{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ZQQR6FQHKHBBWJWVZZOPLCISIR","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":"2b3ac2b5ba929077c595bac6cd9ce0840418a5471c3ac0826700045ac8e0acb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-08-25T07:06:54Z","title_canon_sha256":"be9d66011bdc33878eec22a371dcdb6714b136c9748d18e5a00e86d9855d8579"},"schema_version":"1.0","source":{"id":"2308.13209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.13209","created_at":"2026-07-05T06:44:40Z"},{"alias_kind":"arxiv_version","alias_value":"2308.13209v1","created_at":"2026-07-05T06:44:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.13209","created_at":"2026-07-05T06:44:40Z"},{"alias_kind":"pith_short_12","alias_value":"ZQQR6FQHKHBB","created_at":"2026-07-05T06:44:40Z"},{"alias_kind":"pith_short_16","alias_value":"ZQQR6FQHKHBBWJWV","created_at":"2026-07-05T06:44:40Z"},{"alias_kind":"pith_short_8","alias_value":"ZQQR6FQH","created_at":"2026-07-05T06:44:40Z"}],"graph_snapshots":[{"event_id":"sha256:a8ccf4e1525ffd8c9bd77d3ebcbb8e003d5c4ac311f8b35fdea133aabe48f355","target":"graph","created_at":"2026-07-05T06:44:40Z","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/2308.13209/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we show the generic uniqueness of minimizers for a large class of energies, including the Alt-Caffarelli and Alt-Phillips functionals.\n  We then prove the generic regularity of free boundaries for minimizers of the one-phase Alt-Caffarelli and Alt-Phillips functionals, for a monotone family of boundary data $\\{\\varphi_t\\}_{t\\in(-1,1)}$. More precisely, we show that for a co-countable subset of $\\{\\varphi_t\\}_{t\\in(-1,1)}$, minimizers have smooth free boundaries in $\\mathbb{R}^5$ for the Alt-Caffarelli and in $\\mathbb{R}^3$ for the Alt-Phillips functional. In general dimensions, w","authors_text":"Hui Yu, Xavier Fern\\'andez-Real","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-08-25T07:06:54Z","title":"Generic properties in free boundary problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.13209","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":"sha256:2ac0e054310810797ab23f3987de1a4ddd89bc3d1d9177a5b2ef942210f79f50","target":"record","created_at":"2026-07-05T06:44:40Z","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":"2b3ac2b5ba929077c595bac6cd9ce0840418a5471c3ac0826700045ac8e0acb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-08-25T07:06:54Z","title_canon_sha256":"be9d66011bdc33878eec22a371dcdb6714b136c9748d18e5a00e86d9855d8579"},"schema_version":"1.0","source":{"id":"2308.13209","kind":"arxiv","version":1}},"canonical_sha256":"cc211f160751c21b26d5ce5cf5891244687701acbe1d72874404971767af46e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc211f160751c21b26d5ce5cf5891244687701acbe1d72874404971767af46e3","first_computed_at":"2026-07-05T06:44:40.161399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:44:40.161399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jq7QGdCTVtG4g1y3JMnDCQ9/Kd5mS9VzJAGqU6vE2ENwkw4p9ZStxxMd5xZDl6Y07HVBUh9x1GO50pUybKQKAg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:44:40.161939Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.13209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ac0e054310810797ab23f3987de1a4ddd89bc3d1d9177a5b2ef942210f79f50","sha256:a8ccf4e1525ffd8c9bd77d3ebcbb8e003d5c4ac311f8b35fdea133aabe48f355"],"state_sha256":"755bf7cbd58120297fec08690fb7eceb450cdc3874c25464909bea0b39e991db"}