{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LX42RY3DVTMR3FBHHN3AEE2KEL","short_pith_number":"pith:LX42RY3D","schema_version":"1.0","canonical_sha256":"5df9a8e363acd91d94273b7602134a22cdc4af4378bd4d5db436de764a3fa54c","source":{"kind":"arxiv","id":"1707.00867","version":1},"attestation_state":"computed","paper":{"title":"A pathological example in Nonlinear Spectral Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Giovanni Franzina, Lorenzo Brasco","submitted_at":"2017-07-04T09:10:26Z","abstract_excerpt":"We construct an open set $\\Omega\\subset\\mathbb{R}^N$ on which an eigenvalue problem for the $p-$Laplacian has not isolated first eigenvalue and the spectrum is not discrete. The same example shows that the usual Lusternik-Schnirelmann minimax construction does not exhaust the whole spectrum of this eigenvalue problem."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.00867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-04T09:10:26Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"76facab3059a13472e7f9c114e892c37b5dab762302fc8070f39938ce6ff1b4f","abstract_canon_sha256":"397642eb5400042b4393e1ea605ce98fac2e13a3ef42e10e956835f69914ce40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:56.784345Z","signature_b64":"HJ8tZuvoaneR3q9IIklujZ9dhx3IVf1mAhskfm8+0uXPd+YitQh97sD8tFkHxstVU5xYU6sysOcZ7ivgjjq1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5df9a8e363acd91d94273b7602134a22cdc4af4378bd4d5db436de764a3fa54c","last_reissued_at":"2026-05-18T00:40:56.783815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:56.783815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A pathological example in Nonlinear Spectral Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Giovanni Franzina, Lorenzo Brasco","submitted_at":"2017-07-04T09:10:26Z","abstract_excerpt":"We construct an open set $\\Omega\\subset\\mathbb{R}^N$ on which an eigenvalue problem for the $p-$Laplacian has not isolated first eigenvalue and the spectrum is not discrete. The same example shows that the usual Lusternik-Schnirelmann minimax construction does not exhaust the whole spectrum of this eigenvalue problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00867","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.00867","created_at":"2026-05-18T00:40:56.783887+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.00867v1","created_at":"2026-05-18T00:40:56.783887+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00867","created_at":"2026-05-18T00:40:56.783887+00:00"},{"alias_kind":"pith_short_12","alias_value":"LX42RY3DVTMR","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LX42RY3DVTMR3FBH","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LX42RY3D","created_at":"2026-05-18T12:31:28.150371+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LX42RY3DVTMR3FBHHN3AEE2KEL","json":"https://pith.science/pith/LX42RY3DVTMR3FBHHN3AEE2KEL.json","graph_json":"https://pith.science/api/pith-number/LX42RY3DVTMR3FBHHN3AEE2KEL/graph.json","events_json":"https://pith.science/api/pith-number/LX42RY3DVTMR3FBHHN3AEE2KEL/events.json","paper":"https://pith.science/paper/LX42RY3D"},"agent_actions":{"view_html":"https://pith.science/pith/LX42RY3DVTMR3FBHHN3AEE2KEL","download_json":"https://pith.science/pith/LX42RY3DVTMR3FBHHN3AEE2KEL.json","view_paper":"https://pith.science/paper/LX42RY3D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.00867&json=true","fetch_graph":"https://pith.science/api/pith-number/LX42RY3DVTMR3FBHHN3AEE2KEL/graph.json","fetch_events":"https://pith.science/api/pith-number/LX42RY3DVTMR3FBHHN3AEE2KEL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LX42RY3DVTMR3FBHHN3AEE2KEL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LX42RY3DVTMR3FBHHN3AEE2KEL/action/storage_attestation","attest_author":"https://pith.science/pith/LX42RY3DVTMR3FBHHN3AEE2KEL/action/author_attestation","sign_citation":"https://pith.science/pith/LX42RY3DVTMR3FBHHN3AEE2KEL/action/citation_signature","submit_replication":"https://pith.science/pith/LX42RY3DVTMR3FBHHN3AEE2KEL/action/replication_record"}},"created_at":"2026-05-18T00:40:56.783887+00:00","updated_at":"2026-05-18T00:40:56.783887+00:00"}