{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VZBX5TMIFCL3J4H5TIEEGPDFVO","short_pith_number":"pith:VZBX5TMI","canonical_record":{"source":{"id":"1110.3295","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-14T18:44:56Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"4fb6be331f1281428232739164d345c83fb2ec29fb42ceb36cc61f6bb09c3548","abstract_canon_sha256":"fb4c493f996afb5f52b975bec4d12e4292425a04e78e42b914d7f7074379caa2"},"schema_version":"1.0"},"canonical_sha256":"ae437ecd882897b4f0fd9a08433c65aba1d0a87e7756bd93b61837455af93fe3","source":{"kind":"arxiv","id":"1110.3295","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3295","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3295v3","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3295","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"VZBX5TMIFCL3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VZBX5TMIFCL3J4H5","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VZBX5TMI","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VZBX5TMIFCL3J4H5TIEEGPDFVO","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3295","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-14T18:44:56Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"4fb6be331f1281428232739164d345c83fb2ec29fb42ceb36cc61f6bb09c3548","abstract_canon_sha256":"fb4c493f996afb5f52b975bec4d12e4292425a04e78e42b914d7f7074379caa2"},"schema_version":"1.0"},"canonical_sha256":"ae437ecd882897b4f0fd9a08433c65aba1d0a87e7756bd93b61837455af93fe3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:46.332300Z","signature_b64":"vKUH26cXjqmc567lSnMf4dfEYg34DFtyz016d9cM9Izi9rODfyO1XjMqJYGD5S5GvKEQcwveiIRP7x4kEi/LAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae437ecd882897b4f0fd9a08433c65aba1d0a87e7756bd93b61837455af93fe3","last_reissued_at":"2026-05-18T03:38:46.331609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:46.331609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3295","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2euJ5d4h93VY3hzf701lWRv4VaSMpSOBBgI3+C4Dsp2AyQbAwEFerEsGcXlAWKqwLgzTuiboBP6LKec2Xr4EBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:19:47.976269Z"},"content_sha256":"26632f24073eabc2d888bc7c495c74fc876a3ad14b7e42ea93c63bee2f2df870","schema_version":"1.0","event_id":"sha256:26632f24073eabc2d888bc7c495c74fc876a3ad14b7e42ea93c63bee2f2df870"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VZBX5TMIFCL3J4H5TIEEGPDFVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of solutions to degenerate $p$-Laplacian equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"David Cruz-Uribe, Kabe Moen, Virginia Naibo","submitted_at":"2011-10-14T18:44:56Z","abstract_excerpt":"We prove regularity results for solutions of the equation \\[div(< AXu,X u>^{(p-2)/2} AX u) = 0,\\] $1<p<\\infty$, where $X=(X_1,...,X_m)$ is a family of vector fields satisfying H\\\"ormander's ellipticity condition, $A$ is an $m\\times m$ symmetric matrix that satisfies degenerate ellipticity conditions. If the degeneracy is of the form \\[\\lambda w(x)^{2/p}|\\xi|^2\\leq < A(x)\\xi,\\xi>\\leq \\Lambda w(x)^{2/p}|\\xi|^2,\\] $w \\in A_p$, then we show that solutions are locally H\\\"older continuous. If the degeneracy is of the form \\[ k(x)^{-2/p'}|\\xi|^2\\leq < A(x)\\xi,\\xi>\\leq k(x)^{2/p}|\\xi|^2, \\] $k\\in A_{p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3295","kind":"arxiv","version":3},"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":"2026-05-18T03:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ko8fwhY8uVq6jP0/p+l6yukEEB2H13yh1on5XmzQiGSOfOw22ZnscqagZ/qqOCmKBF6Dzct7nT8MfbKVgax6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:19:47.976853Z"},"content_sha256":"57012219daf35ebeb647c34933d9415a0f1e29fdbaac38c49c70ce25774b34e2","schema_version":"1.0","event_id":"sha256:57012219daf35ebeb647c34933d9415a0f1e29fdbaac38c49c70ce25774b34e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZBX5TMIFCL3J4H5TIEEGPDFVO/bundle.json","state_url":"https://pith.science/pith/VZBX5TMIFCL3J4H5TIEEGPDFVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZBX5TMIFCL3J4H5TIEEGPDFVO/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":"2026-06-08T17:19:47Z","links":{"resolver":"https://pith.science/pith/VZBX5TMIFCL3J4H5TIEEGPDFVO","bundle":"https://pith.science/pith/VZBX5TMIFCL3J4H5TIEEGPDFVO/bundle.json","state":"https://pith.science/pith/VZBX5TMIFCL3J4H5TIEEGPDFVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZBX5TMIFCL3J4H5TIEEGPDFVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VZBX5TMIFCL3J4H5TIEEGPDFVO","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":"fb4c493f996afb5f52b975bec4d12e4292425a04e78e42b914d7f7074379caa2","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-14T18:44:56Z","title_canon_sha256":"4fb6be331f1281428232739164d345c83fb2ec29fb42ceb36cc61f6bb09c3548"},"schema_version":"1.0","source":{"id":"1110.3295","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3295","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3295v3","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3295","created_at":"2026-05-18T03:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"VZBX5TMIFCL3","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VZBX5TMIFCL3J4H5","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VZBX5TMI","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:57012219daf35ebeb647c34933d9415a0f1e29fdbaac38c49c70ce25774b34e2","target":"graph","created_at":"2026-05-18T03:38:46Z","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":"We prove regularity results for solutions of the equation \\[div(< AXu,X u>^{(p-2)/2} AX u) = 0,\\] $1<p<\\infty$, where $X=(X_1,...,X_m)$ is a family of vector fields satisfying H\\\"ormander's ellipticity condition, $A$ is an $m\\times m$ symmetric matrix that satisfies degenerate ellipticity conditions. If the degeneracy is of the form \\[\\lambda w(x)^{2/p}|\\xi|^2\\leq < A(x)\\xi,\\xi>\\leq \\Lambda w(x)^{2/p}|\\xi|^2,\\] $w \\in A_p$, then we show that solutions are locally H\\\"older continuous. If the degeneracy is of the form \\[ k(x)^{-2/p'}|\\xi|^2\\leq < A(x)\\xi,\\xi>\\leq k(x)^{2/p}|\\xi|^2, \\] $k\\in A_{p","authors_text":"David Cruz-Uribe, Kabe Moen, Virginia Naibo","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-14T18:44:56Z","title":"Regularity of solutions to degenerate $p$-Laplacian equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3295","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":"sha256:26632f24073eabc2d888bc7c495c74fc876a3ad14b7e42ea93c63bee2f2df870","target":"record","created_at":"2026-05-18T03:38:46Z","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":"fb4c493f996afb5f52b975bec4d12e4292425a04e78e42b914d7f7074379caa2","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-14T18:44:56Z","title_canon_sha256":"4fb6be331f1281428232739164d345c83fb2ec29fb42ceb36cc61f6bb09c3548"},"schema_version":"1.0","source":{"id":"1110.3295","kind":"arxiv","version":3}},"canonical_sha256":"ae437ecd882897b4f0fd9a08433c65aba1d0a87e7756bd93b61837455af93fe3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae437ecd882897b4f0fd9a08433c65aba1d0a87e7756bd93b61837455af93fe3","first_computed_at":"2026-05-18T03:38:46.331609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:46.331609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vKUH26cXjqmc567lSnMf4dfEYg34DFtyz016d9cM9Izi9rODfyO1XjMqJYGD5S5GvKEQcwveiIRP7x4kEi/LAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:46.332300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3295","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26632f24073eabc2d888bc7c495c74fc876a3ad14b7e42ea93c63bee2f2df870","sha256:57012219daf35ebeb647c34933d9415a0f1e29fdbaac38c49c70ce25774b34e2"],"state_sha256":"30f0eeeadb8591be0ac15c329d1058a290f8ca2669e88664b5936405f2a1bc81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iUMUOuMO9qm62aB2lGfrlbvjm995n9qrXCpG6WibLLVfVhy/8T/x4JAIoT/4Ffl41MIockv1ZE0Re2cTtwaaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:19:47.980714Z","bundle_sha256":"e8edd7ae98679e9f1cf2e6b54321cec11ac03c25c0fdfee092029aa7581c595f"}}