{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BVX2TSI3M2GTUATLXBV2XUHPY7","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":"b12b6d96c098573617178e43a9e17ddf4421fdf2eeb2ad50167c0ab0c4cdd2b2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-09T11:51:26Z","title_canon_sha256":"7b6de1f70387fa8531d7afabdeac5ca9caaabd26cd5dc5a7f6c0f687d04982be"},"schema_version":"1.0","source":{"id":"1608.02770","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02770","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02770v2","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02770","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"BVX2TSI3M2GT","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BVX2TSI3M2GTUATL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BVX2TSI3","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:643caac894f162a3dc81945190c2dbbe747187ebefaab82c3977141148654dbc","target":"graph","created_at":"2026-05-18T00:03:50Z","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 long-time existence and asymptotic behaviour for a class of anisotropic, expanding curvature flows. For this we adapt new curvature estimates, which were developed by Guan, Ren and Wang to treat some stationary prescribed curvature problems. As an application we give a unified flow approach to the existence of smooth, even $L_p$-Minkowski problems in $\\mathbb{R}^{n+1}$ for $p>-n-1.$","authors_text":"Julian Scheuer, Mohammad N. Ivaki, Paul Bryan","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-09T11:51:26Z","title":"A unified flow approach to smooth, even $L_p$-Minkowski problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02770","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":"sha256:96b84d4ecb2dfbaa370128affb8fad4028d03e759d2779fd7257361b5c2d797a","target":"record","created_at":"2026-05-18T00:03:50Z","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":"b12b6d96c098573617178e43a9e17ddf4421fdf2eeb2ad50167c0ab0c4cdd2b2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-09T11:51:26Z","title_canon_sha256":"7b6de1f70387fa8531d7afabdeac5ca9caaabd26cd5dc5a7f6c0f687d04982be"},"schema_version":"1.0","source":{"id":"1608.02770","kind":"arxiv","version":2}},"canonical_sha256":"0d6fa9c91b668d3a026bb86babd0efc7c854064b3c6c5d49a635e296151a4091","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d6fa9c91b668d3a026bb86babd0efc7c854064b3c6c5d49a635e296151a4091","first_computed_at":"2026-05-18T00:03:50.512548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:50.512548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KDLWtrmKVAMdJaJeQhMgMdqMp79ko2fMRqUq7LIJfSb85MTKEb1fcvBJkPluaoLbctdkIEbZSBsPDNENAXfWBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:50.513237Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02770","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96b84d4ecb2dfbaa370128affb8fad4028d03e759d2779fd7257361b5c2d797a","sha256:643caac894f162a3dc81945190c2dbbe747187ebefaab82c3977141148654dbc"],"state_sha256":"697857fb35c8a254b9ea585e4c87a3821d6a6eb863e147e698ea1a3f35512479"}