{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:3GQ6VIPIWIFJSYHLEWURQSPNTU","short_pith_number":"pith:3GQ6VIPI","schema_version":"1.0","canonical_sha256":"d9a1eaa1e8b20a9960eb25a91849ed9d0b70550f7f825375d712ce9a73c3e254","source":{"kind":"arxiv","id":"1906.08077","version":2},"attestation_state":"computed","paper":{"title":"Invariant translators of the Solvable group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Giuseppe Pipoli","submitted_at":"2019-06-19T12:55:28Z","abstract_excerpt":"We classify the translators to the mean curvature flow in the three-dimensional solvable group $Sol_3$ that are invariant under the action of a one-parameter group of isometries of the ambient space. In particular we show that $Sol_3$ admits graphical translators defined on a half-plane, in contrast with a rigidity result of Shahriyari for translators in the Euclidean space. Moreover we exhibit some non-existence results."},"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":"1906.08077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-06-19T12:55:28Z","cross_cats_sorted":[],"title_canon_sha256":"773aa0bc48f115ef8efff3c3b52a01558a774d6d02f44150e0d52f3cbc5c7210","abstract_canon_sha256":"e6edba3470b8fa593b5a9b11d29f5072ddb362bd5a072a05bca36f0ac9184075"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:23.133076Z","signature_b64":"FCTVggb5FO3t6rd6+ci15yHIio752mymaUvLb6PlK2c2ui8BRVkblzombkFsHOc/zPG3v72fWfiak6izelD1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9a1eaa1e8b20a9960eb25a91849ed9d0b70550f7f825375d712ce9a73c3e254","last_reissued_at":"2026-05-17T23:40:23.132206Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:23.132206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant translators of the Solvable group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Giuseppe Pipoli","submitted_at":"2019-06-19T12:55:28Z","abstract_excerpt":"We classify the translators to the mean curvature flow in the three-dimensional solvable group $Sol_3$ that are invariant under the action of a one-parameter group of isometries of the ambient space. In particular we show that $Sol_3$ admits graphical translators defined on a half-plane, in contrast with a rigidity result of Shahriyari for translators in the Euclidean space. Moreover we exhibit some non-existence results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08077","kind":"arxiv","version":2},"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":"1906.08077","created_at":"2026-05-17T23:40:23.132350+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.08077v2","created_at":"2026-05-17T23:40:23.132350+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08077","created_at":"2026-05-17T23:40:23.132350+00:00"},{"alias_kind":"pith_short_12","alias_value":"3GQ6VIPIWIFJ","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"3GQ6VIPIWIFJSYHL","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"3GQ6VIPI","created_at":"2026-05-18T12:33:07.085635+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/3GQ6VIPIWIFJSYHLEWURQSPNTU","json":"https://pith.science/pith/3GQ6VIPIWIFJSYHLEWURQSPNTU.json","graph_json":"https://pith.science/api/pith-number/3GQ6VIPIWIFJSYHLEWURQSPNTU/graph.json","events_json":"https://pith.science/api/pith-number/3GQ6VIPIWIFJSYHLEWURQSPNTU/events.json","paper":"https://pith.science/paper/3GQ6VIPI"},"agent_actions":{"view_html":"https://pith.science/pith/3GQ6VIPIWIFJSYHLEWURQSPNTU","download_json":"https://pith.science/pith/3GQ6VIPIWIFJSYHLEWURQSPNTU.json","view_paper":"https://pith.science/paper/3GQ6VIPI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.08077&json=true","fetch_graph":"https://pith.science/api/pith-number/3GQ6VIPIWIFJSYHLEWURQSPNTU/graph.json","fetch_events":"https://pith.science/api/pith-number/3GQ6VIPIWIFJSYHLEWURQSPNTU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3GQ6VIPIWIFJSYHLEWURQSPNTU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3GQ6VIPIWIFJSYHLEWURQSPNTU/action/storage_attestation","attest_author":"https://pith.science/pith/3GQ6VIPIWIFJSYHLEWURQSPNTU/action/author_attestation","sign_citation":"https://pith.science/pith/3GQ6VIPIWIFJSYHLEWURQSPNTU/action/citation_signature","submit_replication":"https://pith.science/pith/3GQ6VIPIWIFJSYHLEWURQSPNTU/action/replication_record"}},"created_at":"2026-05-17T23:40:23.132350+00:00","updated_at":"2026-05-17T23:40:23.132350+00:00"}