{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OB6O45RASRJF6S6VMB5VIKVDSL","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":"4c6e955033f33b1073312dafe9d019a2da44c9484f922fa43e3550ad3fb170a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-14T17:07:19Z","title_canon_sha256":"031a80ef911553497abf417582b50980ec131e4ccd71fade6dee1361b1f6d47f"},"schema_version":"1.0","source":{"id":"1510.04201","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04201","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04201v2","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04201","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"OB6O45RASRJF","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OB6O45RASRJF6S6V","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OB6O45RA","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:fa9ba0f60eedf2e858c13520edae86590b922f149155354c8c0f0b37a5275158","target":"graph","created_at":"2026-05-18T00:36:48Z","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 a quasilinear elliptic equation, with right hand side measure, which does not satisfy the usual coercivity assumption. We prove an existence result in the line of the Fredholm alternative. For this purpose we develop a variant of degree theory suited to this setting.","authors_text":"Marco Degiovanni, Michele Colturato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-14T17:07:19Z","title":"A Fredholm alternative for quasilinear elliptic equations with right hand side measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04201","kind":"arxiv","version":2},"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:bae00564df33a1eb2abd669da17b484d4f8ee0aed8255dbfba4cbf5c45bf4682","target":"record","created_at":"2026-05-18T00:36:48Z","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":"4c6e955033f33b1073312dafe9d019a2da44c9484f922fa43e3550ad3fb170a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-14T17:07:19Z","title_canon_sha256":"031a80ef911553497abf417582b50980ec131e4ccd71fade6dee1361b1f6d47f"},"schema_version":"1.0","source":{"id":"1510.04201","kind":"arxiv","version":2}},"canonical_sha256":"707cee762094525f4bd5607b542aa392eac00545eac15cb33993e53d388bf58b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"707cee762094525f4bd5607b542aa392eac00545eac15cb33993e53d388bf58b","first_computed_at":"2026-05-18T00:36:48.092510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:48.092510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CUJwyO1c42pzgm0rIQg6uNcQtJNsJEsaasjoRXPB+6JNt7TbjI5fUYlcbmxTHLqNB/ZUg+94kd3+c5zeVDU+Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:48.092964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04201","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bae00564df33a1eb2abd669da17b484d4f8ee0aed8255dbfba4cbf5c45bf4682","sha256:fa9ba0f60eedf2e858c13520edae86590b922f149155354c8c0f0b37a5275158"],"state_sha256":"c0b26988b634fe4a00401a20c9521c15b77f04380a3298ff3c8344329f5ef7a2"}