{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LNOWA75TCWV6DD4YPAKU27WVQX","short_pith_number":"pith:LNOWA75T","canonical_record":{"source":{"id":"1406.3970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-16T11:02:10Z","cross_cats_sorted":[],"title_canon_sha256":"b65c998282415bfe7bb4648937a9bba01ea5aef9f64139b5843c36247dbcbd58","abstract_canon_sha256":"42eafee97a93a38a5e3806782e10ee5f01eeabc35028099f039120847ca37278"},"schema_version":"1.0"},"canonical_sha256":"5b5d607fb315abe18f9878154d7ed585dbdd235ed5f408382c4779e74559a30f","source":{"kind":"arxiv","id":"1406.3970","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3970","created_at":"2026-05-18T01:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3970v1","created_at":"2026-05-18T01:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3970","created_at":"2026-05-18T01:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"LNOWA75TCWV6","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LNOWA75TCWV6DD4Y","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LNOWA75T","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LNOWA75TCWV6DD4YPAKU27WVQX","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-16T11:02:10Z","cross_cats_sorted":[],"title_canon_sha256":"b65c998282415bfe7bb4648937a9bba01ea5aef9f64139b5843c36247dbcbd58","abstract_canon_sha256":"42eafee97a93a38a5e3806782e10ee5f01eeabc35028099f039120847ca37278"},"schema_version":"1.0"},"canonical_sha256":"5b5d607fb315abe18f9878154d7ed585dbdd235ed5f408382c4779e74559a30f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:48.869389Z","signature_b64":"wfrNnfW70UbpCe0I3CXGNDy0OtIFNZt6LwU4wbXkdWwdKFC++rl+k2aZCdmT32BJDg45iGTvFfR2hZXy40VyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b5d607fb315abe18f9878154d7ed585dbdd235ed5f408382c4779e74559a30f","last_reissued_at":"2026-05-18T01:22:48.868675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:48.868675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3970","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":"2026-05-18T01:22:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wCGSXzk5Tm2AUMVOvwDKvzOUGoUWohKgnuZMSJ18q7jlZmpC4QQNLQBVZgoH2Q8jP9aCMm/TJrbMjYx0vo2BCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:25:39.144436Z"},"content_sha256":"deee36e7d34f9615f3c69e678773331884bbb844918f59449642445ca5b178ed","schema_version":"1.0","event_id":"sha256:deee36e7d34f9615f3c69e678773331884bbb844918f59449642445ca5b178ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LNOWA75TCWV6DD4YPAKU27WVQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Morse index and sign changing bubble towers for Lane-Emden problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filomena Pacella, Francesca De Marchis, Isabella Ianni","submitted_at":"2014-06-16T11:02:10Z","abstract_excerpt":"We consider the semilinear Lane-Emden problem \\begin{equation}\\label{problemAbstract}\\left\\{ \\begin{array}{lr} -\\Delta u= |u|^{p-1}u\\qquad \\mbox{ in }\\Omega\\\\ u=0\\qquad\\qquad\\qquad\\mbox{ on }\\partial \\Omega \\end{array} \\right.\\tag{$\\mathcal E_p$} \\end{equation} where $p>1$ and $\\Omega$ is a smooth bounded symmetric domain of $\\mathbb R^2$. We show that for families $(u_p)$ of sign-changing symmetric solutions of \\eqref{problemAbstract} an upper bound on their Morse index implies concentration of the positive and negative part, $u_p^\\pm$, at the same point, as $p\\to+\\infty$. Then an asymptotic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3970","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":"2026-05-18T01:22:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCjzM+boVvzx1R0S/vYmSikFp2xv2R0ds6gehvQZvyVS24yGyysFKU2UBV3RnaKYyPYBoAx7utoKWZN6cOwgAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:25:39.144862Z"},"content_sha256":"ce360e9741771a044cdbfd5bedbb17e3fc4013e48e4e312f688c91650b4eb2ae","schema_version":"1.0","event_id":"sha256:ce360e9741771a044cdbfd5bedbb17e3fc4013e48e4e312f688c91650b4eb2ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LNOWA75TCWV6DD4YPAKU27WVQX/bundle.json","state_url":"https://pith.science/pith/LNOWA75TCWV6DD4YPAKU27WVQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LNOWA75TCWV6DD4YPAKU27WVQX/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":"2026-05-31T10:25:39Z","links":{"resolver":"https://pith.science/pith/LNOWA75TCWV6DD4YPAKU27WVQX","bundle":"https://pith.science/pith/LNOWA75TCWV6DD4YPAKU27WVQX/bundle.json","state":"https://pith.science/pith/LNOWA75TCWV6DD4YPAKU27WVQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LNOWA75TCWV6DD4YPAKU27WVQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LNOWA75TCWV6DD4YPAKU27WVQX","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":"42eafee97a93a38a5e3806782e10ee5f01eeabc35028099f039120847ca37278","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-16T11:02:10Z","title_canon_sha256":"b65c998282415bfe7bb4648937a9bba01ea5aef9f64139b5843c36247dbcbd58"},"schema_version":"1.0","source":{"id":"1406.3970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3970","created_at":"2026-05-18T01:22:48Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3970v1","created_at":"2026-05-18T01:22:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3970","created_at":"2026-05-18T01:22:48Z"},{"alias_kind":"pith_short_12","alias_value":"LNOWA75TCWV6","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LNOWA75TCWV6DD4Y","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LNOWA75T","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:ce360e9741771a044cdbfd5bedbb17e3fc4013e48e4e312f688c91650b4eb2ae","target":"graph","created_at":"2026-05-18T01:22:48Z","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 the semilinear Lane-Emden problem \\begin{equation}\\label{problemAbstract}\\left\\{ \\begin{array}{lr} -\\Delta u= |u|^{p-1}u\\qquad \\mbox{ in }\\Omega\\\\ u=0\\qquad\\qquad\\qquad\\mbox{ on }\\partial \\Omega \\end{array} \\right.\\tag{$\\mathcal E_p$} \\end{equation} where $p>1$ and $\\Omega$ is a smooth bounded symmetric domain of $\\mathbb R^2$. We show that for families $(u_p)$ of sign-changing symmetric solutions of \\eqref{problemAbstract} an upper bound on their Morse index implies concentration of the positive and negative part, $u_p^\\pm$, at the same point, as $p\\to+\\infty$. Then an asymptotic ","authors_text":"Filomena Pacella, Francesca De Marchis, Isabella Ianni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-16T11:02:10Z","title":"Morse index and sign changing bubble towers for Lane-Emden problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3970","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:deee36e7d34f9615f3c69e678773331884bbb844918f59449642445ca5b178ed","target":"record","created_at":"2026-05-18T01:22:48Z","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":"42eafee97a93a38a5e3806782e10ee5f01eeabc35028099f039120847ca37278","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-16T11:02:10Z","title_canon_sha256":"b65c998282415bfe7bb4648937a9bba01ea5aef9f64139b5843c36247dbcbd58"},"schema_version":"1.0","source":{"id":"1406.3970","kind":"arxiv","version":1}},"canonical_sha256":"5b5d607fb315abe18f9878154d7ed585dbdd235ed5f408382c4779e74559a30f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b5d607fb315abe18f9878154d7ed585dbdd235ed5f408382c4779e74559a30f","first_computed_at":"2026-05-18T01:22:48.868675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:48.868675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wfrNnfW70UbpCe0I3CXGNDy0OtIFNZt6LwU4wbXkdWwdKFC++rl+k2aZCdmT32BJDg45iGTvFfR2hZXy40VyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:48.869389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:deee36e7d34f9615f3c69e678773331884bbb844918f59449642445ca5b178ed","sha256:ce360e9741771a044cdbfd5bedbb17e3fc4013e48e4e312f688c91650b4eb2ae"],"state_sha256":"bcf79ec13c4632c8cf8ac024fbe245f6089189bb2a43cd1374e70f3d88821a41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fEG2ZfwLxY1/4l5MtHchMf5Y8x+uvt/dH5CEC2JsDuoQnjyz7rabGZoq0Y+oKnzp7k56Wu2Lr/aYFanRbhvoBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:25:39.148278Z","bundle_sha256":"853700be77e340a155d19ccef8b629d286d8522b279de551ee5d3dfe033a56ca"}}