{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GA5WS2KNMUCC2KLAHQNOT6FUZF","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":"33cb43cbe59d8b63ad9b7bbb84ff34857fd1d6456bd4b1b45d467b545474fa7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-17T22:50:00Z","title_canon_sha256":"abf0afc9a94b0fd1ba36133cb3ddb951f049ac5e5a2e2ae9671db1bb5006b4be"},"schema_version":"1.0","source":{"id":"1401.4487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4487","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4487v1","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4487","created_at":"2026-05-18T03:01:45Z"},{"alias_kind":"pith_short_12","alias_value":"GA5WS2KNMUCC","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"GA5WS2KNMUCC2KLA","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"GA5WS2KN","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:3b03fdb1cde447bf5815a07bf36427293e7db6a1431ef5a8dee86c8a6ab0f11d","target":"graph","created_at":"2026-05-18T03:01:45Z","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 class of scalar field equations with anisotropic nonlocal nonlinearities. We obtain a suitable extension of the well-known compactness lemma of Benci and Cerami to this variable exponent setting, and use it to prove that the Palais-Smale condition holds at all level below a certain threshold. We deduce the existence of a ground state when the variable exponent slowly approaches the limit at infinity from below.","authors_text":"Antonio Iannizzotto, Kanishka Perera, Marco Squassina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-17T22:50:00Z","title":"Ground states for scalar field equations with anisotropic nonlocal nonlinearities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4487","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:b02327a3f344adc3742b8e01296e780c11d6844be57b49614350d06154ab658e","target":"record","created_at":"2026-05-18T03:01:45Z","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":"33cb43cbe59d8b63ad9b7bbb84ff34857fd1d6456bd4b1b45d467b545474fa7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-17T22:50:00Z","title_canon_sha256":"abf0afc9a94b0fd1ba36133cb3ddb951f049ac5e5a2e2ae9671db1bb5006b4be"},"schema_version":"1.0","source":{"id":"1401.4487","kind":"arxiv","version":1}},"canonical_sha256":"303b69694d65042d29603c1ae9f8b4c96ac6797f776a1cb343ff00889b5a8868","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"303b69694d65042d29603c1ae9f8b4c96ac6797f776a1cb343ff00889b5a8868","first_computed_at":"2026-05-18T03:01:45.548334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:45.548334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/5cyUAZZKP0yPj0V6+bcNN8IWhAq5crIKjr232++Fgd+kwokxxBUl8ZI910ibAKqjpC80cZbEqfLvicYDecBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:45.548933Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b02327a3f344adc3742b8e01296e780c11d6844be57b49614350d06154ab658e","sha256:3b03fdb1cde447bf5815a07bf36427293e7db6a1431ef5a8dee86c8a6ab0f11d"],"state_sha256":"7ef913c46a9b4681b6d4c6b346ec3d4c41fe68b27008d2fd8860215ee4ba3a4e"}