{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FP5FMGWGJZZ57TMIDQER7MRSHU","short_pith_number":"pith:FP5FMGWG","canonical_record":{"source":{"id":"1812.09589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-22T19:37:01Z","cross_cats_sorted":[],"title_canon_sha256":"55488c647a09263689ecdd79bd1aac7a3ef3daa2fa8d51a8280c3b3c569bf4e0","abstract_canon_sha256":"e50a3cf31bf41289cd970ab3eff4ebf31667dd37b50f8f651cb2572dc6745638"},"schema_version":"1.0"},"canonical_sha256":"2bfa561ac64e73dfcd881c091fb2323d2e8cf65ff643d4e681cab62ad6befaa4","source":{"kind":"arxiv","id":"1812.09589","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09589","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09589v1","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09589","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"FP5FMGWGJZZ5","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FP5FMGWGJZZ57TMI","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FP5FMGWG","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FP5FMGWGJZZ57TMIDQER7MRSHU","target":"record","payload":{"canonical_record":{"source":{"id":"1812.09589","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-22T19:37:01Z","cross_cats_sorted":[],"title_canon_sha256":"55488c647a09263689ecdd79bd1aac7a3ef3daa2fa8d51a8280c3b3c569bf4e0","abstract_canon_sha256":"e50a3cf31bf41289cd970ab3eff4ebf31667dd37b50f8f651cb2572dc6745638"},"schema_version":"1.0"},"canonical_sha256":"2bfa561ac64e73dfcd881c091fb2323d2e8cf65ff643d4e681cab62ad6befaa4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:27.452381Z","signature_b64":"ZkmN157y5ZdpPNUa2dPrbX7HL0bL2NZvbtyGvBW1NXYrmQ1l/qnC/O4J1t/UNfpHoWqTqeriPF5kMBB9vjE2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bfa561ac64e73dfcd881c091fb2323d2e8cf65ff643d4e681cab62ad6befaa4","last_reissued_at":"2026-05-17T23:57:27.451647Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:27.451647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.09589","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bt6ehew5kCJSZgr7Wzrma41ZFzTHj5WQql8dNtTkW5UaKfK7Pdcs8hv5ATbv0phRSHzNa0jWZOjWMQiEPxNpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T05:46:37.125130Z"},"content_sha256":"b92dcc668ea9ecdd67518f10b2c03343ab427df501aaf2e4ca4ea15ff3c45b22","schema_version":"1.0","event_id":"sha256:b92dcc668ea9ecdd67518f10b2c03343ab427df501aaf2e4ca4ea15ff3c45b22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FP5FMGWGJZZ57TMIDQER7MRSHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Goffi, Martino Bardi","submitted_at":"2018-12-22T19:37:01Z","abstract_excerpt":"We introduce a notion of subunit vector field for fully nonlinear degenerate elliptic equations. We prove that an interior maximum of a viscosity subsolution of such an equation propagates along the trajectories of subunit vector fields. This implies strong maximum and minimum principles when the operator has a family of subunit vector fields satisfying the H\\\"ormander condition. In particular these results hold for a large class of nonlinear subelliptic PDEs in Carnot groups. We prove also a strong comparison principle for degenerate elliptic equations that can be written in Hamilton-Jacobi-B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09589","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"faYQxM2BQZ4rjN1/FwDIlVFk3oKGcshkGvk6KEUBsHQPP8O5LoHPoJIoiEdCNWDD0DGVVgi0npIT4P5h3E8lAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T05:46:37.125514Z"},"content_sha256":"818bf8791ef018d9bc6c2897cba22d0ecdc86a7b4eae39ad6608f17cc9720aad","schema_version":"1.0","event_id":"sha256:818bf8791ef018d9bc6c2897cba22d0ecdc86a7b4eae39ad6608f17cc9720aad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FP5FMGWGJZZ57TMIDQER7MRSHU/bundle.json","state_url":"https://pith.science/pith/FP5FMGWGJZZ57TMIDQER7MRSHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FP5FMGWGJZZ57TMIDQER7MRSHU/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":"2026-06-22T05:46:37Z","links":{"resolver":"https://pith.science/pith/FP5FMGWGJZZ57TMIDQER7MRSHU","bundle":"https://pith.science/pith/FP5FMGWGJZZ57TMIDQER7MRSHU/bundle.json","state":"https://pith.science/pith/FP5FMGWGJZZ57TMIDQER7MRSHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FP5FMGWGJZZ57TMIDQER7MRSHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FP5FMGWGJZZ57TMIDQER7MRSHU","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":"e50a3cf31bf41289cd970ab3eff4ebf31667dd37b50f8f651cb2572dc6745638","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-22T19:37:01Z","title_canon_sha256":"55488c647a09263689ecdd79bd1aac7a3ef3daa2fa8d51a8280c3b3c569bf4e0"},"schema_version":"1.0","source":{"id":"1812.09589","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09589","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09589v1","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09589","created_at":"2026-05-17T23:57:27Z"},{"alias_kind":"pith_short_12","alias_value":"FP5FMGWGJZZ5","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FP5FMGWGJZZ57TMI","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FP5FMGWG","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:818bf8791ef018d9bc6c2897cba22d0ecdc86a7b4eae39ad6608f17cc9720aad","target":"graph","created_at":"2026-05-17T23:57:27Z","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 introduce a notion of subunit vector field for fully nonlinear degenerate elliptic equations. We prove that an interior maximum of a viscosity subsolution of such an equation propagates along the trajectories of subunit vector fields. This implies strong maximum and minimum principles when the operator has a family of subunit vector fields satisfying the H\\\"ormander condition. In particular these results hold for a large class of nonlinear subelliptic PDEs in Carnot groups. We prove also a strong comparison principle for degenerate elliptic equations that can be written in Hamilton-Jacobi-B","authors_text":"Alessandro Goffi, Martino Bardi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-22T19:37:01Z","title":"New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09589","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:b92dcc668ea9ecdd67518f10b2c03343ab427df501aaf2e4ca4ea15ff3c45b22","target":"record","created_at":"2026-05-17T23:57:27Z","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":"e50a3cf31bf41289cd970ab3eff4ebf31667dd37b50f8f651cb2572dc6745638","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-22T19:37:01Z","title_canon_sha256":"55488c647a09263689ecdd79bd1aac7a3ef3daa2fa8d51a8280c3b3c569bf4e0"},"schema_version":"1.0","source":{"id":"1812.09589","kind":"arxiv","version":1}},"canonical_sha256":"2bfa561ac64e73dfcd881c091fb2323d2e8cf65ff643d4e681cab62ad6befaa4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bfa561ac64e73dfcd881c091fb2323d2e8cf65ff643d4e681cab62ad6befaa4","first_computed_at":"2026-05-17T23:57:27.451647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:27.451647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZkmN157y5ZdpPNUa2dPrbX7HL0bL2NZvbtyGvBW1NXYrmQ1l/qnC/O4J1t/UNfpHoWqTqeriPF5kMBB9vjE2Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:27.452381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09589","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b92dcc668ea9ecdd67518f10b2c03343ab427df501aaf2e4ca4ea15ff3c45b22","sha256:818bf8791ef018d9bc6c2897cba22d0ecdc86a7b4eae39ad6608f17cc9720aad"],"state_sha256":"339bdef340ff97cc002a7a79ef92b67102e0a925cc9d23e58dd17fbfb4dd2214"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oaP0ATKGduXkR8Uw1s0y7St+AX4BRj8p8fp6I0vKYX62o0q7QUdBlIAs3KLvkMM+rRiQ/ETdeVlJBmaRRI0uCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T05:46:37.127498Z","bundle_sha256":"eaa2cb9c7556a16ca399911b3549cf49796ea3b27fba5dcbe115e8b728b2bdad"}}