{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:PP6SPVVATNULIEZTRMDEQZRWTH","short_pith_number":"pith:PP6SPVVA","schema_version":"1.0","canonical_sha256":"7bfd27d6a09b68b413338b0648663699f6da69fe5d5b627593ea0ee4944a819f","source":{"kind":"arxiv","id":"1802.08468","version":3},"attestation_state":"computed","paper":{"title":"Translating solitons of the mean curvature flow asymptotic to hyperplanes in $\\mathbb{R}^{n+1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Eddygledson S. Gama, Francisco Martin","submitted_at":"2018-02-23T10:15:46Z","abstract_excerpt":"A translating soliton is a hypersurface $M$ in $\\mathbb{R}^{n+1}$ such that the family $M_t= M- t \\,\\mathbf{e}_{n+1}$ is a mean curvature flow, i.e., such that normal component of the velocity at each point is equal to the mean curvature at that point $\\mathbf{H}=\\mathbf{e}_{n+1}^{\\perp}.$ In this paper we obtain a characterization of hyperplanes which are parallel to $\\mathbf{e}_{n+1}$ and the family of tilted grim reaper cylinders as the only translating solitons in $\\mathbb{R}^{n+1}$ which are $C^1$-asymptotic to two half-hyperplanes outside a non-vertical cylinder. This result was proven f"},"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":"1802.08468","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-02-23T10:15:46Z","cross_cats_sorted":[],"title_canon_sha256":"6483bb2a890aa4738422a4869d8fbe80ada88ba718d3b25e8dc7d1251c4bffb9","abstract_canon_sha256":"1390c4dd56417820409b02a9ebb046301707a57107622fa42b8e4bcc7e451704"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:09.772545Z","signature_b64":"S7DcUxsPIrTS0oMHfVLvqrxVDpSRsBHxw5DX8cEG7uyH7ijsTfAjiyTNq7tTm1PArRS+Mh1Wjok4OUWR5I/XDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bfd27d6a09b68b413338b0648663699f6da69fe5d5b627593ea0ee4944a819f","last_reissued_at":"2026-05-18T00:01:09.771905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:09.771905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Translating solitons of the mean curvature flow asymptotic to hyperplanes in $\\mathbb{R}^{n+1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Eddygledson S. Gama, Francisco Martin","submitted_at":"2018-02-23T10:15:46Z","abstract_excerpt":"A translating soliton is a hypersurface $M$ in $\\mathbb{R}^{n+1}$ such that the family $M_t= M- t \\,\\mathbf{e}_{n+1}$ is a mean curvature flow, i.e., such that normal component of the velocity at each point is equal to the mean curvature at that point $\\mathbf{H}=\\mathbf{e}_{n+1}^{\\perp}.$ In this paper we obtain a characterization of hyperplanes which are parallel to $\\mathbf{e}_{n+1}$ and the family of tilted grim reaper cylinders as the only translating solitons in $\\mathbb{R}^{n+1}$ which are $C^1$-asymptotic to two half-hyperplanes outside a non-vertical cylinder. This result was proven f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08468","kind":"arxiv","version":3},"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":"1802.08468","created_at":"2026-05-18T00:01:09.771989+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.08468v3","created_at":"2026-05-18T00:01:09.771989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08468","created_at":"2026-05-18T00:01:09.771989+00:00"},{"alias_kind":"pith_short_12","alias_value":"PP6SPVVATNUL","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"PP6SPVVATNULIEZT","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"PP6SPVVA","created_at":"2026-05-18T12:32:46.962924+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/PP6SPVVATNULIEZTRMDEQZRWTH","json":"https://pith.science/pith/PP6SPVVATNULIEZTRMDEQZRWTH.json","graph_json":"https://pith.science/api/pith-number/PP6SPVVATNULIEZTRMDEQZRWTH/graph.json","events_json":"https://pith.science/api/pith-number/PP6SPVVATNULIEZTRMDEQZRWTH/events.json","paper":"https://pith.science/paper/PP6SPVVA"},"agent_actions":{"view_html":"https://pith.science/pith/PP6SPVVATNULIEZTRMDEQZRWTH","download_json":"https://pith.science/pith/PP6SPVVATNULIEZTRMDEQZRWTH.json","view_paper":"https://pith.science/paper/PP6SPVVA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.08468&json=true","fetch_graph":"https://pith.science/api/pith-number/PP6SPVVATNULIEZTRMDEQZRWTH/graph.json","fetch_events":"https://pith.science/api/pith-number/PP6SPVVATNULIEZTRMDEQZRWTH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PP6SPVVATNULIEZTRMDEQZRWTH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PP6SPVVATNULIEZTRMDEQZRWTH/action/storage_attestation","attest_author":"https://pith.science/pith/PP6SPVVATNULIEZTRMDEQZRWTH/action/author_attestation","sign_citation":"https://pith.science/pith/PP6SPVVATNULIEZTRMDEQZRWTH/action/citation_signature","submit_replication":"https://pith.science/pith/PP6SPVVATNULIEZTRMDEQZRWTH/action/replication_record"}},"created_at":"2026-05-18T00:01:09.771989+00:00","updated_at":"2026-05-18T00:01:09.771989+00:00"}