{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SLOXVS6DYELEWWOFAJFEYUCSYH","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":"86dccadba9398ce8bfbd4922914aa3864d59a4aa73e489020b5f214417421026","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-06T06:50:44Z","title_canon_sha256":"415b678d288feadb154c834d7686f50cefabfca888fde6d49b0e200b73ab36ee"},"schema_version":"1.0","source":{"id":"2607.04725","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.04725","created_at":"2026-07-07T02:19:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.04725v1","created_at":"2026-07-07T02:19:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.04725","created_at":"2026-07-07T02:19:59Z"},{"alias_kind":"pith_short_12","alias_value":"SLOXVS6DYELE","created_at":"2026-07-07T02:19:59Z"},{"alias_kind":"pith_short_16","alias_value":"SLOXVS6DYELEWWOF","created_at":"2026-07-07T02:19:59Z"},{"alias_kind":"pith_short_8","alias_value":"SLOXVS6D","created_at":"2026-07-07T02:19:59Z"}],"graph_snapshots":[{"event_id":"sha256:2a3893c8f9771aa60f02f3b66c76286c7abfb18f1bc055d094de14255c7d4bbc","target":"graph","created_at":"2026-07-07T02:19:59Z","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/2607.04725/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the obstacle problem for the parabolic fractional $p-$Laplace equation \\[\\partial_t u+(-\\Delta_p)^su = 0\\] in the degenerate range $2<p<2/(1-s)$. We prove that viscosity solutions are locally Lipschitz continuous in space and H\\\"older continuous in time. If, in addition, $p>1/(1-s)$, the time regularity improves to Lipschitz continuity.","authors_text":"Aelson Sobral, David Jesus, Jos\\'e Miguel Urbano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-06T06:50:44Z","title":"Lipschitz regularity for the parabolic $(s,p)-$obstacle problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.04725","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":"sha256:86f79d0ee94b60a26f7528358bfec31ddb31c117ebfee9f5ecc95381311b39aa","target":"record","created_at":"2026-07-07T02:19:59Z","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":"86dccadba9398ce8bfbd4922914aa3864d59a4aa73e489020b5f214417421026","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-06T06:50:44Z","title_canon_sha256":"415b678d288feadb154c834d7686f50cefabfca888fde6d49b0e200b73ab36ee"},"schema_version":"1.0","source":{"id":"2607.04725","kind":"arxiv","version":1}},"canonical_sha256":"92dd7acbc3c1164b59c5024a4c5052c1c0e6dcabb1e9087f6055b99d43244fd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92dd7acbc3c1164b59c5024a4c5052c1c0e6dcabb1e9087f6055b99d43244fd8","first_computed_at":"2026-07-07T02:19:59.980274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T02:19:59.980274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ItX/w+vhVIvHfOXmcILgNkDhdSvLjXFQiWsGyEmXqZ2f0CRWtoiQLpMgqJziuoyZgE1S+kh+33vYN5olZlqwDA==","signature_status":"signed_v1","signed_at":"2026-07-07T02:19:59.980977Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.04725","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86f79d0ee94b60a26f7528358bfec31ddb31c117ebfee9f5ecc95381311b39aa","sha256:2a3893c8f9771aa60f02f3b66c76286c7abfb18f1bc055d094de14255c7d4bbc"],"state_sha256":"4ddd212edf9fe72ac206dbdeb1e2bde4a11da5201ce8bc4a74299246888a331a"}