{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SX3MO5BH7LHSLXUMAXEJHLWZHS","short_pith_number":"pith:SX3MO5BH","canonical_record":{"source":{"id":"1706.09223","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-28T11:39:11Z","cross_cats_sorted":[],"title_canon_sha256":"7a385868c1ebe3d1fd1a024bb0bf94e1bc4d281bd92b0047062f946ad487d487","abstract_canon_sha256":"14a92254851e26e6975ddd0ffcd92323a3f7d8463f8b822f2fc818681f3f2017"},"schema_version":"1.0"},"canonical_sha256":"95f6c77427facf25de8c05c893aed93c88bb49a816e085183e7bb2586d4758f3","source":{"kind":"arxiv","id":"1706.09223","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09223","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09223v2","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09223","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"SX3MO5BH7LHS","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SX3MO5BH7LHSLXUM","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SX3MO5BH","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SX3MO5BH7LHSLXUMAXEJHLWZHS","target":"record","payload":{"canonical_record":{"source":{"id":"1706.09223","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-28T11:39:11Z","cross_cats_sorted":[],"title_canon_sha256":"7a385868c1ebe3d1fd1a024bb0bf94e1bc4d281bd92b0047062f946ad487d487","abstract_canon_sha256":"14a92254851e26e6975ddd0ffcd92323a3f7d8463f8b822f2fc818681f3f2017"},"schema_version":"1.0"},"canonical_sha256":"95f6c77427facf25de8c05c893aed93c88bb49a816e085183e7bb2586d4758f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:06.676923Z","signature_b64":"f2UFV+Mbwu4StfhQFuptsoFq7D7mcweaQZJlFv1DobvNFVAGiouQmgyD/waqERfxjAnRxa+m3OsbNkCj1e8vAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95f6c77427facf25de8c05c893aed93c88bb49a816e085183e7bb2586d4758f3","last_reissued_at":"2026-05-18T00:41:06.676231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:06.676231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.09223","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NoRxObYXLcuiv9L0ISGK78G68Hh9woiu+1kSR7JhVqPyIgJpDFZtqq1od44OD8tGdIRsR8HIaRNLjYvLBrsiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T02:05:52.588149Z"},"content_sha256":"47d14685927f85945f45c2dcb54ad36e061ca8798bda38a56de2a0724ccf6635","schema_version":"1.0","event_id":"sha256:47d14685927f85945f45c2dcb54ad36e061ca8798bda38a56de2a0724ccf6635"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SX3MO5BH7LHSLXUMAXEJHLWZHS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Blow-up analysis for nodal radial solutions in Moser-Trudinger critical equations in $R^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daisuke Naimen, Massimo Grossi","submitted_at":"2017-06-28T11:39:11Z","abstract_excerpt":"In this paper we consider nodal radial solutions $u_\\epsilon$ to the problem \\[ \\begin{cases} -\\Delta u=\\lambda ue^{u^2+|u|^{1+\\epsilon}}&\\text{ in }B,\\\\ u=0&\\text{ on }\\partial B. \\end{cases} \\] and we study their asymptotic behaviour as $\\epsilon\\searrow0$, $\\epsilon>0$. We show that when $u_\\epsilon$ has $k$ interior zeros, it exhibits a multiple blow-up behaviour in the first $k$ nodal sets while it converges to the least energy solution of the problem with $\\epsilon=0$ in the $(k+1)$-th one. We also prove that in each concentration set, with an appropriate scaling, $u_\\epsilon$ converges "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09223","kind":"arxiv","version":2},"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":"2026-05-18T00:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gM2Bt77evHmCbCBTUEISQzfOHu8fiTqUE7KjPo2qKs1ugexyPcn2BsFNDbgtbYdrnCjkD5uLsZ+sClsAwKihBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T02:05:52.588801Z"},"content_sha256":"3f4bc282cb566784280b0836eac801206f534738adbc4145384199e11f0b72ec","schema_version":"1.0","event_id":"sha256:3f4bc282cb566784280b0836eac801206f534738adbc4145384199e11f0b72ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SX3MO5BH7LHSLXUMAXEJHLWZHS/bundle.json","state_url":"https://pith.science/pith/SX3MO5BH7LHSLXUMAXEJHLWZHS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SX3MO5BH7LHSLXUMAXEJHLWZHS/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":"2026-06-08T02:05:52Z","links":{"resolver":"https://pith.science/pith/SX3MO5BH7LHSLXUMAXEJHLWZHS","bundle":"https://pith.science/pith/SX3MO5BH7LHSLXUMAXEJHLWZHS/bundle.json","state":"https://pith.science/pith/SX3MO5BH7LHSLXUMAXEJHLWZHS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SX3MO5BH7LHSLXUMAXEJHLWZHS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SX3MO5BH7LHSLXUMAXEJHLWZHS","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":"14a92254851e26e6975ddd0ffcd92323a3f7d8463f8b822f2fc818681f3f2017","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-28T11:39:11Z","title_canon_sha256":"7a385868c1ebe3d1fd1a024bb0bf94e1bc4d281bd92b0047062f946ad487d487"},"schema_version":"1.0","source":{"id":"1706.09223","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09223","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09223v2","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09223","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"SX3MO5BH7LHS","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SX3MO5BH7LHSLXUM","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SX3MO5BH","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:3f4bc282cb566784280b0836eac801206f534738adbc4145384199e11f0b72ec","target":"graph","created_at":"2026-05-18T00:41:06Z","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 consider nodal radial solutions $u_\\epsilon$ to the problem \\[ \\begin{cases} -\\Delta u=\\lambda ue^{u^2+|u|^{1+\\epsilon}}&\\text{ in }B,\\\\ u=0&\\text{ on }\\partial B. \\end{cases} \\] and we study their asymptotic behaviour as $\\epsilon\\searrow0$, $\\epsilon>0$. We show that when $u_\\epsilon$ has $k$ interior zeros, it exhibits a multiple blow-up behaviour in the first $k$ nodal sets while it converges to the least energy solution of the problem with $\\epsilon=0$ in the $(k+1)$-th one. We also prove that in each concentration set, with an appropriate scaling, $u_\\epsilon$ converges ","authors_text":"Daisuke Naimen, Massimo Grossi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-28T11:39:11Z","title":"Blow-up analysis for nodal radial solutions in Moser-Trudinger critical equations in $R^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09223","kind":"arxiv","version":2},"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":"sha256:47d14685927f85945f45c2dcb54ad36e061ca8798bda38a56de2a0724ccf6635","target":"record","created_at":"2026-05-18T00:41:06Z","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":"14a92254851e26e6975ddd0ffcd92323a3f7d8463f8b822f2fc818681f3f2017","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-28T11:39:11Z","title_canon_sha256":"7a385868c1ebe3d1fd1a024bb0bf94e1bc4d281bd92b0047062f946ad487d487"},"schema_version":"1.0","source":{"id":"1706.09223","kind":"arxiv","version":2}},"canonical_sha256":"95f6c77427facf25de8c05c893aed93c88bb49a816e085183e7bb2586d4758f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95f6c77427facf25de8c05c893aed93c88bb49a816e085183e7bb2586d4758f3","first_computed_at":"2026-05-18T00:41:06.676231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:06.676231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f2UFV+Mbwu4StfhQFuptsoFq7D7mcweaQZJlFv1DobvNFVAGiouQmgyD/waqERfxjAnRxa+m3OsbNkCj1e8vAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:06.676923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.09223","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47d14685927f85945f45c2dcb54ad36e061ca8798bda38a56de2a0724ccf6635","sha256:3f4bc282cb566784280b0836eac801206f534738adbc4145384199e11f0b72ec"],"state_sha256":"53e85c462ba54922a5605dc0f50f31af0774292af856cd104ba9d48e50d29f76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UH2TFMYndqnyXQVntPW32joaGZAojJ4TFgtNV52n91sJZOVmydBmYT0E5NfUa4evvJHRWrWkmfqxiu+WWhULAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T02:05:52.592232Z","bundle_sha256":"58a415a60448b3f7a6a3f9d8e154dfada4d90afc3b07802859ac0f6e6181353e"}}