{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YFO3DHA7YRA2CXF4P2ZXDIFQJG","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":"a3aa16a38f88080c2b04c9b377be090c2a6e120982a8d2f53b54163f8e46f219","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-03T12:33:14Z","title_canon_sha256":"fd0441e24713a06df312349ec47d1f48c42cfa1ab967cdecd6400bddc2fa92b1"},"schema_version":"1.0","source":{"id":"1407.0889","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0889","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0889v2","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0889","created_at":"2026-05-18T01:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"YFO3DHA7YRA2","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YFO3DHA7YRA2CXF4","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YFO3DHA7","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:9c86c14ad0eb4bdac510f45a4bbb4450af6f6aef1213380b56aa088b18db63e3","target":"graph","created_at":"2026-05-18T01:33:32Z","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":"We prove local Lipschitz continuity and Harnack's inequality for value functions of the stochastic game tug-of-war with noise and running payoff. As a consequence, we obtain game-theoretic proofs for the same regularity properties for viscosity solutions of the inhomogeneous $p$-Laplace equation when $p>2$.","authors_text":"Eero Ruosteenoja","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-03T12:33:14Z","title":"Local regularity results for value functions of tug-of-war with noise and running payoff"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0889","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":"sha256:697a811696f6608a784b668d6df725a090aa4d2d674735c81dae724f2cbd67f3","target":"record","created_at":"2026-05-18T01:33:32Z","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":"a3aa16a38f88080c2b04c9b377be090c2a6e120982a8d2f53b54163f8e46f219","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-03T12:33:14Z","title_canon_sha256":"fd0441e24713a06df312349ec47d1f48c42cfa1ab967cdecd6400bddc2fa92b1"},"schema_version":"1.0","source":{"id":"1407.0889","kind":"arxiv","version":2}},"canonical_sha256":"c15db19c1fc441a15cbc7eb371a0b049ae9ca8a60f5a15dec08ef5eba6bd1c29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c15db19c1fc441a15cbc7eb371a0b049ae9ca8a60f5a15dec08ef5eba6bd1c29","first_computed_at":"2026-05-18T01:33:32.589491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:32.589491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ieuT4PsMaZIvcielta8FjzQB94ImrfQRf9CpF40hx+rqLpG3mRos7JXtdUujGdN0dfp8/jzDH1Bz5wsKchg5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:32.590134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0889","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:697a811696f6608a784b668d6df725a090aa4d2d674735c81dae724f2cbd67f3","sha256:9c86c14ad0eb4bdac510f45a4bbb4450af6f6aef1213380b56aa088b18db63e3"],"state_sha256":"73c0969ad7b9feafb9dadbc072d242b8a153605df37e9ff02662960be59ec726"}