{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:L5ECSNLQJ3UOKXPAYS2VIURFCX","short_pith_number":"pith:L5ECSNLQ","schema_version":"1.0","canonical_sha256":"5f482935704ee8e55de0c4b554522515df70ea0d7a9d31879f602563db9d17d0","source":{"kind":"arxiv","id":"1905.11120","version":1},"attestation_state":"computed","paper":{"title":"On the Schr\\\"{o}dinger-Poisson system with indefinite potential and $3$-sublinear nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Shibo Liu, Sunra J. N. Mosconi","submitted_at":"2019-05-27T11:05:59Z","abstract_excerpt":"We consider a class of stationary Schr\\\"{o}dinger-Poisson systems with a general nonlinearity $f(u)$ and coercive sign-changing potential $V$ so that the Schr\\\"{o}dinger operator $-\\Delta+V$ is indefinite. Previous results in this framework required $f$ to be strictly $3$-superlinear, thus missing the paramount case of the Gross-Pitaevskii-Poisson system, where $f(t)=|t|^{2}t$; in this paper we fill this gap, obtaining non-trivial solutions when $f$ is not necessarily $3$-superlinear."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1905.11120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-27T11:05:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"631f7a85d7d6bb701046255fafcdefbcf854eb5ad9295fcb4c2cb90fdb40fcb7","abstract_canon_sha256":"d48fc469d8a0eff661107308bd68788860a9a149c7094808e6fa3a3b1ba8ac4f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:02.858465Z","signature_b64":"E/qiUBbsIt7IXDDOh+qmq09EXS9jy4BB6zPrFbYSluLnMe9952qcrDA8DIYFRgCtQvyVgw2//1JsWNDaY+p2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f482935704ee8e55de0c4b554522515df70ea0d7a9d31879f602563db9d17d0","last_reissued_at":"2026-05-17T23:45:02.857988Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:02.857988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Schr\\\"{o}dinger-Poisson system with indefinite potential and $3$-sublinear nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Shibo Liu, Sunra J. N. Mosconi","submitted_at":"2019-05-27T11:05:59Z","abstract_excerpt":"We consider a class of stationary Schr\\\"{o}dinger-Poisson systems with a general nonlinearity $f(u)$ and coercive sign-changing potential $V$ so that the Schr\\\"{o}dinger operator $-\\Delta+V$ is indefinite. Previous results in this framework required $f$ to be strictly $3$-superlinear, thus missing the paramount case of the Gross-Pitaevskii-Poisson system, where $f(t)=|t|^{2}t$; in this paper we fill this gap, obtaining non-trivial solutions when $f$ is not necessarily $3$-superlinear."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11120","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.11120","created_at":"2026-05-17T23:45:02.858067+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.11120v1","created_at":"2026-05-17T23:45:02.858067+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11120","created_at":"2026-05-17T23:45:02.858067+00:00"},{"alias_kind":"pith_short_12","alias_value":"L5ECSNLQJ3UO","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"L5ECSNLQJ3UOKXPA","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"L5ECSNLQ","created_at":"2026-05-18T12:33:21.387695+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L5ECSNLQJ3UOKXPAYS2VIURFCX","json":"https://pith.science/pith/L5ECSNLQJ3UOKXPAYS2VIURFCX.json","graph_json":"https://pith.science/api/pith-number/L5ECSNLQJ3UOKXPAYS2VIURFCX/graph.json","events_json":"https://pith.science/api/pith-number/L5ECSNLQJ3UOKXPAYS2VIURFCX/events.json","paper":"https://pith.science/paper/L5ECSNLQ"},"agent_actions":{"view_html":"https://pith.science/pith/L5ECSNLQJ3UOKXPAYS2VIURFCX","download_json":"https://pith.science/pith/L5ECSNLQJ3UOKXPAYS2VIURFCX.json","view_paper":"https://pith.science/paper/L5ECSNLQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.11120&json=true","fetch_graph":"https://pith.science/api/pith-number/L5ECSNLQJ3UOKXPAYS2VIURFCX/graph.json","fetch_events":"https://pith.science/api/pith-number/L5ECSNLQJ3UOKXPAYS2VIURFCX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L5ECSNLQJ3UOKXPAYS2VIURFCX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L5ECSNLQJ3UOKXPAYS2VIURFCX/action/storage_attestation","attest_author":"https://pith.science/pith/L5ECSNLQJ3UOKXPAYS2VIURFCX/action/author_attestation","sign_citation":"https://pith.science/pith/L5ECSNLQJ3UOKXPAYS2VIURFCX/action/citation_signature","submit_replication":"https://pith.science/pith/L5ECSNLQJ3UOKXPAYS2VIURFCX/action/replication_record"}},"created_at":"2026-05-17T23:45:02.858067+00:00","updated_at":"2026-05-17T23:45:02.858067+00:00"}