{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:PQXXFJACM2G2ASKACZ43UX4DTM","short_pith_number":"pith:PQXXFJAC","canonical_record":{"source":{"id":"math/0604365","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2006-04-17T10:17:54Z","cross_cats_sorted":[],"title_canon_sha256":"a130fd1dcf76fc96c9a73a556f28470bac4c505eb0c13ca51ae6c0c0c204c32a","abstract_canon_sha256":"259db5fa82122beb94e7ef441302f26465e3c114de41b3e3b998fb575cc0f5f5"},"schema_version":"1.0"},"canonical_sha256":"7c2f72a402668da049401679ba5f839b2cf73a00abc55c959e80edc73e83e6e5","source":{"kind":"arxiv","id":"math/0604365","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604365","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604365v1","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604365","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"PQXXFJACM2G2","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"PQXXFJACM2G2ASKA","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"PQXXFJAC","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:PQXXFJACM2G2ASKACZ43UX4DTM","target":"record","payload":{"canonical_record":{"source":{"id":"math/0604365","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2006-04-17T10:17:54Z","cross_cats_sorted":[],"title_canon_sha256":"a130fd1dcf76fc96c9a73a556f28470bac4c505eb0c13ca51ae6c0c0c204c32a","abstract_canon_sha256":"259db5fa82122beb94e7ef441302f26465e3c114de41b3e3b998fb575cc0f5f5"},"schema_version":"1.0"},"canonical_sha256":"7c2f72a402668da049401679ba5f839b2cf73a00abc55c959e80edc73e83e6e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:24.215404Z","signature_b64":"0iOa3cqbcvLosN4vIhQYZMEvgoBSyU79lRkGdd9Ne1Z1fLvbimGo7YmIdux78nsk3ubTjzXPhtoYHyp7wpWGDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c2f72a402668da049401679ba5f839b2cf73a00abc55c959e80edc73e83e6e5","last_reissued_at":"2026-05-18T01:38:24.214638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:24.214638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0604365","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":"2026-05-18T01:38:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGDqoMIWfuBLwE9UjknrppmpXxjixRrYRAxqJiPMOaA7M2Nu7JixWkDa3e3Hs6h9f75VEkbeXPg/22aGHqqpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T16:50:15.741285Z"},"content_sha256":"231f4f58b16a0cba5f071b7d96f64e54c433da60ab0e780725b62d757795892e","schema_version":"1.0","event_id":"sha256:231f4f58b16a0cba5f071b7d96f64e54c433da60ab0e780725b62d757795892e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:PQXXFJACM2G2ASKACZ43UX4DTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular limits for 4-dimensional semilinear elliptic problems with exponential nonlinearity","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Frank Pacard, Makkia Dammak, Sami Baraket, Taieb Ouni","submitted_at":"2006-04-17T10:17:54Z","abstract_excerpt":"Using some nonlinear domain decomposition method, we prove the existence of singular limits for solution of semilinear elliptic problems with exponential nonlinearity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604365","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":"2026-05-18T01:38:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/F96J92MG7NsTRrth1os9APZbGR3ybOX6ZRGCz2oLfq7Qg9mJyqvb2ZMa80Kud6UzcmSGlJ/Rjl7qvTScFSOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T16:50:15.741655Z"},"content_sha256":"04fe8c11dcf8afb4727f13f4aaaa9478d32f748a7f37d83d1ab04fe643e6f3be","schema_version":"1.0","event_id":"sha256:04fe8c11dcf8afb4727f13f4aaaa9478d32f748a7f37d83d1ab04fe643e6f3be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQXXFJACM2G2ASKACZ43UX4DTM/bundle.json","state_url":"https://pith.science/pith/PQXXFJACM2G2ASKACZ43UX4DTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQXXFJACM2G2ASKACZ43UX4DTM/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":"2026-06-25T16:50:15Z","links":{"resolver":"https://pith.science/pith/PQXXFJACM2G2ASKACZ43UX4DTM","bundle":"https://pith.science/pith/PQXXFJACM2G2ASKACZ43UX4DTM/bundle.json","state":"https://pith.science/pith/PQXXFJACM2G2ASKACZ43UX4DTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQXXFJACM2G2ASKACZ43UX4DTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:PQXXFJACM2G2ASKACZ43UX4DTM","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":"259db5fa82122beb94e7ef441302f26465e3c114de41b3e3b998fb575cc0f5f5","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2006-04-17T10:17:54Z","title_canon_sha256":"a130fd1dcf76fc96c9a73a556f28470bac4c505eb0c13ca51ae6c0c0c204c32a"},"schema_version":"1.0","source":{"id":"math/0604365","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604365","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604365v1","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604365","created_at":"2026-05-18T01:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"PQXXFJACM2G2","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"PQXXFJACM2G2ASKA","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"PQXXFJAC","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:04fe8c11dcf8afb4727f13f4aaaa9478d32f748a7f37d83d1ab04fe643e6f3be","target":"graph","created_at":"2026-05-18T01:38:24Z","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":"Using some nonlinear domain decomposition method, we prove the existence of singular limits for solution of semilinear elliptic problems with exponential nonlinearity.","authors_text":"Frank Pacard, Makkia Dammak, Sami Baraket, Taieb Ouni","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2006-04-17T10:17:54Z","title":"Singular limits for 4-dimensional semilinear elliptic problems with exponential nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604365","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":"sha256:231f4f58b16a0cba5f071b7d96f64e54c433da60ab0e780725b62d757795892e","target":"record","created_at":"2026-05-18T01:38:24Z","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":"259db5fa82122beb94e7ef441302f26465e3c114de41b3e3b998fb575cc0f5f5","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2006-04-17T10:17:54Z","title_canon_sha256":"a130fd1dcf76fc96c9a73a556f28470bac4c505eb0c13ca51ae6c0c0c204c32a"},"schema_version":"1.0","source":{"id":"math/0604365","kind":"arxiv","version":1}},"canonical_sha256":"7c2f72a402668da049401679ba5f839b2cf73a00abc55c959e80edc73e83e6e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c2f72a402668da049401679ba5f839b2cf73a00abc55c959e80edc73e83e6e5","first_computed_at":"2026-05-18T01:38:24.214638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:24.214638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0iOa3cqbcvLosN4vIhQYZMEvgoBSyU79lRkGdd9Ne1Z1fLvbimGo7YmIdux78nsk3ubTjzXPhtoYHyp7wpWGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:24.215404Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0604365","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:231f4f58b16a0cba5f071b7d96f64e54c433da60ab0e780725b62d757795892e","sha256:04fe8c11dcf8afb4727f13f4aaaa9478d32f748a7f37d83d1ab04fe643e6f3be"],"state_sha256":"899891a591e6d9d4d1ed6575d5ef98fa336a3ab5e09e4e9e49ed1bf140a37769"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/c5IESGE+I7FFMkMz6YvS1WAkiQVIiOlExTfSGDhSU807vZpv2T1pxaI2xeuCLdDHxBSxgxCiKL594G7F5v+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T16:50:15.743716Z","bundle_sha256":"6c32cc77c722d31b705a5b112a8b35eadb95d36c3bc80729500d23939be7b0ed"}}