{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZMXO3VINLBRWM4UIMINPKPHQMM","short_pith_number":"pith:ZMXO3VIN","schema_version":"1.0","canonical_sha256":"cb2eedd50d5863667288621af53cf0633775b48629324c68ee3be467365ba4d4","source":{"kind":"arxiv","id":"1209.4431","version":2},"attestation_state":"computed","paper":{"title":"A weak comparison principle for solutions of very degenerate elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giulio Ciraolo","submitted_at":"2012-09-20T05:32:45Z","abstract_excerpt":"We prove a comparison principle for weak solutions of elliptic quasilinear equations in divergence form whose ellipticity constants degenerate at every point where $\\nabla u \\in K$, where $K\\subset \\mathbb{R}^N$ is a Borel set containing the origin."},"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":"1209.4431","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-09-20T05:32:45Z","cross_cats_sorted":[],"title_canon_sha256":"ddde1fb45cfe775479027e222ee7594ef82d67848c6bab36b445ad2c59b709bf","abstract_canon_sha256":"a554141b944011afcda3be6096cbd93968dc6c432ece65e81d8417696b51d2a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:04.791491Z","signature_b64":"Jc9j3eEZyKxNRxKN5+zuz0W/Zubm14JmKUbjLi1jpA6ZGvwW86vq/k6z6Ra15+vrAGxPPNPfZNmJi5gIoL87Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb2eedd50d5863667288621af53cf0633775b48629324c68ee3be467365ba4d4","last_reissued_at":"2026-05-18T03:38:04.790819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:04.790819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A weak comparison principle for solutions of very degenerate elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giulio Ciraolo","submitted_at":"2012-09-20T05:32:45Z","abstract_excerpt":"We prove a comparison principle for weak solutions of elliptic quasilinear equations in divergence form whose ellipticity constants degenerate at every point where $\\nabla u \\in K$, where $K\\subset \\mathbb{R}^N$ is a Borel set containing the origin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4431","kind":"arxiv","version":2},"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":"1209.4431","created_at":"2026-05-18T03:38:04.790928+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.4431v2","created_at":"2026-05-18T03:38:04.790928+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4431","created_at":"2026-05-18T03:38:04.790928+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZMXO3VINLBRW","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZMXO3VINLBRWM4UI","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZMXO3VIN","created_at":"2026-05-18T12:27:30.460161+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/ZMXO3VINLBRWM4UIMINPKPHQMM","json":"https://pith.science/pith/ZMXO3VINLBRWM4UIMINPKPHQMM.json","graph_json":"https://pith.science/api/pith-number/ZMXO3VINLBRWM4UIMINPKPHQMM/graph.json","events_json":"https://pith.science/api/pith-number/ZMXO3VINLBRWM4UIMINPKPHQMM/events.json","paper":"https://pith.science/paper/ZMXO3VIN"},"agent_actions":{"view_html":"https://pith.science/pith/ZMXO3VINLBRWM4UIMINPKPHQMM","download_json":"https://pith.science/pith/ZMXO3VINLBRWM4UIMINPKPHQMM.json","view_paper":"https://pith.science/paper/ZMXO3VIN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.4431&json=true","fetch_graph":"https://pith.science/api/pith-number/ZMXO3VINLBRWM4UIMINPKPHQMM/graph.json","fetch_events":"https://pith.science/api/pith-number/ZMXO3VINLBRWM4UIMINPKPHQMM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZMXO3VINLBRWM4UIMINPKPHQMM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZMXO3VINLBRWM4UIMINPKPHQMM/action/storage_attestation","attest_author":"https://pith.science/pith/ZMXO3VINLBRWM4UIMINPKPHQMM/action/author_attestation","sign_citation":"https://pith.science/pith/ZMXO3VINLBRWM4UIMINPKPHQMM/action/citation_signature","submit_replication":"https://pith.science/pith/ZMXO3VINLBRWM4UIMINPKPHQMM/action/replication_record"}},"created_at":"2026-05-18T03:38:04.790928+00:00","updated_at":"2026-05-18T03:38:04.790928+00:00"}