{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6MEE23BDE7RCULEL7XLRNKZSV6","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":"e35ccbd02266af32d579890438246c9d4e012972d9e5897ed3e60a69fd8ff37f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-30T17:37:57Z","title_canon_sha256":"0c173d2b495e144d81457ee592abc50f98f605b1873541731164a4bee34626b0"},"schema_version":"1.0","source":{"id":"1208.6245","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6245","created_at":"2026-05-18T03:01:47Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6245v1","created_at":"2026-05-18T03:01:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6245","created_at":"2026-05-18T03:01:47Z"},{"alias_kind":"pith_short_12","alias_value":"6MEE23BDE7RC","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6MEE23BDE7RCULEL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6MEE23BD","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:06545305d9f29b31bf919878724590125947f58d40224d1ab4db447cc20fe9fd","target":"graph","created_at":"2026-05-18T03:01:47Z","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":"In this paper we use probabilistic arguments (Tug-of-War games) to obtain existence of viscosity solutions to a parabolic problem of the form $$ {cases} K_{(x,t)}(D u)u_t (x,t)= \\frac12 <D^2 u J_{(x,t)}(D u),J_{(x,t)}(D u) (x,t)  &{in} \\Omega_T, u(x,t)=F(x)&{on}\\Gamma, {cases} $$ where $\\Omega_T=\\Omega\\times(0,T]$ and $\\Gamma$ is its parabolic boundary. This problem can be viewed as a version with spatial and time dependence of the evolution problem given by the infinity Laplacian, $ u_t (x,t)= <D^2 u (x,t) \\frac{D u}{|Du|} (x,t),\\, \\frac{D u}{|Du|} (x,t)>$.","authors_text":"Julio D. Rossi, Leandro M. Del Pezzo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-30T17:37:57Z","title":"Tug-of-War games and parabolic problems with spatial and time dependence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6245","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":"sha256:1937d3b314f23783411b1d02a52e4b44664ab2b079f6ed86aa6e6d2a18678b0e","target":"record","created_at":"2026-05-18T03:01:47Z","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":"e35ccbd02266af32d579890438246c9d4e012972d9e5897ed3e60a69fd8ff37f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-30T17:37:57Z","title_canon_sha256":"0c173d2b495e144d81457ee592abc50f98f605b1873541731164a4bee34626b0"},"schema_version":"1.0","source":{"id":"1208.6245","kind":"arxiv","version":1}},"canonical_sha256":"f3084d6c2327e22a2c8bfdd716ab32af9c0dcfadd21813f93cfc5a9dd5abdbdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3084d6c2327e22a2c8bfdd716ab32af9c0dcfadd21813f93cfc5a9dd5abdbdf","first_computed_at":"2026-05-18T03:01:47.033000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:47.033000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9kbOQSTxeXkb0Ft35/Da5kBb+KxLNnz/lm7Nx5s9CwYN2HV08WxIeF9IgtHcQeyG/3YKoPuKhuTu5+Y4f9NYAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:47.033618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.6245","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1937d3b314f23783411b1d02a52e4b44664ab2b079f6ed86aa6e6d2a18678b0e","sha256:06545305d9f29b31bf919878724590125947f58d40224d1ab4db447cc20fe9fd"],"state_sha256":"eae31f980edf75409804eb4eb837c7e07d8d57bd0de982c25a2fac78a8a0aa1c"}