{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LX2CE7WYMXNHKE6SWNT5ZBHX47","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":"b89ced456b24a3505da7a176031205c0e02657dab220937291a2920659beab5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-31T17:15:47Z","title_canon_sha256":"07b538e9d8b236059c9217df4409629730ab08fed462ee6c31f9fd71cba3020c"},"schema_version":"1.0","source":{"id":"1210.8401","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.8401","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1210.8401v3","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.8401","created_at":"2026-05-18T03:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"LX2CE7WYMXNH","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LX2CE7WYMXNHKE6S","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LX2CE7WY","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:ffdc49a9e63b990db35343cf31baee6d43a98bcb1cb2d8f3b60b6b0802b6b6d0","target":"graph","created_at":"2026-05-18T03:12:35Z","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 paper deals with equations driven by a non-local integrodifferential operator $\\mathcal L_K$ with homogeneous Dirichlet boundary conditions. These equations have a variational structure and we find a solution for them using the Saddle Point Theorem.","authors_text":"Alessio Fiscella","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-31T17:15:47Z","title":"Saddle point solutions for non-local elliptic operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8401","kind":"arxiv","version":3},"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":"sha256:1221242311a63ffb8ab0f4d8236686d04b918d0f787c9fb06445629b33c63d84","target":"record","created_at":"2026-05-18T03:12:35Z","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":"b89ced456b24a3505da7a176031205c0e02657dab220937291a2920659beab5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-31T17:15:47Z","title_canon_sha256":"07b538e9d8b236059c9217df4409629730ab08fed462ee6c31f9fd71cba3020c"},"schema_version":"1.0","source":{"id":"1210.8401","kind":"arxiv","version":3}},"canonical_sha256":"5df4227ed865da7513d2b367dc84f7e7e9965120bec5c7b2f088dbd26fdae41e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5df4227ed865da7513d2b367dc84f7e7e9965120bec5c7b2f088dbd26fdae41e","first_computed_at":"2026-05-18T03:12:35.098725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:35.098725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oJp4FaMout52RE0D54xHgz3EebXYN/igXcjOwN3UW3uylxFtbMT3nBl67hj0v/EoZgiRG5aUSyH2EtueIVM2Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:35.099489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.8401","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1221242311a63ffb8ab0f4d8236686d04b918d0f787c9fb06445629b33c63d84","sha256:ffdc49a9e63b990db35343cf31baee6d43a98bcb1cb2d8f3b60b6b0802b6b6d0"],"state_sha256":"c88c887a3611ed4cdc1b0349ac9bab62333cc82e438590886cdcab3c662e80a8"}