{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JTHHV3Q2MY7PQGJM34JMBR4EXC","short_pith_number":"pith:JTHHV3Q2","schema_version":"1.0","canonical_sha256":"4cce7aee1a663ef8192cdf12c0c784b8989029f816f2f392adbfca7eff2f7f04","source":{"kind":"arxiv","id":"1204.6119","version":1},"attestation_state":"computed","paper":{"title":"Harnack's inequality for p-harmonic functions via stochastic games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Eero Saksman, Hannes Luiro, Mikko Parviainen","submitted_at":"2012-04-27T07:02:32Z","abstract_excerpt":"We give a proof of Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of Harnack's inequality for p-harmonic functions in the case $p>2$ that avoids classical techniques like Moser iteration, but instead relies on suitable choices of strategies for the stochastic tug-of-war 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":"1204.6119","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-27T07:02:32Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"ae74355ddb86317a57585ce5acb0e33bd5b86f3a23613e759e3d5db4f62a11bc","abstract_canon_sha256":"8b4a63d9749baa0bb2428aada309b2c6888a426808080e834387f6cfe5616593"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:46.965725Z","signature_b64":"E2IDPKzS0PPHDcg4Hxh/53r1TMlwbmYBD20LWEWemR8fv0burhpa2udyKFpbv772EuPB2dZLI4eOw0t8h0NHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cce7aee1a663ef8192cdf12c0c784b8989029f816f2f392adbfca7eff2f7f04","last_reissued_at":"2026-05-18T03:56:46.965250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:46.965250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harnack's inequality for p-harmonic functions via stochastic games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Eero Saksman, Hannes Luiro, Mikko Parviainen","submitted_at":"2012-04-27T07:02:32Z","abstract_excerpt":"We give a proof of Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of Harnack's inequality for p-harmonic functions in the case $p>2$ that avoids classical techniques like Moser iteration, but instead relies on suitable choices of strategies for the stochastic tug-of-war game."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6119","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":"1204.6119","created_at":"2026-05-18T03:56:46.965326+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.6119v1","created_at":"2026-05-18T03:56:46.965326+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6119","created_at":"2026-05-18T03:56:46.965326+00:00"},{"alias_kind":"pith_short_12","alias_value":"JTHHV3Q2MY7P","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JTHHV3Q2MY7PQGJM","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JTHHV3Q2","created_at":"2026-05-18T12:27:11.947152+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/JTHHV3Q2MY7PQGJM34JMBR4EXC","json":"https://pith.science/pith/JTHHV3Q2MY7PQGJM34JMBR4EXC.json","graph_json":"https://pith.science/api/pith-number/JTHHV3Q2MY7PQGJM34JMBR4EXC/graph.json","events_json":"https://pith.science/api/pith-number/JTHHV3Q2MY7PQGJM34JMBR4EXC/events.json","paper":"https://pith.science/paper/JTHHV3Q2"},"agent_actions":{"view_html":"https://pith.science/pith/JTHHV3Q2MY7PQGJM34JMBR4EXC","download_json":"https://pith.science/pith/JTHHV3Q2MY7PQGJM34JMBR4EXC.json","view_paper":"https://pith.science/paper/JTHHV3Q2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.6119&json=true","fetch_graph":"https://pith.science/api/pith-number/JTHHV3Q2MY7PQGJM34JMBR4EXC/graph.json","fetch_events":"https://pith.science/api/pith-number/JTHHV3Q2MY7PQGJM34JMBR4EXC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JTHHV3Q2MY7PQGJM34JMBR4EXC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JTHHV3Q2MY7PQGJM34JMBR4EXC/action/storage_attestation","attest_author":"https://pith.science/pith/JTHHV3Q2MY7PQGJM34JMBR4EXC/action/author_attestation","sign_citation":"https://pith.science/pith/JTHHV3Q2MY7PQGJM34JMBR4EXC/action/citation_signature","submit_replication":"https://pith.science/pith/JTHHV3Q2MY7PQGJM34JMBR4EXC/action/replication_record"}},"created_at":"2026-05-18T03:56:46.965326+00:00","updated_at":"2026-05-18T03:56:46.965326+00:00"}