{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3TORLZQJN75ET5G43D33YQ4XOC","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":"605553029e75cc3ef5195b7f66f6649592c3dc0d2d9d233785ea7778a8a1b662","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-06T08:39:45Z","title_canon_sha256":"884cd6e79a5eebd893c08943853b2d35efb8fe2ddf64315fc21fc572b16e1e18"},"schema_version":"1.0","source":{"id":"1501.01110","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01110","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01110v2","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01110","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"pith_short_12","alias_value":"3TORLZQJN75E","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3TORLZQJN75ET5G4","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3TORLZQJ","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:1b55b95f1cd7d6aca6bb56055d29640098431e9253a6fdce85d6d4f2254c8dcd","target":"graph","created_at":"2026-05-18T01:24:30Z","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 consider a Schr\\\"odinger-Poisson system involving a general nonlinearity at critical growth and we prove the existence of positive solutions. The Ambrosetti-Rabinowitz condition is not required. We also study the asymptotics of solutions with respect to a parameter.","authors_text":"Jianjun Zhang, Jo\\~ao Marcos do \\'O, Marco Squassina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-06T08:39:45Z","title":"Schr\\\"odinger-Poisson systems with a general critical nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01110","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":"sha256:73daa3f91af4b2b610c6c553c0b1980d26994f2449f3bc2b1ac952e41e698b5d","target":"record","created_at":"2026-05-18T01:24:30Z","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":"605553029e75cc3ef5195b7f66f6649592c3dc0d2d9d233785ea7778a8a1b662","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-06T08:39:45Z","title_canon_sha256":"884cd6e79a5eebd893c08943853b2d35efb8fe2ddf64315fc21fc572b16e1e18"},"schema_version":"1.0","source":{"id":"1501.01110","kind":"arxiv","version":2}},"canonical_sha256":"dcdd15e6096ffa49f4dcd8f7bc4397708b090833f30586626bbf554c35f23779","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcdd15e6096ffa49f4dcd8f7bc4397708b090833f30586626bbf554c35f23779","first_computed_at":"2026-05-18T01:24:30.461928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:30.461928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vMyBR/riM0McloVsYcNa6xZq8b++L8K44KArKddoEzwRdCGSl88ncsm3Zpk6clr8c0EeWYQakSKIabrgXjZAAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:30.462638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01110","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73daa3f91af4b2b610c6c553c0b1980d26994f2449f3bc2b1ac952e41e698b5d","sha256:1b55b95f1cd7d6aca6bb56055d29640098431e9253a6fdce85d6d4f2254c8dcd"],"state_sha256":"66738477f6f32be8d446873a94f25b2ea77c96e20dd1b61442f05ff2bdaea6f4"}