{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:E4IODYABZJU5ZN7LWBHXUIQLP6","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":"eff1b0d908b4e246d999b4d030ec4b6fe8788a4779e351df437d7d4779ef6ce9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-09-03T20:34:25Z","title_canon_sha256":"c1b4097b09ba42df0e7af1fec586b9562ed42d869bfd9eba4d9569519164cfbe"},"schema_version":"1.0","source":{"id":"1809.00714","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00714","created_at":"2026-05-17T23:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00714v2","created_at":"2026-05-17T23:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00714","created_at":"2026-05-17T23:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"E4IODYABZJU5","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E4IODYABZJU5ZN7L","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E4IODYAB","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:fcfbdb721bc5c9dacd3b1756a665de93e9ce6054b0c8cb2756f12f5df8e2df41","target":"graph","created_at":"2026-05-17T23:43:17Z","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":"The Dominative $p$-Laplacian is the operator defined for $2\\le p < \\infty$ as follows: \\begin{equation}\\label{dominativep} \\mathcal{L}_{p}u(x)=\\frac{1}{p}\\left(\\lambda_{1}+\\ldots+\\lambda_{N-1}\\right)+\\frac{(p-1)}{p}\\lambda_{N},\n  \\end{equation} where we have ordered the eigenvalues of $D^{2}u(x)$ as $\\lambda_{1}\\le \\lambda_{2}\\ldots\\le\\lambda_{N}$. The operator $\\mathcal{L}_{p}u(x)$ was introduced by Brustand to give a natural explanation of the superposition principle for the $p$-Laplace equation.\n  In this paper, we present a discrete stochastic approximation to the unique viscosity solution","authors_text":"Juan J. Manfredi, Karl K. Brustad, Peter Lindqvist","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-09-03T20:34:25Z","title":"A discrete stochastic interpretation of the Dominative $p$-Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00714","kind":"arxiv","version":2},"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":"sha256:008253e060b54870c91c50c1b31897615af6b24ff4b291192799aa4ffb6de3cd","target":"record","created_at":"2026-05-17T23:43:17Z","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":"eff1b0d908b4e246d999b4d030ec4b6fe8788a4779e351df437d7d4779ef6ce9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-09-03T20:34:25Z","title_canon_sha256":"c1b4097b09ba42df0e7af1fec586b9562ed42d869bfd9eba4d9569519164cfbe"},"schema_version":"1.0","source":{"id":"1809.00714","kind":"arxiv","version":2}},"canonical_sha256":"2710e1e001ca69dcb7ebb04f7a220b7faa0b7b67edd55812190856f150d78bb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2710e1e001ca69dcb7ebb04f7a220b7faa0b7b67edd55812190856f150d78bb2","first_computed_at":"2026-05-17T23:43:17.581621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:17.581621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"62HUkdn+GW5LjCiqBYxTjhLTcMUSUB1EfdsvWOsPH7SamTXMbmzR64+N93lzQOCEOVY8NorR2gvO+mhbo+5/DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:17.582112Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.00714","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:008253e060b54870c91c50c1b31897615af6b24ff4b291192799aa4ffb6de3cd","sha256:fcfbdb721bc5c9dacd3b1756a665de93e9ce6054b0c8cb2756f12f5df8e2df41"],"state_sha256":"6847a0485e3cb0ada9f7c4f6a0a8029b7cd89f9905be63bb45124b9d36fdfafd"}