{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UJOV72GPSFWVQEFZWB4HJN5QOS","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":"fa7d565af9b22d1d1595eebb888eca8ea9d0fb24a0d4362440433c2a184f882a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-22T13:07:52Z","title_canon_sha256":"8a227bb24213cd15a80be5cfa0f1a57baf4c4ea4ad95f3e960cf52375dfdfbf5"},"schema_version":"1.0","source":{"id":"1310.5907","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5907","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5907v1","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5907","created_at":"2026-05-18T03:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"UJOV72GPSFWV","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UJOV72GPSFWVQEFZ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UJOV72GP","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:fce22a233f255992741f7cdb40a8b67fed76c68dc8c6ef0829a09f5d0f2598d1","target":"graph","created_at":"2026-05-18T03:09:24Z","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 develop arguments on convexity and minimization of energy functionals on Orlicz-Sobolev spaces to investigate existence of solution to the equation $\\displaystyle -\\mbox{div} (\\phi(|\\nabla u|) \\nabla u) = f(x,u) + h \\mbox{in} \\Omega$ under Dirichlet boundary conditions, where $\\Omega \\subset {\\bf R}^{N}$ is a bounded smooth domain, $\\phi : (0,\\infty)\\longrightarrow (0,\\infty)$ is a suitable continuous function and $f: \\Omega \\times {\\bf R} \\to {\\bf R}$ satisfies the Carath\\'eodory conditions, while $h$ is a measure.","authors_text":"J. V. Goncalves, M. L. M. Carvalho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-22T13:07:52Z","title":"Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5907","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:bf1800c5670daf6f092fee31b4f89b01fb0e6dbf2bbf12a274f58a4564aef3ae","target":"record","created_at":"2026-05-18T03:09:24Z","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":"fa7d565af9b22d1d1595eebb888eca8ea9d0fb24a0d4362440433c2a184f882a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-22T13:07:52Z","title_canon_sha256":"8a227bb24213cd15a80be5cfa0f1a57baf4c4ea4ad95f3e960cf52375dfdfbf5"},"schema_version":"1.0","source":{"id":"1310.5907","kind":"arxiv","version":1}},"canonical_sha256":"a25d5fe8cf916d5810b9b07874b7b0748f9c4efd0358e60124d42ca7a01baeab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a25d5fe8cf916d5810b9b07874b7b0748f9c4efd0358e60124d42ca7a01baeab","first_computed_at":"2026-05-18T03:09:24.145850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:24.145850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GAfwDY+hgFp7H9fBN4qoqEwEIqd06u7D93H+eK7VNfIWqHgn5xf7QG1f05BIYfWsbJs90jLR7VZE0bT73W/XAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:24.146644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5907","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf1800c5670daf6f092fee31b4f89b01fb0e6dbf2bbf12a274f58a4564aef3ae","sha256:fce22a233f255992741f7cdb40a8b67fed76c68dc8c6ef0829a09f5d0f2598d1"],"state_sha256":"008a423b1a4c3d68420963f53c31bacd5d1a4701b6af9dc0c4c512c008e6e3cc"}