{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZF7P5OXZ2IOGAWLN3XT6EY54EO","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":"32912cd92aff9550c9f746e8c91efe07120664723c15e74388a386723fe3fccb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-31T15:49:02Z","title_canon_sha256":"0fde1966388b993069c25a5d94cbb5de586e1ee5bfb10f1d8c5cdf252ce3492b"},"schema_version":"1.0","source":{"id":"1801.01028","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.01028","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"1801.01028v3","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01028","created_at":"2026-05-18T00:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"ZF7P5OXZ2IOG","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZF7P5OXZ2IOGAWLN","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZF7P5OXZ","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:a297ab91d94e086b20423ffaed7ca506490098f89e36d4c61d7d752bc57d450d","target":"graph","created_at":"2026-05-18T00:05:51Z","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":"This paper is concerned with existence of a $C^{\\alpha}$ viscosity solution of a second order non-translation invariant integro-PDE. We first obtain a weak Harnack inequality for such integro-PDE. We then use the weak Harnack inequality to prove H\\\"older regularity and existence of solutions of the integro-PDEs.","authors_text":"Chenchen Mou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-31T15:49:02Z","title":"Existence of $C^\\alpha$ solutions to integro-PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01028","kind":"arxiv","version":3},"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":"sha256:6aa5d129b65127a4ffed4aa7d71e5036c591456f149472ced8fc5c4de12b3fc4","target":"record","created_at":"2026-05-18T00:05:51Z","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":"32912cd92aff9550c9f746e8c91efe07120664723c15e74388a386723fe3fccb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-31T15:49:02Z","title_canon_sha256":"0fde1966388b993069c25a5d94cbb5de586e1ee5bfb10f1d8c5cdf252ce3492b"},"schema_version":"1.0","source":{"id":"1801.01028","kind":"arxiv","version":3}},"canonical_sha256":"c97efebaf9d21c60596ddde7e263bc2391bded00b94759bb3865f355067d428f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c97efebaf9d21c60596ddde7e263bc2391bded00b94759bb3865f355067d428f","first_computed_at":"2026-05-18T00:05:51.037853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:51.037853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KVMpazgft8+RjoN9CXvc9U72gNkhe3gaTRD74T0dzVAEYksI9N0rDVPIAl9U/XgcfnuE25ccHFK1LYmgc2mXDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:51.038644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.01028","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6aa5d129b65127a4ffed4aa7d71e5036c591456f149472ced8fc5c4de12b3fc4","sha256:a297ab91d94e086b20423ffaed7ca506490098f89e36d4c61d7d752bc57d450d"],"state_sha256":"edeaad00acc5eedf3a8bc5098aa5c7dae00fc13b535ca4f020ffe1aeaefa7c7c"}