{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QYV742P5HEYXQDUM3U7BGCAN5E","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":"c823c7142677897370a603172456ca179f9382fd34511f18050caa562bd2707f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-10T12:19:04Z","title_canon_sha256":"6657bc546c3c230752d8f549f8307103925e7ecc281fe80a90a5becc0e681cd2"},"schema_version":"1.0","source":{"id":"1305.2326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2326","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2326v1","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2326","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"pith_short_12","alias_value":"QYV742P5HEYX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QYV742P5HEYXQDUM","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QYV742P5","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:1d17b659964e96d336ade1504bd0bc85482b484c54214ca6b1a570dbcd805b78","target":"graph","created_at":"2026-05-18T03:26:00Z","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 study a degenerate elliptic equation, proving existence results of distributional solutions in some borderline cases.","authors_text":"Gisella Croce (LMAH), Lucio Boccardo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-10T12:19:04Z","title":"$W^{1,1}_0(\\Omega)$ in some borderline cases of elliptic equations with degenerate coercivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2326","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":"sha256:5a7bb46939f11aada95574bd282eaf28e95825bf6ca39a5eaf563a417755b512","target":"record","created_at":"2026-05-18T03:26:00Z","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":"c823c7142677897370a603172456ca179f9382fd34511f18050caa562bd2707f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-10T12:19:04Z","title_canon_sha256":"6657bc546c3c230752d8f549f8307103925e7ecc281fe80a90a5becc0e681cd2"},"schema_version":"1.0","source":{"id":"1305.2326","kind":"arxiv","version":1}},"canonical_sha256":"862bfe69fd3931780e8cdd3e13080de91074a9acd2e056f0d58cdddf57ab128b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"862bfe69fd3931780e8cdd3e13080de91074a9acd2e056f0d58cdddf57ab128b","first_computed_at":"2026-05-18T03:26:00.523657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:00.523657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zVQdeevdnmoXdqDBpbphndfdmM4aJnv5bCQ5+Y/j/3tg4ar4aVfHUHVaW4StoNrgxRR15f9wA+5QL3OLqPZHDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:00.524417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.2326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a7bb46939f11aada95574bd282eaf28e95825bf6ca39a5eaf563a417755b512","sha256:1d17b659964e96d336ade1504bd0bc85482b484c54214ca6b1a570dbcd805b78"],"state_sha256":"f998b0224ea8b3168db129b52720598c7fa118d2a3dce3c6e0884150b66314a0"}