{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WJ5OK5MFZ6KVRQ3HGZXTG5RULP","short_pith_number":"pith:WJ5OK5MF","schema_version":"1.0","canonical_sha256":"b27ae57585cf9558c367366f3376345bc5c723825a695e80f6737ad5f148ec0e","source":{"kind":"arxiv","id":"1803.00528","version":1},"attestation_state":"computed","paper":{"title":"Differential games and Hamilton-Jacobi equations in the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Calogero","submitted_at":"2018-03-01T17:50:43Z","abstract_excerpt":"The purpose of this work is twofold. First we study the solutions of a Hamilton-Jacobi equation of the form $u_t(t,x)+\\mathcal{H}(t,x,\\nabla_H u(t,x))=0$, where $\\nabla_H u$ represents the horizontal gradient of a function $u$ defined on the Heisenberg group ${I\\!\\!H}$. Motivated by the recent paper by Liu, Manfredi and Zhou (\\cite{LiMaZh2016}), we prove a Lipschitz continuity preserving property for $u$ with respect to the Kor\\'anyi homogeneous distances $d_G$ in ${I\\!\\!H}$. Secondly, we are keenly interested in introducing the game theory in ${I\\!\\!H}$, taking into account its Sub-Riemannian"},"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":"1803.00528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-01T17:50:43Z","cross_cats_sorted":[],"title_canon_sha256":"9017bf3a9d1bd12c73cd00e8eccb4b7bf82a0897ec76870673f4c48257c43411","abstract_canon_sha256":"912a52c0952a49f12eb3a4abf8913626c495aa72604e2927002e2fd97effde94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:11.514585Z","signature_b64":"raQeprYjIf6lkKnexAJIGZxa3z5lwy9K4itbAZvnKnyU2RjhRXhVF/q9Ezuhj437lfqBFxaPq6StROZf8KSkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b27ae57585cf9558c367366f3376345bc5c723825a695e80f6737ad5f148ec0e","last_reissued_at":"2026-05-18T00:22:11.513935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:11.513935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differential games and Hamilton-Jacobi equations in the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Calogero","submitted_at":"2018-03-01T17:50:43Z","abstract_excerpt":"The purpose of this work is twofold. First we study the solutions of a Hamilton-Jacobi equation of the form $u_t(t,x)+\\mathcal{H}(t,x,\\nabla_H u(t,x))=0$, where $\\nabla_H u$ represents the horizontal gradient of a function $u$ defined on the Heisenberg group ${I\\!\\!H}$. Motivated by the recent paper by Liu, Manfredi and Zhou (\\cite{LiMaZh2016}), we prove a Lipschitz continuity preserving property for $u$ with respect to the Kor\\'anyi homogeneous distances $d_G$ in ${I\\!\\!H}$. Secondly, we are keenly interested in introducing the game theory in ${I\\!\\!H}$, taking into account its Sub-Riemannian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00528","kind":"arxiv","version":1},"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":"1803.00528","created_at":"2026-05-18T00:22:11.514027+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.00528v1","created_at":"2026-05-18T00:22:11.514027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00528","created_at":"2026-05-18T00:22:11.514027+00:00"},{"alias_kind":"pith_short_12","alias_value":"WJ5OK5MFZ6KV","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"WJ5OK5MFZ6KVRQ3H","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"WJ5OK5MF","created_at":"2026-05-18T12:32:59.047623+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/WJ5OK5MFZ6KVRQ3HGZXTG5RULP","json":"https://pith.science/pith/WJ5OK5MFZ6KVRQ3HGZXTG5RULP.json","graph_json":"https://pith.science/api/pith-number/WJ5OK5MFZ6KVRQ3HGZXTG5RULP/graph.json","events_json":"https://pith.science/api/pith-number/WJ5OK5MFZ6KVRQ3HGZXTG5RULP/events.json","paper":"https://pith.science/paper/WJ5OK5MF"},"agent_actions":{"view_html":"https://pith.science/pith/WJ5OK5MFZ6KVRQ3HGZXTG5RULP","download_json":"https://pith.science/pith/WJ5OK5MFZ6KVRQ3HGZXTG5RULP.json","view_paper":"https://pith.science/paper/WJ5OK5MF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.00528&json=true","fetch_graph":"https://pith.science/api/pith-number/WJ5OK5MFZ6KVRQ3HGZXTG5RULP/graph.json","fetch_events":"https://pith.science/api/pith-number/WJ5OK5MFZ6KVRQ3HGZXTG5RULP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WJ5OK5MFZ6KVRQ3HGZXTG5RULP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WJ5OK5MFZ6KVRQ3HGZXTG5RULP/action/storage_attestation","attest_author":"https://pith.science/pith/WJ5OK5MFZ6KVRQ3HGZXTG5RULP/action/author_attestation","sign_citation":"https://pith.science/pith/WJ5OK5MFZ6KVRQ3HGZXTG5RULP/action/citation_signature","submit_replication":"https://pith.science/pith/WJ5OK5MFZ6KVRQ3HGZXTG5RULP/action/replication_record"}},"created_at":"2026-05-18T00:22:11.514027+00:00","updated_at":"2026-05-18T00:22:11.514027+00:00"}