{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CC3KIMCRDQUQSKEYBMBTMSZSGW","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":"00bde8a2f970e1e3463bc04463ec3cc403d9b25e89919b1f38c73d5b76efb496","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-14T13:57:24Z","title_canon_sha256":"30c9d12d4cf06d6a793abb9597a5d86503a689f42b44ec8ba888e2a2dbb1e898"},"schema_version":"1.0","source":{"id":"1805.05173","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.05173","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1805.05173v3","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05173","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"CC3KIMCRDQUQ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CC3KIMCRDQUQSKEY","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CC3KIMCR","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:d198c144356bb52f761b4e733903ee3fa687e9ce4e5d405cc2dd9c98195ec711","target":"graph","created_at":"2026-05-18T00:13:21Z","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 prove, in all dimensions $n\\geq 2$, that there exists a convex translator lying in a slab of width $\\pi\\sec\\theta$ in $\\mathbb{R}^{n+1}$ (and in no smaller slab) if and only if $\\theta\\in[0,\\frac{\\pi}{2}]$. We also obtain convexity and regularity results for translators which admit appropriate symmetries and study the asymptotics and reflection symmetry of translators lying in slab regions.","authors_text":"Giuseppe Tinaglia, Mat Langford, Theodora Bourni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-14T13:57:24Z","title":"On the existence of translating solutions of mean curvature flow in slab regions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05173","kind":"arxiv","version":3},"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:c134ba26d772a30d798007b2ccbecc74315d337fa2183776befef238c315ac76","target":"record","created_at":"2026-05-18T00:13:21Z","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":"00bde8a2f970e1e3463bc04463ec3cc403d9b25e89919b1f38c73d5b76efb496","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-14T13:57:24Z","title_canon_sha256":"30c9d12d4cf06d6a793abb9597a5d86503a689f42b44ec8ba888e2a2dbb1e898"},"schema_version":"1.0","source":{"id":"1805.05173","kind":"arxiv","version":3}},"canonical_sha256":"10b6a430511c290928980b03364b32359eaf7972557cce3690c1d6b303ee8508","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10b6a430511c290928980b03364b32359eaf7972557cce3690c1d6b303ee8508","first_computed_at":"2026-05-18T00:13:21.317495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:21.317495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lP/NUvuBnn1d8HeiiD8/xmUP13oq7O3EgalWnPzHQFefSwsqgcFcDHVeFLreDa1BSy9ZdyWZl2Of8PW60dTjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:21.317974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.05173","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c134ba26d772a30d798007b2ccbecc74315d337fa2183776befef238c315ac76","sha256:d198c144356bb52f761b4e733903ee3fa687e9ce4e5d405cc2dd9c98195ec711"],"state_sha256":"428a86cf88a9a8064da1200e26ce3ec287878f454d3c7172a728864c6aef8c88"}