{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:P4ZRU2FUTO6G7L4NSHPU3U6PKT","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":"dc72a7dcef347304faaae58133accaf0ef75925de8fb868ba47051c69b4238d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-16T08:23:47Z","title_canon_sha256":"287054287877d744b52d991bbcb418eac0c7f8c95f038d83e778c161092e6fe8"},"schema_version":"1.0","source":{"id":"1612.05392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05392","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05392v1","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05392","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"pith_short_12","alias_value":"P4ZRU2FUTO6G","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P4ZRU2FUTO6G7L4N","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P4ZRU2FU","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:9f4af8243d8f31744df991b6317acc8d0a70511efb10209df6aa9838e5dab661","target":"graph","created_at":"2026-05-18T00:54:51Z","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":"The main aim of the paper is to prove a fountain theorem without assuming the $\\tau$-upper semicontinuity condition on the variational functional. Using this improved fountain theorem, we may deal with more general strongly indefinite elliptic problems with various sign-changing nonlinear terms. As an application, we obtain infinitely many solutions for a semilinear Schr\\\"odinger equation with strongly indefinite structure and sign-changing nonlinearity.","authors_text":"Huan-Song Zhou, Long-Jiang Gu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-16T08:23:47Z","title":"An Improved Fountain Theorem and its Application"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05392","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:c1e1ade0ebec37a52fc738f1048e58712b7b0358c336ae81cbe8c26ab14e0d04","target":"record","created_at":"2026-05-18T00:54:51Z","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":"dc72a7dcef347304faaae58133accaf0ef75925de8fb868ba47051c69b4238d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-16T08:23:47Z","title_canon_sha256":"287054287877d744b52d991bbcb418eac0c7f8c95f038d83e778c161092e6fe8"},"schema_version":"1.0","source":{"id":"1612.05392","kind":"arxiv","version":1}},"canonical_sha256":"7f331a68b49bbc6faf8d91df4dd3cf54e8dd1ec8259c28ae2ad1e8f796ecd18e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f331a68b49bbc6faf8d91df4dd3cf54e8dd1ec8259c28ae2ad1e8f796ecd18e","first_computed_at":"2026-05-18T00:54:51.891341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:51.891341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dOB7IqqOjEEoocJ6ti2OjMOSMu8+RFnxKHG7Mq9K0bCzwJDMa25aSyELbLHrIGbtaThm1l9FxRbxb1fh0w1NCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:51.891864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1e1ade0ebec37a52fc738f1048e58712b7b0358c336ae81cbe8c26ab14e0d04","sha256:9f4af8243d8f31744df991b6317acc8d0a70511efb10209df6aa9838e5dab661"],"state_sha256":"bb841599b9825780161a6d99c5d195c8721ebd6175db3ec0da6a961e21f8ca22"}