{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:Q7GOIVI22LTTZXCBURNFPTIONI","short_pith_number":"pith:Q7GOIVI2","schema_version":"1.0","canonical_sha256":"87cce4551ad2e73cdc41a45a57cd0e6a0ff650203b819a54a40b20689fa5825e","source":{"kind":"arxiv","id":"0808.1457","version":2},"attestation_state":"computed","paper":{"title":"A stochastic differential game for the inhomogeneous $\\infty$-Laplace equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amarjit Budhiraja, Rami Atar","submitted_at":"2008-08-11T07:31:29Z","abstract_excerpt":"Given a bounded $\\mathcaligr{C}^2$ domain $G\\subset{\\mathbb{R}}^m$, functions $g\\in\\mathcaligr{C}(\\partial G,{\\mathbb{R}})$ and $h\\in\\mathcaligr {C}(\\bar{G},{\\mathbb{R}}\\setminus\\{0\\})$, let $u$ denote the unique viscosity solution to the equation $-2\\Delta_{\\infty}u=h$ in $G$ with boundary data $g$. We provide a representation for $u$ as the value of a two-player zero-sum stochastic differential game."},"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":"0808.1457","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-08-11T07:31:29Z","cross_cats_sorted":[],"title_canon_sha256":"e2b691f47e0828401379ad18a8f9b1793c2eafcfbd71ee3f738001d7c9951ef0","abstract_canon_sha256":"2d542ceeac534b307a46d627856fbfc01369d79fa8eb734e3f5baae9f571ec1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:59.743468Z","signature_b64":"Gy1FE9tbRdsAVFfhbDonAxBYXXyF85UVdqqDBJ4zKelT9hnWk4CVdxeRg7TyivVfc5Nta98q5V+rOSPgX1HKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87cce4551ad2e73cdc41a45a57cd0e6a0ff650203b819a54a40b20689fa5825e","last_reissued_at":"2026-05-18T04:39:59.742843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:59.742843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A stochastic differential game for the inhomogeneous $\\infty$-Laplace equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amarjit Budhiraja, Rami Atar","submitted_at":"2008-08-11T07:31:29Z","abstract_excerpt":"Given a bounded $\\mathcaligr{C}^2$ domain $G\\subset{\\mathbb{R}}^m$, functions $g\\in\\mathcaligr{C}(\\partial G,{\\mathbb{R}})$ and $h\\in\\mathcaligr {C}(\\bar{G},{\\mathbb{R}}\\setminus\\{0\\})$, let $u$ denote the unique viscosity solution to the equation $-2\\Delta_{\\infty}u=h$ in $G$ with boundary data $g$. We provide a representation for $u$ as the value of a two-player zero-sum stochastic differential game."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1457","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":"0808.1457","created_at":"2026-05-18T04:39:59.742924+00:00"},{"alias_kind":"arxiv_version","alias_value":"0808.1457v2","created_at":"2026-05-18T04:39:59.742924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.1457","created_at":"2026-05-18T04:39:59.742924+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q7GOIVI22LTT","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q7GOIVI22LTTZXCB","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q7GOIVI2","created_at":"2026-05-18T12:25:57.157939+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/Q7GOIVI22LTTZXCBURNFPTIONI","json":"https://pith.science/pith/Q7GOIVI22LTTZXCBURNFPTIONI.json","graph_json":"https://pith.science/api/pith-number/Q7GOIVI22LTTZXCBURNFPTIONI/graph.json","events_json":"https://pith.science/api/pith-number/Q7GOIVI22LTTZXCBURNFPTIONI/events.json","paper":"https://pith.science/paper/Q7GOIVI2"},"agent_actions":{"view_html":"https://pith.science/pith/Q7GOIVI22LTTZXCBURNFPTIONI","download_json":"https://pith.science/pith/Q7GOIVI22LTTZXCBURNFPTIONI.json","view_paper":"https://pith.science/paper/Q7GOIVI2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0808.1457&json=true","fetch_graph":"https://pith.science/api/pith-number/Q7GOIVI22LTTZXCBURNFPTIONI/graph.json","fetch_events":"https://pith.science/api/pith-number/Q7GOIVI22LTTZXCBURNFPTIONI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q7GOIVI22LTTZXCBURNFPTIONI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q7GOIVI22LTTZXCBURNFPTIONI/action/storage_attestation","attest_author":"https://pith.science/pith/Q7GOIVI22LTTZXCBURNFPTIONI/action/author_attestation","sign_citation":"https://pith.science/pith/Q7GOIVI22LTTZXCBURNFPTIONI/action/citation_signature","submit_replication":"https://pith.science/pith/Q7GOIVI22LTTZXCBURNFPTIONI/action/replication_record"}},"created_at":"2026-05-18T04:39:59.742924+00:00","updated_at":"2026-05-18T04:39:59.742924+00:00"}