{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:F2HN6YFLHBHG2JNPLNIGM3PHNP","short_pith_number":"pith:F2HN6YFL","canonical_record":{"source":{"id":"1105.3870","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2011-05-19T13:43:48Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"71047a1ef64678bcd256120bbc9d1b12be31e11cb507edf86e6a1542fcd0b027","abstract_canon_sha256":"727863cae3eb53ec869ff4a4cb9919a81fea59f87da96cb6c61634ae5b32315d"},"schema_version":"1.0"},"canonical_sha256":"2e8edf60ab384e6d25af5b50666de76bc56c432a279f28095bce1017e6082089","source":{"kind":"arxiv","id":"1105.3870","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3870","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3870v1","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3870","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"pith_short_12","alias_value":"F2HN6YFLHBHG","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F2HN6YFLHBHG2JNP","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F2HN6YFL","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:F2HN6YFLHBHG2JNPLNIGM3PHNP","target":"record","payload":{"canonical_record":{"source":{"id":"1105.3870","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2011-05-19T13:43:48Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"71047a1ef64678bcd256120bbc9d1b12be31e11cb507edf86e6a1542fcd0b027","abstract_canon_sha256":"727863cae3eb53ec869ff4a4cb9919a81fea59f87da96cb6c61634ae5b32315d"},"schema_version":"1.0"},"canonical_sha256":"2e8edf60ab384e6d25af5b50666de76bc56c432a279f28095bce1017e6082089","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:51.162623Z","signature_b64":"Fh8/Gb17lglvzRbSimSTPQXQZg7S8aPRHnZXe9xWE16vlL2NFHme19QG/9GlpeReWcozIGtcvYzrDY+fsfD5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e8edf60ab384e6d25af5b50666de76bc56c432a279f28095bce1017e6082089","last_reissued_at":"2026-05-18T04:21:51.161788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:51.161788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.3870","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:21:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p4aDkwdv73gsVltqocWRk2ice4jDy1Na7EPnY3sAOP5H+riFyvtMVJ55jKg82G/WZveI94+UNQycibItdscbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T12:35:59.305602Z"},"content_sha256":"64710a963da9c3f48bdfdebb801863724622a9f316495269debeb9e166634d00","schema_version":"1.0","event_id":"sha256:64710a963da9c3f48bdfdebb801863724622a9f316495269debeb9e166634d00"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:F2HN6YFLHBHG2JNPLNIGM3PHNP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear elliptic boundary value problems at resonance with nonlinear Wentzell boundary conditions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.DS","authors_text":"Ciprian G. Gal, Mahamadi Warma","submitted_at":"2011-05-19T13:43:48Z","abstract_excerpt":"In the first part of the article, we give necessary and sufficient conditions for the solvability of a class of nonlinear elliptic boundary value problems with nonlinear boundary conditions involving the q-Laplace-Beltrami operator. In the second part, we give some additional results on existence, uniqueness and continuous dependence estimates of the weak solutions for these classes of nonlinear problems. Finally, we show that these solutions are also bounded and provide explicit estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3870","kind":"arxiv","version":1},"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":"2026-05-18T04:21:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7qwJNyBA9ZPLZUlxB2qebIePKyCRcHdfXiiPDbJdc22c/xuz+SqqZNpBw3WfUHVs4JLbHCCHD5w4iEe7f/dQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T12:35:59.305948Z"},"content_sha256":"b56c1a09e49e376831b7d87f74cac4d2784c2a42b26c66370a60c1572767bedc","schema_version":"1.0","event_id":"sha256:b56c1a09e49e376831b7d87f74cac4d2784c2a42b26c66370a60c1572767bedc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F2HN6YFLHBHG2JNPLNIGM3PHNP/bundle.json","state_url":"https://pith.science/pith/F2HN6YFLHBHG2JNPLNIGM3PHNP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F2HN6YFLHBHG2JNPLNIGM3PHNP/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":"2026-06-21T12:35:59Z","links":{"resolver":"https://pith.science/pith/F2HN6YFLHBHG2JNPLNIGM3PHNP","bundle":"https://pith.science/pith/F2HN6YFLHBHG2JNPLNIGM3PHNP/bundle.json","state":"https://pith.science/pith/F2HN6YFLHBHG2JNPLNIGM3PHNP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F2HN6YFLHBHG2JNPLNIGM3PHNP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:F2HN6YFLHBHG2JNPLNIGM3PHNP","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":"727863cae3eb53ec869ff4a4cb9919a81fea59f87da96cb6c61634ae5b32315d","cross_cats_sorted":["math.AP","math.FA"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2011-05-19T13:43:48Z","title_canon_sha256":"71047a1ef64678bcd256120bbc9d1b12be31e11cb507edf86e6a1542fcd0b027"},"schema_version":"1.0","source":{"id":"1105.3870","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3870","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3870v1","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3870","created_at":"2026-05-18T04:21:51Z"},{"alias_kind":"pith_short_12","alias_value":"F2HN6YFLHBHG","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F2HN6YFLHBHG2JNP","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F2HN6YFL","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:b56c1a09e49e376831b7d87f74cac4d2784c2a42b26c66370a60c1572767bedc","target":"graph","created_at":"2026-05-18T04:21:51Z","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":"In the first part of the article, we give necessary and sufficient conditions for the solvability of a class of nonlinear elliptic boundary value problems with nonlinear boundary conditions involving the q-Laplace-Beltrami operator. In the second part, we give some additional results on existence, uniqueness and continuous dependence estimates of the weak solutions for these classes of nonlinear problems. Finally, we show that these solutions are also bounded and provide explicit estimates.","authors_text":"Ciprian G. Gal, Mahamadi Warma","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2011-05-19T13:43:48Z","title":"Nonlinear elliptic boundary value problems at resonance with nonlinear Wentzell boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3870","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":"sha256:64710a963da9c3f48bdfdebb801863724622a9f316495269debeb9e166634d00","target":"record","created_at":"2026-05-18T04:21:51Z","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":"727863cae3eb53ec869ff4a4cb9919a81fea59f87da96cb6c61634ae5b32315d","cross_cats_sorted":["math.AP","math.FA"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DS","submitted_at":"2011-05-19T13:43:48Z","title_canon_sha256":"71047a1ef64678bcd256120bbc9d1b12be31e11cb507edf86e6a1542fcd0b027"},"schema_version":"1.0","source":{"id":"1105.3870","kind":"arxiv","version":1}},"canonical_sha256":"2e8edf60ab384e6d25af5b50666de76bc56c432a279f28095bce1017e6082089","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e8edf60ab384e6d25af5b50666de76bc56c432a279f28095bce1017e6082089","first_computed_at":"2026-05-18T04:21:51.161788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:51.161788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fh8/Gb17lglvzRbSimSTPQXQZg7S8aPRHnZXe9xWE16vlL2NFHme19QG/9GlpeReWcozIGtcvYzrDY+fsfD5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:51.162623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3870","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64710a963da9c3f48bdfdebb801863724622a9f316495269debeb9e166634d00","sha256:b56c1a09e49e376831b7d87f74cac4d2784c2a42b26c66370a60c1572767bedc"],"state_sha256":"02d546544e10a7982a0c0b9c97809f0477bc7d238692d124515221bc5c5b3b4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"md/hURd1v01Xz4B4QXxjiCCKsjY4gtpx7rfjFhp0kNF3zhfc1gEh5xW299z+92PGY4Ot7318OgsZJ3nwIMDKCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T12:35:59.307893Z","bundle_sha256":"62fa2c2bc4fade466ee606e6d1b33513c518448fd065f07fe5e7dbb4b54b13b0"}}