{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OD2IDTXATFA2TSHYJDPTZOUODE","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":"d0fc0d419cfdc94bc48034f4fe2940334322106528ff716a498b8d9a76043983","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-03-12T15:32:23Z","title_canon_sha256":"d8144296193fe2ff16013652944928a5c73ece5c942f11226325093a28ce52f5"},"schema_version":"1.0","source":{"id":"2603.12065","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.12065","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"2603.12065v2","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.12065","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"OD2IDTXATFA2","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"pith_short_16","alias_value":"OD2IDTXATFA2TSHY","created_at":"2026-06-11T01:10:34Z"},{"alias_kind":"pith_short_8","alias_value":"OD2IDTXA","created_at":"2026-06-11T01:10:34Z"}],"graph_snapshots":[{"event_id":"sha256:221ab87be5bb7cf2434df76a140034c1e0cf29fa7cb355f3d08ffa7ad29cdacc","target":"graph","created_at":"2026-06-11T01:10:34Z","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/2603.12065/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the parabolic fractional $p-$Laplace equation $\\partial_t u+(-\\Delta_p)^su = 0$ in the degenerate range $2 < p < 2/(1-s)$. We show that weak solutions are Lipschitz continuous in space and, if $p > 1/(1-s)$, also in time. We also prove a comparison principle for both weak and viscosity solutions, and establish the equivalence between the two notions of solution.","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":"2026-03-12T15:32:23Z","title":"Fractional $p$-caloric functions are Lipschitz"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.12065","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:bae01748a9c17cefa5dddf8de3047c0b9b4312a9f11e8c53e32cbbfe89e29c40","target":"record","created_at":"2026-06-11T01:10:34Z","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":"d0fc0d419cfdc94bc48034f4fe2940334322106528ff716a498b8d9a76043983","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-03-12T15:32:23Z","title_canon_sha256":"d8144296193fe2ff16013652944928a5c73ece5c942f11226325093a28ce52f5"},"schema_version":"1.0","source":{"id":"2603.12065","kind":"arxiv","version":2}},"canonical_sha256":"70f481cee09941a9c8f848df3cba8e1935ba1315c50386173ef3afe5a0e33f50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70f481cee09941a9c8f848df3cba8e1935ba1315c50386173ef3afe5a0e33f50","first_computed_at":"2026-06-11T01:10:34.971180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:10:34.971180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OYQURqx9Vp0NG8ZTyTBCniN62A4FS5aHsK9H+gS8SfRBA7ZQpQhL1JzuyO0ThrYyhAloT1Hs+1mMGGd2XXKGCw==","signature_status":"signed_v1","signed_at":"2026-06-11T01:10:34.972205Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.12065","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bae01748a9c17cefa5dddf8de3047c0b9b4312a9f11e8c53e32cbbfe89e29c40","sha256:221ab87be5bb7cf2434df76a140034c1e0cf29fa7cb355f3d08ffa7ad29cdacc"],"state_sha256":"a87dd2164dc33a5588a981efa4cd50c9c82c4483878d6be33766d91c39788bd1"}