{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5IPVBWRT2MHNLXUNQSWUX223ER","short_pith_number":"pith:5IPVBWRT","canonical_record":{"source":{"id":"1309.7450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-28T10:46:22Z","cross_cats_sorted":[],"title_canon_sha256":"b2a5b2c1f94b17e3969c2d3eded8b188b412e9ee6e294b96450861d401314366","abstract_canon_sha256":"f4000405bd29554a64c02fdeb9fd780a869dc57ad7a86b8a1ea364214b269dd9"},"schema_version":"1.0"},"canonical_sha256":"ea1f50da33d30ed5de8d84ad4beb5b24772e758994e4eed97a708c546b775296","source":{"kind":"arxiv","id":"1309.7450","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7450","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7450v1","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7450","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"5IPVBWRT2MHN","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5IPVBWRT2MHNLXUN","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5IPVBWRT","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5IPVBWRT2MHNLXUNQSWUX223ER","target":"record","payload":{"canonical_record":{"source":{"id":"1309.7450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-28T10:46:22Z","cross_cats_sorted":[],"title_canon_sha256":"b2a5b2c1f94b17e3969c2d3eded8b188b412e9ee6e294b96450861d401314366","abstract_canon_sha256":"f4000405bd29554a64c02fdeb9fd780a869dc57ad7a86b8a1ea364214b269dd9"},"schema_version":"1.0"},"canonical_sha256":"ea1f50da33d30ed5de8d84ad4beb5b24772e758994e4eed97a708c546b775296","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:58.666109Z","signature_b64":"KxXfc/gDTeQCt5yM0todwJtsWwSeD5yfwFnyb2b8Unbbb2BTZGpRr5bitak8U+Kt26ni1mXAKDpvTh6eR+eMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea1f50da33d30ed5de8d84ad4beb5b24772e758994e4eed97a708c546b775296","last_reissued_at":"2026-05-18T03:11:58.665440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:58.665440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.7450","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":"2026-05-18T03:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1mUiaRSrwQLpkQHjOcfU4aywKynupuvUG5UqYfKb4BRY/prhTw6yRDCkvLnpdMWvq8LPYZs7SUHkvpk198tPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T10:20:05.914098Z"},"content_sha256":"8fa7d0bcb6550d3716251c7335eac4fb985e4190a1dfd4f0008dccfb4afe1ef4","schema_version":"1.0","event_id":"sha256:8fa7d0bcb6550d3716251c7335eac4fb985e4190a1dfd4f0008dccfb4afe1ef4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5IPVBWRT2MHNLXUNQSWUX223ER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear nonhomogeneous Dirichlet equations with a superlinear reaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikolaos S. Papageorgiou, Patrick Winkert","submitted_at":"2013-09-28T10:46:22Z","abstract_excerpt":"We consider a nonlinear elliptic Dirichlet equation driven by a nonlinear nonhomogeneous differential operator involving a Carath\\'{e}odory reaction which is $(p-1)$-superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a three-solutions-theorem extending an earlier classical result of Wang (Ann. Inst. H. Poincar\\'e Anal. Non Lin\\'eaire 8 (1991), no. 1, 43--57). Subsequently, by imposing additional conditions on the reaction $f(x,\\cdot)$, we produce two more nontrivial constant sign solutions and a nodal solution for a total of five nontrivial solutions. In the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7450","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":"2026-05-18T03:11:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sCwXRebl41Wjg/1+1Z4l/t04/FTQpdNKUTn0UjcTRxPDZZuukTmtlz6GAl3ims7O79765vI4FgstQkpse0fVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T10:20:05.914597Z"},"content_sha256":"9507cdf0c9745f7ada085561d4d4b8d39398a8874b085f713a80b26799078e8b","schema_version":"1.0","event_id":"sha256:9507cdf0c9745f7ada085561d4d4b8d39398a8874b085f713a80b26799078e8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5IPVBWRT2MHNLXUNQSWUX223ER/bundle.json","state_url":"https://pith.science/pith/5IPVBWRT2MHNLXUNQSWUX223ER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5IPVBWRT2MHNLXUNQSWUX223ER/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":"2026-05-26T10:20:05Z","links":{"resolver":"https://pith.science/pith/5IPVBWRT2MHNLXUNQSWUX223ER","bundle":"https://pith.science/pith/5IPVBWRT2MHNLXUNQSWUX223ER/bundle.json","state":"https://pith.science/pith/5IPVBWRT2MHNLXUNQSWUX223ER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5IPVBWRT2MHNLXUNQSWUX223ER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5IPVBWRT2MHNLXUNQSWUX223ER","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":"f4000405bd29554a64c02fdeb9fd780a869dc57ad7a86b8a1ea364214b269dd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-28T10:46:22Z","title_canon_sha256":"b2a5b2c1f94b17e3969c2d3eded8b188b412e9ee6e294b96450861d401314366"},"schema_version":"1.0","source":{"id":"1309.7450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7450","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7450v1","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7450","created_at":"2026-05-18T03:11:58Z"},{"alias_kind":"pith_short_12","alias_value":"5IPVBWRT2MHN","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5IPVBWRT2MHNLXUN","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5IPVBWRT","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:9507cdf0c9745f7ada085561d4d4b8d39398a8874b085f713a80b26799078e8b","target":"graph","created_at":"2026-05-18T03:11:58Z","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 nonlinear elliptic Dirichlet equation driven by a nonlinear nonhomogeneous differential operator involving a Carath\\'{e}odory reaction which is $(p-1)$-superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a three-solutions-theorem extending an earlier classical result of Wang (Ann. Inst. H. Poincar\\'e Anal. Non Lin\\'eaire 8 (1991), no. 1, 43--57). Subsequently, by imposing additional conditions on the reaction $f(x,\\cdot)$, we produce two more nontrivial constant sign solutions and a nodal solution for a total of five nontrivial solutions. In the s","authors_text":"Nikolaos S. Papageorgiou, Patrick Winkert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-28T10:46:22Z","title":"Nonlinear nonhomogeneous Dirichlet equations with a superlinear reaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7450","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":"sha256:8fa7d0bcb6550d3716251c7335eac4fb985e4190a1dfd4f0008dccfb4afe1ef4","target":"record","created_at":"2026-05-18T03:11:58Z","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":"f4000405bd29554a64c02fdeb9fd780a869dc57ad7a86b8a1ea364214b269dd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-28T10:46:22Z","title_canon_sha256":"b2a5b2c1f94b17e3969c2d3eded8b188b412e9ee6e294b96450861d401314366"},"schema_version":"1.0","source":{"id":"1309.7450","kind":"arxiv","version":1}},"canonical_sha256":"ea1f50da33d30ed5de8d84ad4beb5b24772e758994e4eed97a708c546b775296","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea1f50da33d30ed5de8d84ad4beb5b24772e758994e4eed97a708c546b775296","first_computed_at":"2026-05-18T03:11:58.665440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:58.665440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KxXfc/gDTeQCt5yM0todwJtsWwSeD5yfwFnyb2b8Unbbb2BTZGpRr5bitak8U+Kt26ni1mXAKDpvTh6eR+eMAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:58.666109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fa7d0bcb6550d3716251c7335eac4fb985e4190a1dfd4f0008dccfb4afe1ef4","sha256:9507cdf0c9745f7ada085561d4d4b8d39398a8874b085f713a80b26799078e8b"],"state_sha256":"2b6ec58dfdc422080f2ce5c461c554f3f41404a84f5b219a571090207a2b615f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l+THzqHWjbJqtvlO48KJ2Relm6732VdgYJdVsG5bwAZ8KNIpYPNwcADP+JA0cLWeKGb42J2AiRLVtDHnDcYtBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T10:20:05.917304Z","bundle_sha256":"23c835788910902fedd96d90f19fd6b67355eb71a140c4e5ce7152c8912d580f"}}