{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NMKIRQOEAMUO56DVBPWNE3255O","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":"65df958fcdd8d488a46717d2dc64a4388812f4610924f42d5bf4c131eaadafba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-18T08:39:50Z","title_canon_sha256":"78434ddfcae9bd728c8be583393e0ac3bb1e30991a70c04eb317af05dc822d20"},"schema_version":"1.0","source":{"id":"1812.07232","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07232","created_at":"2026-05-17T23:58:01Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07232v1","created_at":"2026-05-17T23:58:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07232","created_at":"2026-05-17T23:58:01Z"},{"alias_kind":"pith_short_12","alias_value":"NMKIRQOEAMUO","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NMKIRQOEAMUO56DV","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NMKIRQOE","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:0a7c49cd6e3c10e53644318b5c8b45f298f2c4754280712e162b98139346a767","target":"graph","created_at":"2026-05-17T23:58:01Z","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":"A class of generalized Schr\\\"{o}dinger elliptic problems involving concave-convex and other types of nonlinearities is studied. A reasonable overview about the set of solutions is provided when the parameters involved in the equation assume different real values.","authors_text":"Andrelino V. Santos, Jo\\~ao R. Santos J\\'unior","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-18T08:39:50Z","title":"Multiple solutions for a generalized Schr\\\"{o}dinger problem with 'concave-convex' nonlinearities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07232","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":"sha256:57dc349b0e0098bfb59a336ceb3ad58684d4364753d02fd5b8818d07cce09001","target":"record","created_at":"2026-05-17T23:58:01Z","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":"65df958fcdd8d488a46717d2dc64a4388812f4610924f42d5bf4c131eaadafba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-18T08:39:50Z","title_canon_sha256":"78434ddfcae9bd728c8be583393e0ac3bb1e30991a70c04eb317af05dc822d20"},"schema_version":"1.0","source":{"id":"1812.07232","kind":"arxiv","version":1}},"canonical_sha256":"6b1488c1c40328eef8750becd26f5deba1b2b5598a0317ae2373d7dc7d0d6771","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b1488c1c40328eef8750becd26f5deba1b2b5598a0317ae2373d7dc7d0d6771","first_computed_at":"2026-05-17T23:58:01.100254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:01.100254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7cy3QdNnNgCNP8JkS8cP1JL6P5LcVaRulxmR6sw18HXZ0go24uvkdvvV08iLoSnKi1vMuSfdE2bRSb5mJTCvBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:01.100787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.07232","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57dc349b0e0098bfb59a336ceb3ad58684d4364753d02fd5b8818d07cce09001","sha256:0a7c49cd6e3c10e53644318b5c8b45f298f2c4754280712e162b98139346a767"],"state_sha256":"d74fd352b6d482a817268872aa6ee1d31160510be326299a92a9ded1ec688dd0"}