{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:25A2Y33F6Z2JWBSUEL2TYIGPLJ","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":"67c5d86ac11a3c7eb25980e86c8808ecab0855297dbe7087ca772882e60e61de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-20T13:07:36Z","title_canon_sha256":"b6e5fd30d9adb815290afcb64ded4baf6f55b77d8d83eb9f030964fc925e31aa"},"schema_version":"1.0","source":{"id":"2607.17912","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.17912","created_at":"2026-07-21T02:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"2607.17912v1","created_at":"2026-07-21T02:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.17912","created_at":"2026-07-21T02:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"25A2Y33F6Z2J","created_at":"2026-07-21T02:22:06Z"},{"alias_kind":"pith_short_16","alias_value":"25A2Y33F6Z2JWBSU","created_at":"2026-07-21T02:22:06Z"},{"alias_kind":"pith_short_8","alias_value":"25A2Y33F","created_at":"2026-07-21T02:22:06Z"}],"graph_snapshots":[{"event_id":"sha256:9f4b8b091ea1751d18f58ef439ba5815d2d02a377a1cb1690dd892871fd6a024","target":"graph","created_at":"2026-07-21T02:22:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.17912/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We carry on a study of the point-wise regularity theory for the nonlocal Trudinger equation, with measurable and bounded singular kernel. We establish refined quantitative upper bounds, weak and strong parabolic Harnack inequalities, both under optimal tail conditions. Our analysis relies on the adaptation of a refined De Giorgi-Moser machinery based on the parabolic approach \\'{a} la Di Benedetto, specifically designed to overcome the technical intricacies of the nonlocal, doubly nonlinear framework.","authors_text":"Kenta Nakamura, Simone Ciani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-20T13:07:36Z","title":"Harnack estimates for the nonlocal Trudinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17912","kind":"arxiv","version":1},"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":"sha256:60505404fcb129439112bb11f85fa209cecc69b13306270891656c99c928613a","target":"record","created_at":"2026-07-21T02:22:06Z","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":"67c5d86ac11a3c7eb25980e86c8808ecab0855297dbe7087ca772882e60e61de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-20T13:07:36Z","title_canon_sha256":"b6e5fd30d9adb815290afcb64ded4baf6f55b77d8d83eb9f030964fc925e31aa"},"schema_version":"1.0","source":{"id":"2607.17912","kind":"arxiv","version":1}},"canonical_sha256":"d741ac6f65f6749b065422f53c20cf5a6adc7143d9bcd2290341c70930d28b79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d741ac6f65f6749b065422f53c20cf5a6adc7143d9bcd2290341c70930d28b79","first_computed_at":"2026-07-21T02:22:06.294310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T02:22:06.294310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bhH48OrJaRv5MN9ixX++N8dmqbFJqyp5ns7BDFUvhCq3DEUG3UhVSUQt/iRe9ZxUpQz92bAqFqeesDiV2w6CCQ==","signature_status":"signed_v1","signed_at":"2026-07-21T02:22:06.295132Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.17912","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60505404fcb129439112bb11f85fa209cecc69b13306270891656c99c928613a","sha256:9f4b8b091ea1751d18f58ef439ba5815d2d02a377a1cb1690dd892871fd6a024"],"state_sha256":"10a37925f70972bc8193caaaf994016ca53bc6bac0939f7fcf4f7dc92d492e0e"}