{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MQKJEXDI7ZQKTKNIX7GNGLRLLC","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":"4809f698d0b4cfefccef20579311e302791d2d00fa1c1d78a93fb56614e4b0a4","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-08T17:36:24Z","title_canon_sha256":"62b33d02b62795ebf4045b0e26ac60a58376ddbd62461f63be7debf8c255dcc3"},"schema_version":"1.0","source":{"id":"1607.02468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02468","created_at":"2026-05-18T01:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02468v1","created_at":"2026-05-18T01:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02468","created_at":"2026-05-18T01:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"MQKJEXDI7ZQK","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MQKJEXDI7ZQKTKNI","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MQKJEXDI","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:162e9c7d6a318cacfc9eda9931492450640c3ad8e49ea8f554ebd37a4dea4331","target":"graph","created_at":"2026-05-18T01:11:18Z","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 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.","authors_text":"Anderson L. A. de Araujo","cross_cats":["math.CA"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-08T17:36:24Z","title":"Infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annulus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02468","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":"sha256:1ab723cd369004a020f07b6ae9665c1187c07741c27756ade580b0f58dec480c","target":"record","created_at":"2026-05-18T01:11:18Z","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":"4809f698d0b4cfefccef20579311e302791d2d00fa1c1d78a93fb56614e4b0a4","cross_cats_sorted":["math.CA"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-08T17:36:24Z","title_canon_sha256":"62b33d02b62795ebf4045b0e26ac60a58376ddbd62461f63be7debf8c255dcc3"},"schema_version":"1.0","source":{"id":"1607.02468","kind":"arxiv","version":1}},"canonical_sha256":"6414925c68fe60a9a9a8bfccd32e2b58b42a6e7e792225e43b0ab09a2d95b638","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6414925c68fe60a9a9a8bfccd32e2b58b42a6e7e792225e43b0ab09a2d95b638","first_computed_at":"2026-05-18T01:11:18.903959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:18.903959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OUrpdoil0NdVUjpgt1ylqDiOtJnlwHuFdbQ0MaMZZ2uM3TWVjXoP8+c1nE0XvAlNdzFruTx4AyBvI1tvS7kHAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:18.904817Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.02468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ab723cd369004a020f07b6ae9665c1187c07741c27756ade580b0f58dec480c","sha256:162e9c7d6a318cacfc9eda9931492450640c3ad8e49ea8f554ebd37a4dea4331"],"state_sha256":"e361a135227aecc49be6c09b79b91eca56825514b0e08b153f4b1621936141f6"}