{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OVEDCEELBVEENCFRM6C45VKWEU","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":"91acc04ca84a6156d422ab381a2c5fa8b7d46e90ffe4355f444911d27d196105","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-04T15:37:37Z","title_canon_sha256":"753c056a1f7c40ffef9a61b7c2d1d6a98c4f3842ea8144cb83cd3e3a93ecfc3d"},"schema_version":"1.0","source":{"id":"1808.01494","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01494","created_at":"2026-05-18T00:08:52Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01494v1","created_at":"2026-05-18T00:08:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01494","created_at":"2026-05-18T00:08:52Z"},{"alias_kind":"pith_short_12","alias_value":"OVEDCEELBVEE","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OVEDCEELBVEENCFR","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OVEDCEEL","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:cc59bd8603cc756bf68d7b5c5efa5d6f410c9e6f675e38e948c305ea85438e15","target":"graph","created_at":"2026-05-18T00:08:52Z","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":"In this paper, we investigate steady two-dimensional free-surface flows of an inviscid and incompressible fluid emerging from a nozzle, falling under gravity and impinging onto a horizontal wall. More precisely, for any given atmosphere pressure $p_{atm}$ and any appropriate incoming total flux $Q$, we establish the existence of two-dimensional incompressible impinging jet with gravity. The two free surfaces initiate smoothly at the endpoints of the nozzle and become to be horizontal in downstream. By transforming the free boundary problem into a minimum problem, we establish the properties of","authors_text":"Jianfeng Cheng, Lili Du, Zhouping Xin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-04T15:37:37Z","title":"Incompressible impinging jet flow with gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01494","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":"sha256:28324ccefaae6afc6e448116349f578dcb1527857c88c585f2a4e989804b2962","target":"record","created_at":"2026-05-18T00:08:52Z","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":"91acc04ca84a6156d422ab381a2c5fa8b7d46e90ffe4355f444911d27d196105","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-04T15:37:37Z","title_canon_sha256":"753c056a1f7c40ffef9a61b7c2d1d6a98c4f3842ea8144cb83cd3e3a93ecfc3d"},"schema_version":"1.0","source":{"id":"1808.01494","kind":"arxiv","version":1}},"canonical_sha256":"754831108b0d484688b16785ced5562520295dbceede80dccb35e075b1e69aa7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"754831108b0d484688b16785ced5562520295dbceede80dccb35e075b1e69aa7","first_computed_at":"2026-05-18T00:08:52.772280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:52.772280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AguXScQiV4EvAN7Yvcm6QKKQt+omW/GUhmjaXrevZZsVSotbzQQepfsiCVZnLSGsvh0txu5FHbrnBFRiz0NUAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:52.773070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01494","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28324ccefaae6afc6e448116349f578dcb1527857c88c585f2a4e989804b2962","sha256:cc59bd8603cc756bf68d7b5c5efa5d6f410c9e6f675e38e948c305ea85438e15"],"state_sha256":"52a42873de71fc9a22146672624319c493975df122c0cc963a66df63a888fe7f"}