{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IQVN5GT65GWNCKGTVIYRITBHHX","short_pith_number":"pith:IQVN5GT6","canonical_record":{"source":{"id":"1602.04147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-12T18:20:02Z","cross_cats_sorted":[],"title_canon_sha256":"ab6d910733345d02dfd8b2da61cb2f551869563373bc381191d865de36d8356c","abstract_canon_sha256":"efe60c8c2c42bc5db22ce8918e0d1af902341010d7672579b79db28f2af5dc74"},"schema_version":"1.0"},"canonical_sha256":"442ade9a7ee9acd128d3aa31144c273dd54d8eeecc99c47638b3ffa2c249a729","source":{"kind":"arxiv","id":"1602.04147","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04147","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04147v1","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04147","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"pith_short_12","alias_value":"IQVN5GT65GWN","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IQVN5GT65GWNCKGT","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IQVN5GT6","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IQVN5GT65GWNCKGTVIYRITBHHX","target":"record","payload":{"canonical_record":{"source":{"id":"1602.04147","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-12T18:20:02Z","cross_cats_sorted":[],"title_canon_sha256":"ab6d910733345d02dfd8b2da61cb2f551869563373bc381191d865de36d8356c","abstract_canon_sha256":"efe60c8c2c42bc5db22ce8918e0d1af902341010d7672579b79db28f2af5dc74"},"schema_version":"1.0"},"canonical_sha256":"442ade9a7ee9acd128d3aa31144c273dd54d8eeecc99c47638b3ffa2c249a729","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:54.433392Z","signature_b64":"PVLTsR70PIlQ4QidP5Es10xTNG0wuCXr9tBjtGxArewjviYDEdhWhAV0j6qrK0BQquKNHR3T8czj2Qv8qjK/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"442ade9a7ee9acd128d3aa31144c273dd54d8eeecc99c47638b3ffa2c249a729","last_reissued_at":"2026-05-18T01:20:54.432680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:54.432680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.04147","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":"2026-05-18T01:20:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hH0jvj+ZiUmjvBOKhX4d3PWDcUYRIXzq2kvZrc5k+Crnz+qfu5wsX72CDbiyTReto8LVmzbVuZ3CAwyZ+YE1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:18:10.690718Z"},"content_sha256":"1c33d2b1e6758a70f370e91d0125b1605e042d4b93b124d404a85074d3975e2e","schema_version":"1.0","event_id":"sha256:1c33d2b1e6758a70f370e91d0125b1605e042d4b93b124d404a85074d3975e2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IQVN5GT65GWNCKGTVIYRITBHHX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Schr\\\"odinger-Maxwell system involving sublinear terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandru Krist\\'aly, Du\\v{s}an Repov\\v{s}","submitted_at":"2016-02-12T18:20:02Z","abstract_excerpt":"In this paper we study the coupled Schr\\\"odinger-Maxwell system $$\\left\\{ \\begin{array}{lll} -\\triangle u+u +\\phi u=\\lambda \\alpha(x) f(u)& {\\rm in} & \\mathbb R^3,\\\\ -\\triangle \\phi =u^2 & {\\rm in} & \\mathbb R^3, \\end{array}\\right. $$ where $\\alpha\\in L^\\infty(\\mathbb R^3)\\cap L^{6/(5-q)}(\\mathbb R^3)$ for some $q\\in (0,1)$, and the continuous function $f:\\mathbb{R}\\to\\mathbb{R}$ is superlinear at zero and sublinear at infinity, e.g., $f(s) = \\min(|s|^r,|s|^p)$ with $0<r<1<p.$ Depending on the range of $\\lambda>0$, non-existence and multiplicity results are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04147","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":"2026-05-18T01:20:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ow9GTOGFKOEYsOq0YY9tGSgrJl176NULq/PfdDjrB4lMlE8NjDvuglfJ8kARSVReMq7CeOSRtFCjSRE/Nw8lBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:18:10.691376Z"},"content_sha256":"f6e37813a84dcd1fc8dc5d6bc41ea2eb4cb183a9670c78ba9e55be5ef1d4f2b3","schema_version":"1.0","event_id":"sha256:f6e37813a84dcd1fc8dc5d6bc41ea2eb4cb183a9670c78ba9e55be5ef1d4f2b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IQVN5GT65GWNCKGTVIYRITBHHX/bundle.json","state_url":"https://pith.science/pith/IQVN5GT65GWNCKGTVIYRITBHHX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IQVN5GT65GWNCKGTVIYRITBHHX/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":"2026-06-08T16:18:10Z","links":{"resolver":"https://pith.science/pith/IQVN5GT65GWNCKGTVIYRITBHHX","bundle":"https://pith.science/pith/IQVN5GT65GWNCKGTVIYRITBHHX/bundle.json","state":"https://pith.science/pith/IQVN5GT65GWNCKGTVIYRITBHHX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IQVN5GT65GWNCKGTVIYRITBHHX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IQVN5GT65GWNCKGTVIYRITBHHX","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":"efe60c8c2c42bc5db22ce8918e0d1af902341010d7672579b79db28f2af5dc74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-12T18:20:02Z","title_canon_sha256":"ab6d910733345d02dfd8b2da61cb2f551869563373bc381191d865de36d8356c"},"schema_version":"1.0","source":{"id":"1602.04147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04147","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04147v1","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04147","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"pith_short_12","alias_value":"IQVN5GT65GWN","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IQVN5GT65GWNCKGT","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IQVN5GT6","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:f6e37813a84dcd1fc8dc5d6bc41ea2eb4cb183a9670c78ba9e55be5ef1d4f2b3","target":"graph","created_at":"2026-05-18T01:20:54Z","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 study the coupled Schr\\\"odinger-Maxwell system $$\\left\\{ \\begin{array}{lll} -\\triangle u+u +\\phi u=\\lambda \\alpha(x) f(u)& {\\rm in} & \\mathbb R^3,\\\\ -\\triangle \\phi =u^2 & {\\rm in} & \\mathbb R^3, \\end{array}\\right. $$ where $\\alpha\\in L^\\infty(\\mathbb R^3)\\cap L^{6/(5-q)}(\\mathbb R^3)$ for some $q\\in (0,1)$, and the continuous function $f:\\mathbb{R}\\to\\mathbb{R}$ is superlinear at zero and sublinear at infinity, e.g., $f(s) = \\min(|s|^r,|s|^p)$ with $0<r<1<p.$ Depending on the range of $\\lambda>0$, non-existence and multiplicity results are obtained.","authors_text":"Alexandru Krist\\'aly, Du\\v{s}an Repov\\v{s}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-12T18:20:02Z","title":"On the Schr\\\"odinger-Maxwell system involving sublinear terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04147","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":"sha256:1c33d2b1e6758a70f370e91d0125b1605e042d4b93b124d404a85074d3975e2e","target":"record","created_at":"2026-05-18T01:20:54Z","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":"efe60c8c2c42bc5db22ce8918e0d1af902341010d7672579b79db28f2af5dc74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-12T18:20:02Z","title_canon_sha256":"ab6d910733345d02dfd8b2da61cb2f551869563373bc381191d865de36d8356c"},"schema_version":"1.0","source":{"id":"1602.04147","kind":"arxiv","version":1}},"canonical_sha256":"442ade9a7ee9acd128d3aa31144c273dd54d8eeecc99c47638b3ffa2c249a729","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"442ade9a7ee9acd128d3aa31144c273dd54d8eeecc99c47638b3ffa2c249a729","first_computed_at":"2026-05-18T01:20:54.432680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:54.432680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PVLTsR70PIlQ4QidP5Es10xTNG0wuCXr9tBjtGxArewjviYDEdhWhAV0j6qrK0BQquKNHR3T8czj2Qv8qjK/AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:54.433392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c33d2b1e6758a70f370e91d0125b1605e042d4b93b124d404a85074d3975e2e","sha256:f6e37813a84dcd1fc8dc5d6bc41ea2eb4cb183a9670c78ba9e55be5ef1d4f2b3"],"state_sha256":"e1e51b0216edbda97ba7de8d2cdc809ebff44b4302ba7b8bc08369f0d0f44a98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"421mfMMSi/V3FLcGM7uwU1twNQAPHX73jy324VshlVN2WeNpQGxuQAlIinZLLba53TuB0FdFZbJ6GTxWUetwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T16:18:10.695493Z","bundle_sha256":"6bb9e2e5fac6af2823eaf620d48adfede31db1c4c5df14badaf618b458d123ff"}}