{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ULQACGC2F52QXOA7VN2NZCFN5Z","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":"44515891c4d5efeebe5931befeba542aa29178048fb8e9d49b9bb30816a9faac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-17T20:38:11Z","title_canon_sha256":"61b5c4ede16bcfb72de88f879c21862fac32d0f231c715b78c648dc0e8789a00"},"schema_version":"1.0","source":{"id":"1407.4834","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4834","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4834v2","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4834","created_at":"2026-05-18T02:46:15Z"},{"alias_kind":"pith_short_12","alias_value":"ULQACGC2F52Q","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"ULQACGC2F52QXOA7","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"ULQACGC2","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:00a475916b6fdb723fbfcd02b114a9cd0bb02a330896b17a2588c661ba0bd160","target":"graph","created_at":"2026-05-18T02:46:15Z","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 show that singular sets of free boundaries arising in codimension one anisotropic geometric variational problems are $\\mathcal H ^{n-3}$-negligible, where $n$ is the ambient space dimension. In particular our results apply to capillarity type problems, and establish everywhere regularity in the three-dimensional case.","authors_text":"Francesco Maggi, Guido De Philippis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-17T20:38:11Z","title":"Dimensional estimates for singular sets in geometric variational problems with free boundaries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4834","kind":"arxiv","version":2},"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:ba8ca061a9f501c68b716e1cb1d0f800ba981bf18a9775b5478181d75cf1fadd","target":"record","created_at":"2026-05-18T02:46:15Z","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":"44515891c4d5efeebe5931befeba542aa29178048fb8e9d49b9bb30816a9faac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-17T20:38:11Z","title_canon_sha256":"61b5c4ede16bcfb72de88f879c21862fac32d0f231c715b78c648dc0e8789a00"},"schema_version":"1.0","source":{"id":"1407.4834","kind":"arxiv","version":2}},"canonical_sha256":"a2e001185a2f750bb81fab74dc88adee71d43949084e1d530f7feb33b8e80ce2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2e001185a2f750bb81fab74dc88adee71d43949084e1d530f7feb33b8e80ce2","first_computed_at":"2026-05-18T02:46:15.652134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:15.652134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XSPu0U5gOaTj4kjuhpZNWXlYn3wRyrnM4dLJgr8L+NiO1nPxmo4y7vosz3WjfwXoi48swjoCQDhYluhVW0+SCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:15.652852Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4834","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba8ca061a9f501c68b716e1cb1d0f800ba981bf18a9775b5478181d75cf1fadd","sha256:00a475916b6fdb723fbfcd02b114a9cd0bb02a330896b17a2588c661ba0bd160"],"state_sha256":"75ea695afcb0d4d409468d581ab6aa6e47f4eccd24ee2f3f3e55d68ea244b31b"}