{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LOMUEQDRSEUNWXTQP7J4WUBR5R","short_pith_number":"pith:LOMUEQDR","canonical_record":{"source":{"id":"1305.4332","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-19T06:57:23Z","cross_cats_sorted":[],"title_canon_sha256":"7be1e532aa7d580b78bdf3d2a8115ae01e156398d3593e7386b738c7ac7f35e5","abstract_canon_sha256":"6b8a024c6be12634d3b8e4e1f66a7e5d021e2da0ce4099632adc31e3c3158fb6"},"schema_version":"1.0"},"canonical_sha256":"5b994240719128db5e707fd3cb5031ec53e9a103cb968ac7cbedd954b7bd80ca","source":{"kind":"arxiv","id":"1305.4332","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4332","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4332v6","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4332","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"LOMUEQDRSEUN","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LOMUEQDRSEUNWXTQ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LOMUEQDR","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LOMUEQDRSEUNWXTQP7J4WUBR5R","target":"record","payload":{"canonical_record":{"source":{"id":"1305.4332","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-19T06:57:23Z","cross_cats_sorted":[],"title_canon_sha256":"7be1e532aa7d580b78bdf3d2a8115ae01e156398d3593e7386b738c7ac7f35e5","abstract_canon_sha256":"6b8a024c6be12634d3b8e4e1f66a7e5d021e2da0ce4099632adc31e3c3158fb6"},"schema_version":"1.0"},"canonical_sha256":"5b994240719128db5e707fd3cb5031ec53e9a103cb968ac7cbedd954b7bd80ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:31.036152Z","signature_b64":"CQDNMbLT8byPNJ94Zc9wOBtPA1tCTOqQDkGmmLBD0Fh/57+lZXOOEJ5AoCibiHE5s3PS1vJzSeMlmJxDekuQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b994240719128db5e707fd3cb5031ec53e9a103cb968ac7cbedd954b7bd80ca","last_reissued_at":"2026-05-18T00:43:31.035579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:31.035579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.4332","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nj2HN7eXF6g4IgZ34uTc7NlVPpeHxPEreI0fOjiKBrMmtTNtFIo7ntHLtdwo9aoXVA+TdsIbz67fy2j7j13sCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:35:32.790150Z"},"content_sha256":"ef6c4d5caf5ed9b213dc0fbf3a101d74e85b0c9548fe672b2625466b1e7b2a52","schema_version":"1.0","event_id":"sha256:ef6c4d5caf5ed9b213dc0fbf3a101d74e85b0c9548fe672b2625466b1e7b2a52"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LOMUEQDRSEUNWXTQP7J4WUBR5R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasilinear and Hessian type equations with exponential reaction and measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laurent Veron (LMPT), Quoc-Hung Nguyen (LMPT)","submitted_at":"2013-05-19T06:57:23Z","abstract_excerpt":"We prove existence results concerning equations of the type $-\\Delta_pu=P(u)+\\mu$ for $p>1$ and $F_k[-u]=P(u)+\\mu$ with $1\\leq k<\\frac{N}{2}$ in a bounded domain $\\Omega$ or the whole $\\mathbb{R}^N$, where $\\mu$ is a positive Radon measure and $P(u)\\sim e^{au^\\beta}$ with $a>0$ and $\\beta\\geq 1$. Sufficient conditions for existence are expressed in terms of the fractional maximal potential of $\\mu$. Two-sided estimates on the solutions are obtained in terms of some precise Wolff potentials of $\\mu$. Necessary conditions are obtained in terms of Orlicz capacities. We also establish existence re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4332","kind":"arxiv","version":6},"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":"2026-05-18T00:43:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CgXWKB/FYHUU2DCqiMkNY8AU/zKO0iIv8qktJJymm8UbWU/A1N4QiP67sD/jkQ38Evm8S/Mcy290M9k9eQUQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:35:32.790546Z"},"content_sha256":"fc118a5f9c25a3783b1842ee260236ff450081153868128d75a5f1012cf5af0b","schema_version":"1.0","event_id":"sha256:fc118a5f9c25a3783b1842ee260236ff450081153868128d75a5f1012cf5af0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LOMUEQDRSEUNWXTQP7J4WUBR5R/bundle.json","state_url":"https://pith.science/pith/LOMUEQDRSEUNWXTQP7J4WUBR5R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LOMUEQDRSEUNWXTQP7J4WUBR5R/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":"2026-06-23T15:35:32Z","links":{"resolver":"https://pith.science/pith/LOMUEQDRSEUNWXTQP7J4WUBR5R","bundle":"https://pith.science/pith/LOMUEQDRSEUNWXTQP7J4WUBR5R/bundle.json","state":"https://pith.science/pith/LOMUEQDRSEUNWXTQP7J4WUBR5R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LOMUEQDRSEUNWXTQP7J4WUBR5R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LOMUEQDRSEUNWXTQP7J4WUBR5R","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":"6b8a024c6be12634d3b8e4e1f66a7e5d021e2da0ce4099632adc31e3c3158fb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-19T06:57:23Z","title_canon_sha256":"7be1e532aa7d580b78bdf3d2a8115ae01e156398d3593e7386b738c7ac7f35e5"},"schema_version":"1.0","source":{"id":"1305.4332","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4332","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4332v6","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4332","created_at":"2026-05-18T00:43:31Z"},{"alias_kind":"pith_short_12","alias_value":"LOMUEQDRSEUN","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LOMUEQDRSEUNWXTQ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LOMUEQDR","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:fc118a5f9c25a3783b1842ee260236ff450081153868128d75a5f1012cf5af0b","target":"graph","created_at":"2026-05-18T00:43:31Z","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 prove existence results concerning equations of the type $-\\Delta_pu=P(u)+\\mu$ for $p>1$ and $F_k[-u]=P(u)+\\mu$ with $1\\leq k<\\frac{N}{2}$ in a bounded domain $\\Omega$ or the whole $\\mathbb{R}^N$, where $\\mu$ is a positive Radon measure and $P(u)\\sim e^{au^\\beta}$ with $a>0$ and $\\beta\\geq 1$. Sufficient conditions for existence are expressed in terms of the fractional maximal potential of $\\mu$. Two-sided estimates on the solutions are obtained in terms of some precise Wolff potentials of $\\mu$. Necessary conditions are obtained in terms of Orlicz capacities. We also establish existence re","authors_text":"Laurent Veron (LMPT), Quoc-Hung Nguyen (LMPT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-19T06:57:23Z","title":"Quasilinear and Hessian type equations with exponential reaction and measure data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4332","kind":"arxiv","version":6},"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:ef6c4d5caf5ed9b213dc0fbf3a101d74e85b0c9548fe672b2625466b1e7b2a52","target":"record","created_at":"2026-05-18T00:43:31Z","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":"6b8a024c6be12634d3b8e4e1f66a7e5d021e2da0ce4099632adc31e3c3158fb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-19T06:57:23Z","title_canon_sha256":"7be1e532aa7d580b78bdf3d2a8115ae01e156398d3593e7386b738c7ac7f35e5"},"schema_version":"1.0","source":{"id":"1305.4332","kind":"arxiv","version":6}},"canonical_sha256":"5b994240719128db5e707fd3cb5031ec53e9a103cb968ac7cbedd954b7bd80ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b994240719128db5e707fd3cb5031ec53e9a103cb968ac7cbedd954b7bd80ca","first_computed_at":"2026-05-18T00:43:31.035579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:31.035579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CQDNMbLT8byPNJ94Zc9wOBtPA1tCTOqQDkGmmLBD0Fh/57+lZXOOEJ5AoCibiHE5s3PS1vJzSeMlmJxDekuQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:31.036152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4332","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef6c4d5caf5ed9b213dc0fbf3a101d74e85b0c9548fe672b2625466b1e7b2a52","sha256:fc118a5f9c25a3783b1842ee260236ff450081153868128d75a5f1012cf5af0b"],"state_sha256":"54297ec797257091ac2d668293afa1ce1a673ab37c1532917415edf7c269e567"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Bxt05SaN0edEzAYhqKEC1s6Az/uAUEqtSgK6jgkgJNbyPXpzG3OqfaK4PW576ernRJKLRPZE5wf+I3i86VBAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:35:32.792563Z","bundle_sha256":"1874079b4b59813c676492d8b458aa61fb07db410a5429cb57d01a2c0fb02438"}}