{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IJDMJPKRCC6EVY2MPP7UA7F3IJ","short_pith_number":"pith:IJDMJPKR","schema_version":"1.0","canonical_sha256":"4246c4bd5110bc4ae34c7bff407cbb427677108d07a802ace636f2fedb9f35c4","source":{"kind":"arxiv","id":"1707.06272","version":1},"attestation_state":"computed","paper":{"title":"Strong Comparison Principle for $p-$harmonic functions in Carnot-Caratheodory spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MG"],"primary_cat":"math.AP","authors_text":"Luca Capogna, Xiaodan Zhou","submitted_at":"2017-07-19T19:49:32Z","abstract_excerpt":"We extend Bony's propagation of support argument \\cite{Bony} to $C^1$ solutions of the non-homogeneous sub-elliptic $p-$Laplacian associated to a system of smooth vector fields satisfying H\\\"ormander's finite rank condition. As a consequence we prove a strong maximum principle and strong comparison principle that generalize results of Tolksdorf \\cite{Tolksdorf}."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.06272","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-19T19:49:32Z","cross_cats_sorted":["math.DG","math.MG"],"title_canon_sha256":"a2b0d68fb22f99d78bbb7e20cd5a520a751348f786ded2528bbd83225d58f148","abstract_canon_sha256":"f74f0331d6646761f80a36667ae09d74eef8d90954e10d9b5981c901579466df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:54.292860Z","signature_b64":"wsWIXMnrI+3nJPJLothx5FeeFiLQrk/+7PygFGBAraWFT39xgxZgJ1lu8N8fb2S37tF5yrCEkZYBVjUPPe1NDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4246c4bd5110bc4ae34c7bff407cbb427677108d07a802ace636f2fedb9f35c4","last_reissued_at":"2026-05-18T00:39:54.291943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:54.291943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong Comparison Principle for $p-$harmonic functions in Carnot-Caratheodory spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MG"],"primary_cat":"math.AP","authors_text":"Luca Capogna, Xiaodan Zhou","submitted_at":"2017-07-19T19:49:32Z","abstract_excerpt":"We extend Bony's propagation of support argument \\cite{Bony} to $C^1$ solutions of the non-homogeneous sub-elliptic $p-$Laplacian associated to a system of smooth vector fields satisfying H\\\"ormander's finite rank condition. As a consequence we prove a strong maximum principle and strong comparison principle that generalize results of Tolksdorf \\cite{Tolksdorf}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06272","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.06272","created_at":"2026-05-18T00:39:54.292082+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06272v1","created_at":"2026-05-18T00:39:54.292082+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06272","created_at":"2026-05-18T00:39:54.292082+00:00"},{"alias_kind":"pith_short_12","alias_value":"IJDMJPKRCC6E","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IJDMJPKRCC6EVY2M","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IJDMJPKR","created_at":"2026-05-18T12:31:21.493067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IJDMJPKRCC6EVY2MPP7UA7F3IJ","json":"https://pith.science/pith/IJDMJPKRCC6EVY2MPP7UA7F3IJ.json","graph_json":"https://pith.science/api/pith-number/IJDMJPKRCC6EVY2MPP7UA7F3IJ/graph.json","events_json":"https://pith.science/api/pith-number/IJDMJPKRCC6EVY2MPP7UA7F3IJ/events.json","paper":"https://pith.science/paper/IJDMJPKR"},"agent_actions":{"view_html":"https://pith.science/pith/IJDMJPKRCC6EVY2MPP7UA7F3IJ","download_json":"https://pith.science/pith/IJDMJPKRCC6EVY2MPP7UA7F3IJ.json","view_paper":"https://pith.science/paper/IJDMJPKR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06272&json=true","fetch_graph":"https://pith.science/api/pith-number/IJDMJPKRCC6EVY2MPP7UA7F3IJ/graph.json","fetch_events":"https://pith.science/api/pith-number/IJDMJPKRCC6EVY2MPP7UA7F3IJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IJDMJPKRCC6EVY2MPP7UA7F3IJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IJDMJPKRCC6EVY2MPP7UA7F3IJ/action/storage_attestation","attest_author":"https://pith.science/pith/IJDMJPKRCC6EVY2MPP7UA7F3IJ/action/author_attestation","sign_citation":"https://pith.science/pith/IJDMJPKRCC6EVY2MPP7UA7F3IJ/action/citation_signature","submit_replication":"https://pith.science/pith/IJDMJPKRCC6EVY2MPP7UA7F3IJ/action/replication_record"}},"created_at":"2026-05-18T00:39:54.292082+00:00","updated_at":"2026-05-18T00:39:54.292082+00:00"}