{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:J5UPEZHUUBPVDPQEWGAUQBCWDC","short_pith_number":"pith:J5UPEZHU","canonical_record":{"source":{"id":"1307.6578","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-24T20:50:22Z","cross_cats_sorted":[],"title_canon_sha256":"2992250c8b41ce13e5a2db71e0ab4ed36e64e2600cf33f0e17d8325b96bb5c53","abstract_canon_sha256":"325b0301c2e1774e3efc73b4f2ea26f22c630d3a0bb31f39651517bf761825ad"},"schema_version":"1.0"},"canonical_sha256":"4f68f264f4a05f51be04b1814804561885edda7606e2d3ea36ad16c178964fd1","source":{"kind":"arxiv","id":"1307.6578","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6578","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6578v2","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6578","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"pith_short_12","alias_value":"J5UPEZHUUBPV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J5UPEZHUUBPVDPQE","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J5UPEZHU","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:J5UPEZHUUBPVDPQEWGAUQBCWDC","target":"record","payload":{"canonical_record":{"source":{"id":"1307.6578","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-24T20:50:22Z","cross_cats_sorted":[],"title_canon_sha256":"2992250c8b41ce13e5a2db71e0ab4ed36e64e2600cf33f0e17d8325b96bb5c53","abstract_canon_sha256":"325b0301c2e1774e3efc73b4f2ea26f22c630d3a0bb31f39651517bf761825ad"},"schema_version":"1.0"},"canonical_sha256":"4f68f264f4a05f51be04b1814804561885edda7606e2d3ea36ad16c178964fd1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:08.637422Z","signature_b64":"38b9D+UKFSkjR4LY2cn6OsRgRoxbzC/GhPAY3CZWJek+iNRPqY9eHuJSvhLHoAYxXzSz1xh19vIz9kNpe/ABBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f68f264f4a05f51be04b1814804561885edda7606e2d3ea36ad16c178964fd1","last_reissued_at":"2026-05-18T02:59:08.636834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:08.636834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.6578","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:59:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cuxrj/vRwxkI9iz3PWA8Ms3lghfoJq8hOktkjvb9j9RfemJafOdXbFNbIaLUag3rfZMPX/Jld8qArzBiSXmiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:32:52.805900Z"},"content_sha256":"b2fcb2a6c148c046ba771cf2abc6100ca136ff6a6cb5c5648fa19a5774d6de06","schema_version":"1.0","event_id":"sha256:b2fcb2a6c148c046ba771cf2abc6100ca136ff6a6cb5c5648fa19a5774d6de06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:J5UPEZHUUBPVDPQEWGAUQBCWDC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence and symmetry for elliptic equations in R^n with arbitrary growth in the gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lucas C. F. Ferreira, Marcelo Montenegro, Matheus C. Santos","submitted_at":"2013-07-24T20:50:22Z","abstract_excerpt":"We study the semilinear elliptic equation $\\Delta u + g(x,u,Du) = 0$ in $\\R^n$. The nonlinearities $g$ can have arbitrary growth in $u$ and $Du$, including in particular the exponential behavior. No restriction is imposed on the behavior of $g(x,z,p)$ at infinity except in the variable $x$. We obtain a solution $u$ that is locally unique and inherits many of the symmetry properties of $g$. Positivity and asymptotic behavior of the solution are also addressed. Our results can be extended to other domains like half-space and exterior domains. We give some examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6578","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:59:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"raPJzzhTw3HYUcDINgORNjNQ4SZKCfJBRkQhPNvYFjjidtsuUKy6xnNZy2mjbZRSDKeKMQ4X5siuKKELiuALCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:32:52.806249Z"},"content_sha256":"ac180b722527ec1a89d21545db022598fd7ec3a9932d687e367ebfea84a15b82","schema_version":"1.0","event_id":"sha256:ac180b722527ec1a89d21545db022598fd7ec3a9932d687e367ebfea84a15b82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J5UPEZHUUBPVDPQEWGAUQBCWDC/bundle.json","state_url":"https://pith.science/pith/J5UPEZHUUBPVDPQEWGAUQBCWDC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J5UPEZHUUBPVDPQEWGAUQBCWDC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T06:32:52Z","links":{"resolver":"https://pith.science/pith/J5UPEZHUUBPVDPQEWGAUQBCWDC","bundle":"https://pith.science/pith/J5UPEZHUUBPVDPQEWGAUQBCWDC/bundle.json","state":"https://pith.science/pith/J5UPEZHUUBPVDPQEWGAUQBCWDC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J5UPEZHUUBPVDPQEWGAUQBCWDC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J5UPEZHUUBPVDPQEWGAUQBCWDC","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":"325b0301c2e1774e3efc73b4f2ea26f22c630d3a0bb31f39651517bf761825ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-24T20:50:22Z","title_canon_sha256":"2992250c8b41ce13e5a2db71e0ab4ed36e64e2600cf33f0e17d8325b96bb5c53"},"schema_version":"1.0","source":{"id":"1307.6578","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6578","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6578v2","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6578","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"pith_short_12","alias_value":"J5UPEZHUUBPV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J5UPEZHUUBPVDPQE","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J5UPEZHU","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:ac180b722527ec1a89d21545db022598fd7ec3a9932d687e367ebfea84a15b82","target":"graph","created_at":"2026-05-18T02:59:08Z","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 study the semilinear elliptic equation $\\Delta u + g(x,u,Du) = 0$ in $\\R^n$. The nonlinearities $g$ can have arbitrary growth in $u$ and $Du$, including in particular the exponential behavior. No restriction is imposed on the behavior of $g(x,z,p)$ at infinity except in the variable $x$. We obtain a solution $u$ that is locally unique and inherits many of the symmetry properties of $g$. Positivity and asymptotic behavior of the solution are also addressed. Our results can be extended to other domains like half-space and exterior domains. We give some examples.","authors_text":"Lucas C. F. Ferreira, Marcelo Montenegro, Matheus C. Santos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-24T20:50:22Z","title":"Existence and symmetry for elliptic equations in R^n with arbitrary growth in the gradient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6578","kind":"arxiv","version":2},"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:b2fcb2a6c148c046ba771cf2abc6100ca136ff6a6cb5c5648fa19a5774d6de06","target":"record","created_at":"2026-05-18T02:59:08Z","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":"325b0301c2e1774e3efc73b4f2ea26f22c630d3a0bb31f39651517bf761825ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-24T20:50:22Z","title_canon_sha256":"2992250c8b41ce13e5a2db71e0ab4ed36e64e2600cf33f0e17d8325b96bb5c53"},"schema_version":"1.0","source":{"id":"1307.6578","kind":"arxiv","version":2}},"canonical_sha256":"4f68f264f4a05f51be04b1814804561885edda7606e2d3ea36ad16c178964fd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f68f264f4a05f51be04b1814804561885edda7606e2d3ea36ad16c178964fd1","first_computed_at":"2026-05-18T02:59:08.636834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:08.636834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"38b9D+UKFSkjR4LY2cn6OsRgRoxbzC/GhPAY3CZWJek+iNRPqY9eHuJSvhLHoAYxXzSz1xh19vIz9kNpe/ABBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:08.637422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6578","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2fcb2a6c148c046ba771cf2abc6100ca136ff6a6cb5c5648fa19a5774d6de06","sha256:ac180b722527ec1a89d21545db022598fd7ec3a9932d687e367ebfea84a15b82"],"state_sha256":"2364ee3633e159e56cfc1d773a5acbe41ddc5ea5292b351881eacf33715b90a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FmjBU8+HPpaDzVFAB/uoID68Vego0D8NKGRWHd7XxQBNuxtESlOUW1vkYq6OlH+3y4CkjPpoRbLtt4VRxiteCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:32:52.809269Z","bundle_sha256":"26c9f86864949fbc1072b3e52a98f960094ad0eb64ef4b95dcd021b560404441"}}