{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UQECH2B3GP646WBQYEMPM62WFG","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":"6424d40f0254735262ddd73bc7f93200eb279373e160462222f7d2badb772f2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-14T01:12:11Z","title_canon_sha256":"ef1e04cdf903802aa2003d00bbd408dbbba1d2dade372fbb88f3bfc55100d0cf"},"schema_version":"1.0","source":{"id":"1901.04099","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.04099","created_at":"2026-05-17T23:56:26Z"},{"alias_kind":"arxiv_version","alias_value":"1901.04099v1","created_at":"2026-05-17T23:56:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04099","created_at":"2026-05-17T23:56:26Z"},{"alias_kind":"pith_short_12","alias_value":"UQECH2B3GP64","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UQECH2B3GP646WBQ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UQECH2B3","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:3b2075ddf75c4062a366aac91cb29320f375383f015af8b3e7040e8098d02692","target":"graph","created_at":"2026-05-17T23:56:26Z","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":"This paper concerns the evolution of complete noncompact locally uniformly convex hypersurface in Euclidean space by curvature flow, for which the normal speed $\\Phi$ is given by a power $\\beta\\geq 1$ of a monotone symmetric and homogeneous of degree one function $F$ of the principal curvatures. Under the assumption that $F$ is inverse concave and its dual function approaches zero on the boundary of positive cone, we prove that the complete smooth strictly convex solution exists and remains a graph until the maximal time of existence. In particular, if $F=K^{s/n}G^{1-s}$ for any $s\\in(0, 1]$, ","authors_text":"Guanghan Li, Yusha Lv","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-14T01:12:11Z","title":"Evolution of complete noncompact graphs by powers of curvature function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04099","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":"sha256:4139c459c2e75a2ba4d60809bb8837d12d4c8a73654fe1ba724abcb8e31ffe22","target":"record","created_at":"2026-05-17T23:56:26Z","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":"6424d40f0254735262ddd73bc7f93200eb279373e160462222f7d2badb772f2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-14T01:12:11Z","title_canon_sha256":"ef1e04cdf903802aa2003d00bbd408dbbba1d2dade372fbb88f3bfc55100d0cf"},"schema_version":"1.0","source":{"id":"1901.04099","kind":"arxiv","version":1}},"canonical_sha256":"a40823e83b33fdcf5830c118f67b5629831f8ccc433b8d623a138c425d6a1486","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a40823e83b33fdcf5830c118f67b5629831f8ccc433b8d623a138c425d6a1486","first_computed_at":"2026-05-17T23:56:26.295232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:26.295232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GPAODRhIa1eCnRfquaQdcyQAfkwoBn1UMFXBisB2v0furPKyAS1Qnb3uuPRVUZ6c04wVybLklerE62gWcZF+BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:26.295673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.04099","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4139c459c2e75a2ba4d60809bb8837d12d4c8a73654fe1ba724abcb8e31ffe22","sha256:3b2075ddf75c4062a366aac91cb29320f375383f015af8b3e7040e8098d02692"],"state_sha256":"8eeff19cc73216c80e0bfcd8dcb50e603b28eb3a7d32f39a94c4ab4f73c694d4"}