{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YWVVM7HZ2BQERUN4UA52T3UTZE","short_pith_number":"pith:YWVVM7HZ","canonical_record":{"source":{"id":"1311.6607","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2013-11-26T10:02:22Z","cross_cats_sorted":[],"title_canon_sha256":"a6b97b0954152b5391eb0c49774a5a2c4a37b86dfc702409f586728494b20c6e","abstract_canon_sha256":"bbb43f49830aca486e9167a02c38d58723adb4e1cdced52e1e66ba8ceb52d247"},"schema_version":"1.0"},"canonical_sha256":"c5ab567cf9d06048d1bca03ba9ee93c92add08daf111be39243a327c7d9abf31","source":{"kind":"arxiv","id":"1311.6607","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6607","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6607v1","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6607","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"pith_short_12","alias_value":"YWVVM7HZ2BQE","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YWVVM7HZ2BQERUN4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YWVVM7HZ","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YWVVM7HZ2BQERUN4UA52T3UTZE","target":"record","payload":{"canonical_record":{"source":{"id":"1311.6607","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2013-11-26T10:02:22Z","cross_cats_sorted":[],"title_canon_sha256":"a6b97b0954152b5391eb0c49774a5a2c4a37b86dfc702409f586728494b20c6e","abstract_canon_sha256":"bbb43f49830aca486e9167a02c38d58723adb4e1cdced52e1e66ba8ceb52d247"},"schema_version":"1.0"},"canonical_sha256":"c5ab567cf9d06048d1bca03ba9ee93c92add08daf111be39243a327c7d9abf31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:12.228828Z","signature_b64":"t2BJFjG+PFTpGVsN+hR/OWs0DlxyOSmQEwE9bdPOoFrWLRZabwKbRfaCUify8ZWSG9IrqscrdoH17P2qh01aBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5ab567cf9d06048d1bca03ba9ee93c92add08daf111be39243a327c7d9abf31","last_reissued_at":"2026-05-18T03:06:12.227579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:12.227579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.6607","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":"2026-05-18T03:06:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PZiMQkLXgMVbnm1dDAAzTCBJykVJ+Duzhs2n2wU0LWLK4XmA6m3/+7D2BtWqrg9rq5y9OHH6m1QbCH3EP83nCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:37:46.554936Z"},"content_sha256":"5dcb997c5b606c84e12ced13c9cfae5d966134104a6ba65f2b8118e3cbf457dc","schema_version":"1.0","event_id":"sha256:5dcb997c5b606c84e12ced13c9cfae5d966134104a6ba65f2b8118e3cbf457dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YWVVM7HZ2BQERUN4UA52T3UTZE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-generated interior blow-up solutions in fractional elliptic equation with absorption","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Quaas, Huyuan Chen, Patricio Felmer","submitted_at":"2013-11-26T10:02:22Z","abstract_excerpt":"In this paper we study positive solutions to problem involving the fractional Laplacian $(E)$ $(-\\Delta)^{\\alpha} u(x)+|u|^{p-1}u(x)=0 in x\\in\\Omega\\setminus\\mathcal{C}$, subject to the conditions $u(x)=0$ $x\\in\\Omega^c$ and $\\lim_{x\\in\\Omega\\setminus\\mathcal{C}, x\\to\\mathcal{C}}u(x)=+\\infty$, where $p>1$ and $\\Omega$ is an open bounded $C^2$ domain in $\\mathbb{R}^N$, $\\mathcal{C}\\subset \\Omega$ is a compact $C^2$ manifold with $N-1$ multiples dimensions and without boundary, the operator $(-\\Delta)^{\\alpha}$ with $\\alpha\\in(0,1)$ is the fractional Laplacian.\n  We consider the existence of pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6607","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":"2026-05-18T03:06:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QheM6D04QxVnCwL3k/tlwaWiw0Y46YFIRie+hcczAcya1WJOzRUWtamahSfVJttZYZQzcV9xf+hud6meMyxVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:37:46.555290Z"},"content_sha256":"4e4fffad2c9e26dfa933faccdf2539e2ae4ece794ed37dd75a1e3a7fbbd095b3","schema_version":"1.0","event_id":"sha256:4e4fffad2c9e26dfa933faccdf2539e2ae4ece794ed37dd75a1e3a7fbbd095b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YWVVM7HZ2BQERUN4UA52T3UTZE/bundle.json","state_url":"https://pith.science/pith/YWVVM7HZ2BQERUN4UA52T3UTZE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YWVVM7HZ2BQERUN4UA52T3UTZE/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":"2026-05-22T18:37:46Z","links":{"resolver":"https://pith.science/pith/YWVVM7HZ2BQERUN4UA52T3UTZE","bundle":"https://pith.science/pith/YWVVM7HZ2BQERUN4UA52T3UTZE/bundle.json","state":"https://pith.science/pith/YWVVM7HZ2BQERUN4UA52T3UTZE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YWVVM7HZ2BQERUN4UA52T3UTZE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YWVVM7HZ2BQERUN4UA52T3UTZE","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":"bbb43f49830aca486e9167a02c38d58723adb4e1cdced52e1e66ba8ceb52d247","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2013-11-26T10:02:22Z","title_canon_sha256":"a6b97b0954152b5391eb0c49774a5a2c4a37b86dfc702409f586728494b20c6e"},"schema_version":"1.0","source":{"id":"1311.6607","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6607","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6607v1","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6607","created_at":"2026-05-18T03:06:12Z"},{"alias_kind":"pith_short_12","alias_value":"YWVVM7HZ2BQE","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YWVVM7HZ2BQERUN4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YWVVM7HZ","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:4e4fffad2c9e26dfa933faccdf2539e2ae4ece794ed37dd75a1e3a7fbbd095b3","target":"graph","created_at":"2026-05-18T03:06:12Z","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 this paper we study positive solutions to problem involving the fractional Laplacian $(E)$ $(-\\Delta)^{\\alpha} u(x)+|u|^{p-1}u(x)=0 in x\\in\\Omega\\setminus\\mathcal{C}$, subject to the conditions $u(x)=0$ $x\\in\\Omega^c$ and $\\lim_{x\\in\\Omega\\setminus\\mathcal{C}, x\\to\\mathcal{C}}u(x)=+\\infty$, where $p>1$ and $\\Omega$ is an open bounded $C^2$ domain in $\\mathbb{R}^N$, $\\mathcal{C}\\subset \\Omega$ is a compact $C^2$ manifold with $N-1$ multiples dimensions and without boundary, the operator $(-\\Delta)^{\\alpha}$ with $\\alpha\\in(0,1)$ is the fractional Laplacian.\n  We consider the existence of pos","authors_text":"Alexander Quaas, Huyuan Chen, Patricio Felmer","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2013-11-26T10:02:22Z","title":"Self-generated interior blow-up solutions in fractional elliptic equation with absorption"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6607","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":"sha256:5dcb997c5b606c84e12ced13c9cfae5d966134104a6ba65f2b8118e3cbf457dc","target":"record","created_at":"2026-05-18T03:06:12Z","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":"bbb43f49830aca486e9167a02c38d58723adb4e1cdced52e1e66ba8ceb52d247","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2013-11-26T10:02:22Z","title_canon_sha256":"a6b97b0954152b5391eb0c49774a5a2c4a37b86dfc702409f586728494b20c6e"},"schema_version":"1.0","source":{"id":"1311.6607","kind":"arxiv","version":1}},"canonical_sha256":"c5ab567cf9d06048d1bca03ba9ee93c92add08daf111be39243a327c7d9abf31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5ab567cf9d06048d1bca03ba9ee93c92add08daf111be39243a327c7d9abf31","first_computed_at":"2026-05-18T03:06:12.227579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:12.227579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t2BJFjG+PFTpGVsN+hR/OWs0DlxyOSmQEwE9bdPOoFrWLRZabwKbRfaCUify8ZWSG9IrqscrdoH17P2qh01aBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:12.228828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6607","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dcb997c5b606c84e12ced13c9cfae5d966134104a6ba65f2b8118e3cbf457dc","sha256:4e4fffad2c9e26dfa933faccdf2539e2ae4ece794ed37dd75a1e3a7fbbd095b3"],"state_sha256":"89ceeb6a6516f7378424084d34ed3df10c272e89c6e4aeebb7fe24e3a8eaa74b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d18OM73Ev0/OfAODC+4ynEzoXDbpN4CFIBFJxrTpqi1eaWHH10NAEEgBH2VQpRitIiTwyjK47Gb2qqr+3rmaBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T18:37:46.557226Z","bundle_sha256":"91741c605b1a275d2467fb8205c018cad1c08520ad4d429b810234247d2213dc"}}