{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IIL55OR3C4TH27O3HPJLCARYVG","short_pith_number":"pith:IIL55OR3","canonical_record":{"source":{"id":"1904.13076","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-30T07:08:18Z","cross_cats_sorted":[],"title_canon_sha256":"aabf5cdfb2fe3b6d2e5e28204ae21263112a56d7e1e153f624fa23480afa47c7","abstract_canon_sha256":"cc8582ab5f771f67ed95b7d74e95850338556fc8ba44e19e975088ca291bf02d"},"schema_version":"1.0"},"canonical_sha256":"4217deba3b17267d7ddb3bd2b10238a9ba6dcd8382f834be78c75213f426e44d","source":{"kind":"arxiv","id":"1904.13076","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.13076","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"arxiv_version","alias_value":"1904.13076v2","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.13076","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"pith_short_12","alias_value":"IIL55OR3C4TH","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IIL55OR3C4TH27O3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IIL55OR3","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IIL55OR3C4TH27O3HPJLCARYVG","target":"record","payload":{"canonical_record":{"source":{"id":"1904.13076","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-30T07:08:18Z","cross_cats_sorted":[],"title_canon_sha256":"aabf5cdfb2fe3b6d2e5e28204ae21263112a56d7e1e153f624fa23480afa47c7","abstract_canon_sha256":"cc8582ab5f771f67ed95b7d74e95850338556fc8ba44e19e975088ca291bf02d"},"schema_version":"1.0"},"canonical_sha256":"4217deba3b17267d7ddb3bd2b10238a9ba6dcd8382f834be78c75213f426e44d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:57.705013Z","signature_b64":"/+bBKUdUVEmXlkD8WEK5xiVF47/3jZ83JyVD69xTfhvzmVqrvutNzM6IVl2c0nMMps5wOhd4NIGQxRa0gAJ7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4217deba3b17267d7ddb3bd2b10238a9ba6dcd8382f834be78c75213f426e44d","last_reissued_at":"2026-05-17T23:45:57.704567Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:57.704567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.13076","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ItoKJr5f4e/Rqgv1/dOrF3wdN9e9iammbodXP0c+AX1JGle/tKUgViwuYLW3Ag8xsbNeSAihMBWFZxwK6tMLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:25:36.818882Z"},"content_sha256":"2e9779004259552627c309998e63e4fa0df587abd6f9c4f2a0cfb82c9da80b58","schema_version":"1.0","event_id":"sha256:2e9779004259552627c309998e63e4fa0df587abd6f9c4f2a0cfb82c9da80b58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IIL55OR3C4TH27O3HPJLCARYVG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient continuity estimates for the normalized $p$-Poisson equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnid Banerjee, Isidro H. Munive","submitted_at":"2019-04-30T07:08:18Z","abstract_excerpt":"In this paper, we obtain gradient continuity estimates for viscosity solutions of $\\Delta_{p}^N u= f$ in terms of the scaling critical $L(n,1 )$ norm of $f$, where $\\Delta_{p}^N$ is the normalized $p-$Laplacian operator defined in (1.2) below. Our main result, Theorem 2.2, corresponds to the borderline gradient continuity estimate in terms of the modified Riesz potential $\\tilde I^{f}_{q}$. Moreover, for $f \\in L^{m}$ with $m>n$, we also obtain $C^{1,\\alpha}$ estimates, see Theorem 2.3 below. This improves one of the regularity results in [3], where a $C^{1,\\alpha}$ estimate was established de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.13076","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EB/qC/2K7SmqJs3Nr3wl+pPlQ/dgYsZKBapg+sqa66fpHK9YkvppeAhVFqYkn59iAFDX0pXijCDgkUoNydZkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:25:36.819519Z"},"content_sha256":"7ba06fdcd8ee97e40e2f5b5f8332333d28c62a8e778e3f99bd65b9b825e6a7f8","schema_version":"1.0","event_id":"sha256:7ba06fdcd8ee97e40e2f5b5f8332333d28c62a8e778e3f99bd65b9b825e6a7f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IIL55OR3C4TH27O3HPJLCARYVG/bundle.json","state_url":"https://pith.science/pith/IIL55OR3C4TH27O3HPJLCARYVG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IIL55OR3C4TH27O3HPJLCARYVG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T21:25:36Z","links":{"resolver":"https://pith.science/pith/IIL55OR3C4TH27O3HPJLCARYVG","bundle":"https://pith.science/pith/IIL55OR3C4TH27O3HPJLCARYVG/bundle.json","state":"https://pith.science/pith/IIL55OR3C4TH27O3HPJLCARYVG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IIL55OR3C4TH27O3HPJLCARYVG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IIL55OR3C4TH27O3HPJLCARYVG","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":"cc8582ab5f771f67ed95b7d74e95850338556fc8ba44e19e975088ca291bf02d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-30T07:08:18Z","title_canon_sha256":"aabf5cdfb2fe3b6d2e5e28204ae21263112a56d7e1e153f624fa23480afa47c7"},"schema_version":"1.0","source":{"id":"1904.13076","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.13076","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"arxiv_version","alias_value":"1904.13076v2","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.13076","created_at":"2026-05-17T23:45:57Z"},{"alias_kind":"pith_short_12","alias_value":"IIL55OR3C4TH","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IIL55OR3C4TH27O3","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IIL55OR3","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:7ba06fdcd8ee97e40e2f5b5f8332333d28c62a8e778e3f99bd65b9b825e6a7f8","target":"graph","created_at":"2026-05-17T23:45:57Z","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":"In this paper, we obtain gradient continuity estimates for viscosity solutions of $\\Delta_{p}^N u= f$ in terms of the scaling critical $L(n,1 )$ norm of $f$, where $\\Delta_{p}^N$ is the normalized $p-$Laplacian operator defined in (1.2) below. Our main result, Theorem 2.2, corresponds to the borderline gradient continuity estimate in terms of the modified Riesz potential $\\tilde I^{f}_{q}$. Moreover, for $f \\in L^{m}$ with $m>n$, we also obtain $C^{1,\\alpha}$ estimates, see Theorem 2.3 below. This improves one of the regularity results in [3], where a $C^{1,\\alpha}$ estimate was established de","authors_text":"Agnid Banerjee, Isidro H. Munive","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-30T07:08:18Z","title":"Gradient continuity estimates for the normalized $p$-Poisson equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.13076","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":"sha256:2e9779004259552627c309998e63e4fa0df587abd6f9c4f2a0cfb82c9da80b58","target":"record","created_at":"2026-05-17T23:45:57Z","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":"cc8582ab5f771f67ed95b7d74e95850338556fc8ba44e19e975088ca291bf02d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-30T07:08:18Z","title_canon_sha256":"aabf5cdfb2fe3b6d2e5e28204ae21263112a56d7e1e153f624fa23480afa47c7"},"schema_version":"1.0","source":{"id":"1904.13076","kind":"arxiv","version":2}},"canonical_sha256":"4217deba3b17267d7ddb3bd2b10238a9ba6dcd8382f834be78c75213f426e44d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4217deba3b17267d7ddb3bd2b10238a9ba6dcd8382f834be78c75213f426e44d","first_computed_at":"2026-05-17T23:45:57.704567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:57.704567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/+bBKUdUVEmXlkD8WEK5xiVF47/3jZ83JyVD69xTfhvzmVqrvutNzM6IVl2c0nMMps5wOhd4NIGQxRa0gAJ7Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:57.705013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.13076","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e9779004259552627c309998e63e4fa0df587abd6f9c4f2a0cfb82c9da80b58","sha256:7ba06fdcd8ee97e40e2f5b5f8332333d28c62a8e778e3f99bd65b9b825e6a7f8"],"state_sha256":"e160e8835f84b8142f2d94c2aa9cf51839fe26e026ddf3f9a4c86cccef9bce98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1UfEeU2pepAx51to93YK6xAz5hdN2GcjLDm5Pr1EMyeCJiEEg6Wq0tDJryj0IPhKnARBQc9N+7uWFUUKR9DUBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:25:36.823384Z","bundle_sha256":"c9bb8debe2e5139713012f2a74ae58c15f3c9fda569f5da66d49f57e99656144"}}