc674b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN/bundle.json","state_url":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN/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":"2026-07-01T10:59:02Z","links":{"resolver":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN","bundle":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN/bundle.json","state":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:CQ46P3SVFUVBTCPB3SRRMRDXZN","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":"5cc0ced8ebef3ec156731db0b32b326301d74eee55fbae02a54b9d0a588f11bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-29T13:49:03Z","title_canon_sha256":"d8f14ded83fe35a5e0fddfdac648838ab35ef52dcdef1229e37fac22871aaca6"},"schema_version":"1.0","source":{"id":"0904.4611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4611","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4611v1","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4611","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"pith_short_12","alias_value":"CQ46P3SVFUVB","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"CQ46P3SVFUVBTCPB","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"CQ46P3SV","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:0318bcdc7ac0a69000439537166052709769e409869800be288da25e60fc674b","target":"graph","created_at":"2026-05-18T02:27:49Z","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":"We study the following Schr\\\"odinger-Poisson system (P_\\lambda){ll}\n  -\\Delta u + V(x)u+\\lambda \\phi (x) u =Q(x)u^{p}, x\\in \\mathbb{R}^3 \\\\\n  -\\Delta\\phi = u^2, \\lim\\limits_{|x|\\to +\\infty}\\phi(x)=0, u>0, where $\\lambda\\geqslant0$ is a parameter, $1 < p < +\\infty$, $V(x)$ and $Q(x)$ are sign-changing or non-positive functions in $ L^{\\infty}(\\mathbb{R}^3)$. When $V(x)\\equiv Q(x)\\equiv1$, D.Ruiz \\cite{RuizD-JFA} proved that ($P_\\lambda$) with $p\\in(2,5)$ has always a positive radial solution, but ($P_\\lambda$) with $p\\in(1,2]$ has solution only if $\\lambda>0$ small enough and no any nontrivial ","authors_text":"Huan-Song Zhou, Yongsheng Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-29T13:49:03Z","title":"Bound states for a stationary nonlinear Schrodinger-Poisson system with sign-changing potential in $R^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4611","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":"sha256:5ab5843dc740a987007cf338c567a3984dec17dc7a0c5d9bbbb9bd326a1641bc","target":"record","created_at":"2026-05-18T02:27:49Z","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":"5cc0ced8ebef3ec156731db0b32b326301d74eee55fbae02a54b9d0a588f11bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-29T13:49:03Z","title_canon_sha256":"d8f14ded83fe35a5e0fddfdac648838ab35ef52dcdef1229e37fac22871aaca6"},"schema_version":"1.0","source":{"id":"0904.4611","kind":"arxiv","version":1}},"canonical_sha256":"1439e7ee552d2a1989e1dca3164477cb523ea6bbf527c3adc38361e20828c914","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1439e7ee552d2a1989e1dca3164477cb523ea6bbf527c3adc38361e20828c914","first_computed_at":"2026-05-18T02:27:49.942635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:49.942635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wmr4Dx1x7eT4/Zmdw3ZpXzpGUWHLQrQ5WA4cX5Jbsuq7GChMCo547Vi0IMzovAnCXXwbDH5vUsCCfZ0hb85HAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:49.943069Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.4611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ab5843dc740a987007cf338c567a3984dec17dc7a0c5d9bbbb9bd326a1641bc","sha256:0318bcdc7ac0a69000439537166052709769e409869800be288da25e60fc674b"],"state_sha256":"920e151f8c0579f5e8965b1ceab3ae3a7c49a7c36ae2b441859ab0e6cf952d3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W5jeaCKXmxXTh/N/t9Lhkf3JDGrMKRBorNdkAEnHYnzqo4TvBIgxLVMeBwSZSnbnEMc95wnxZMV00CACRMeiBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T10:59:02.587832Z","bundle_sha256":"0735096af669d535e11391eea497ea4452448a0d764ac89ee9c87293c6a1848d"}}