{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MQKJEXDI7ZQKTKNIX7GNGLRLLC","short_pith_number":"pith:MQKJEXDI","schema_version":"1.0","canonical_sha256":"6414925c68fe60a9a9a8bfccd32e2b58b42a6e7e792225e43b0ab09a2d95b638","source":{"kind":"arxiv","id":"1607.02468","version":1},"attestation_state":"computed","paper":{"title":"Infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annulus","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Anderson L. A. de Araujo","submitted_at":"2016-07-08T17:36:24Z","abstract_excerpt":"We present a result of existence of infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annular domains, when $p\\leq N$, contouring the failure of compactness of $W^{1,p}(\\Omega)$ in $C^0(\\bar{\\Omega})$ applying a variable change."},"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":"1607.02468","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-08T17:36:24Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"62b33d02b62795ebf4045b0e26ac60a58376ddbd62461f63be7debf8c255dcc3","abstract_canon_sha256":"4809f698d0b4cfefccef20579311e302791d2d00fa1c1d78a93fb56614e4b0a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:18.904817Z","signature_b64":"OUrpdoil0NdVUjpgt1ylqDiOtJnlwHuFdbQ0MaMZZ2uM3TWVjXoP8+c1nE0XvAlNdzFruTx4AyBvI1tvS7kHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6414925c68fe60a9a9a8bfccd32e2b58b42a6e7e792225e43b0ab09a2d95b638","last_reissued_at":"2026-05-18T01:11:18.903959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:18.903959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annulus","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Anderson L. A. de Araujo","submitted_at":"2016-07-08T17:36:24Z","abstract_excerpt":"We present a result of existence of infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annular domains, when $p\\leq N$, contouring the failure of compactness of $W^{1,p}(\\Omega)$ in $C^0(\\bar{\\Omega})$ applying a variable change."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02468","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":"1607.02468","created_at":"2026-05-18T01:11:18.904092+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.02468v1","created_at":"2026-05-18T01:11:18.904092+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02468","created_at":"2026-05-18T01:11:18.904092+00:00"},{"alias_kind":"pith_short_12","alias_value":"MQKJEXDI7ZQK","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MQKJEXDI7ZQKTKNI","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MQKJEXDI","created_at":"2026-05-18T12:30:32.724797+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/MQKJEXDI7ZQKTKNIX7GNGLRLLC","json":"https://pith.science/pith/MQKJEXDI7ZQKTKNIX7GNGLRLLC.json","graph_json":"https://pith.science/api/pith-number/MQKJEXDI7ZQKTKNIX7GNGLRLLC/graph.json","events_json":"https://pith.science/api/pith-number/MQKJEXDI7ZQKTKNIX7GNGLRLLC/events.json","paper":"https://pith.science/paper/MQKJEXDI"},"agent_actions":{"view_html":"https://pith.science/pith/MQKJEXDI7ZQKTKNIX7GNGLRLLC","download_json":"https://pith.science/pith/MQKJEXDI7ZQKTKNIX7GNGLRLLC.json","view_paper":"https://pith.science/paper/MQKJEXDI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.02468&json=true","fetch_graph":"https://pith.science/api/pith-number/MQKJEXDI7ZQKTKNIX7GNGLRLLC/graph.json","fetch_events":"https://pith.science/api/pith-number/MQKJEXDI7ZQKTKNIX7GNGLRLLC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MQKJEXDI7ZQKTKNIX7GNGLRLLC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MQKJEXDI7ZQKTKNIX7GNGLRLLC/action/storage_attestation","attest_author":"https://pith.science/pith/MQKJEXDI7ZQKTKNIX7GNGLRLLC/action/author_attestation","sign_citation":"https://pith.science/pith/MQKJEXDI7ZQKTKNIX7GNGLRLLC/action/citation_signature","submit_replication":"https://pith.science/pith/MQKJEXDI7ZQKTKNIX7GNGLRLLC/action/replication_record"}},"created_at":"2026-05-18T01:11:18.904092+00:00","updated_at":"2026-05-18T01:11:18.904092+00:00"}