{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:V4Z2YJKD5IHIBDUO2H27BKRI2P","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":"022a064e5f845b73030ae463323adaf681946362b67c1a7bd9b951a46af256c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-27T19:24:35Z","title_canon_sha256":"d521fd094735c2f5e012874e81ada6e470ec1ab8fc4fd745808f4034a616607e"},"schema_version":"1.0","source":{"id":"2411.18710","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.18710","created_at":"2026-07-05T09:41:50Z"},{"alias_kind":"arxiv_version","alias_value":"2411.18710v1","created_at":"2026-07-05T09:41:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.18710","created_at":"2026-07-05T09:41:50Z"},{"alias_kind":"pith_short_12","alias_value":"V4Z2YJKD5IHI","created_at":"2026-07-05T09:41:50Z"},{"alias_kind":"pith_short_16","alias_value":"V4Z2YJKD5IHIBDUO","created_at":"2026-07-05T09:41:50Z"},{"alias_kind":"pith_short_8","alias_value":"V4Z2YJKD","created_at":"2026-07-05T09:41:50Z"}],"graph_snapshots":[{"event_id":"sha256:1453a043297e6f3adfbac76313d814e22c6ef2c9997674478cb74707505dbc2c","target":"graph","created_at":"2026-07-05T09:41:50Z","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/2411.18710/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a variational framework for studying the existence of solutions of a class of elliptic free boundary problems on stratified Lie groups. Using the important monotonicity result in a Non-Euclidean setup, we prove that our solution is the limit of mountain pass points of a sequence of C1-functionals approximating the energy","authors_text":"Sabri Bensid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-27T19:24:35Z","title":"Analysis of a free boundary problem on stratified Lie group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.18710","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:f9fa5540c8ea9d4a75cf7f36229710e9a6c6a675d41dcf78b8a66283b7fe1402","target":"record","created_at":"2026-07-05T09:41:50Z","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":"022a064e5f845b73030ae463323adaf681946362b67c1a7bd9b951a46af256c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-27T19:24:35Z","title_canon_sha256":"d521fd094735c2f5e012874e81ada6e470ec1ab8fc4fd745808f4034a616607e"},"schema_version":"1.0","source":{"id":"2411.18710","kind":"arxiv","version":1}},"canonical_sha256":"af33ac2543ea0e808e8ed1f5f0aa28d3c0776b033c94c777db388c1c25b5d935","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af33ac2543ea0e808e8ed1f5f0aa28d3c0776b033c94c777db388c1c25b5d935","first_computed_at":"2026-07-05T09:41:50.122769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:50.122769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"25z1MSoy8lP3JPqcRb25whC/q7JooheUVss+mIMmVC93j4BP03R6GmvfB/ItzJMRgNVSRzfxZo/ptPANJtNABw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:50.124515Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.18710","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9fa5540c8ea9d4a75cf7f36229710e9a6c6a675d41dcf78b8a66283b7fe1402","sha256:1453a043297e6f3adfbac76313d814e22c6ef2c9997674478cb74707505dbc2c"],"state_sha256":"302ee37c9b55edb753a263ca649e59ecd39711dbd078e7bbc9250bcbd0637b2f"}