{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JIRTPHDFUHVUB26A4MTVFG3334","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":"0de7feed6d6067f7d313afbe2f5cd4034c96bb8b5402adf2e7b66b62fe777dcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-21T21:50:17Z","title_canon_sha256":"8b62bce2b05eee8466b14909430d32bc180632953c7721757e04fda28b0a89ea"},"schema_version":"1.0","source":{"id":"1501.05337","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05337","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05337v3","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05337","created_at":"2026-05-18T01:35:35Z"},{"alias_kind":"pith_short_12","alias_value":"JIRTPHDFUHVU","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JIRTPHDFUHVUB26A","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JIRTPHDF","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:e515de0616b07409d183744f3977b5262e359afff436d0bb798755cf083521ac","target":"graph","created_at":"2026-05-18T01:35:35Z","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 prove that the free boundary of some variational inequalities with gradient constraints is as regular as the tangent bundle of the boundary of the domain. To this end, we study a generalized notion of ridge of a domain in the plane, which is the set of singularities of the distance function in the p-norm to the boundary of the domain.","authors_text":"Mohammad Safdari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-21T21:50:17Z","title":"The free boundary of variational inequalities with gradient constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05337","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:e86b67269948773a68a3ea65c22bdb6298b20be29ccc2058dace234d4ad6ff17","target":"record","created_at":"2026-05-18T01:35:35Z","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":"0de7feed6d6067f7d313afbe2f5cd4034c96bb8b5402adf2e7b66b62fe777dcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-21T21:50:17Z","title_canon_sha256":"8b62bce2b05eee8466b14909430d32bc180632953c7721757e04fda28b0a89ea"},"schema_version":"1.0","source":{"id":"1501.05337","kind":"arxiv","version":3}},"canonical_sha256":"4a23379c65a1eb40ebc0e327529b7bdf047241ee6711d0fef72b48394b49f3aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a23379c65a1eb40ebc0e327529b7bdf047241ee6711d0fef72b48394b49f3aa","first_computed_at":"2026-05-18T01:35:35.033893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:35.033893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"21w2947XSlcFFlSDZh+6oN0AnJG8dR2yFq9oFBIqsT5i0Y4zkSiPP3Z9ZehbXmSCTCCuYHmmDITxucElWlezDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:35.034484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05337","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e86b67269948773a68a3ea65c22bdb6298b20be29ccc2058dace234d4ad6ff17","sha256:e515de0616b07409d183744f3977b5262e359afff436d0bb798755cf083521ac"],"state_sha256":"3965e7e3baf37a12414e101ee0392212938349899f42936b8b9eab5132a21e7f"}