{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2IXAH7ROSC3YRR7276MVKYPBCC","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":"9b796226a41b0ab2a7d903674cf041b197a848bcc51f213f7a2179076fd798a1","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-02-11T16:50:40Z","title_canon_sha256":"46e7b7ea037425449ace46441b1a635515d3184104e16f2683e9b4d67c2d6d1c"},"schema_version":"1.0","source":{"id":"2502.07697","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07697","created_at":"2026-07-05T10:12:52Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07697v1","created_at":"2026-07-05T10:12:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07697","created_at":"2026-07-05T10:12:52Z"},{"alias_kind":"pith_short_12","alias_value":"2IXAH7ROSC3Y","created_at":"2026-07-05T10:12:52Z"},{"alias_kind":"pith_short_16","alias_value":"2IXAH7ROSC3YRR72","created_at":"2026-07-05T10:12:52Z"},{"alias_kind":"pith_short_8","alias_value":"2IXAH7RO","created_at":"2026-07-05T10:12:52Z"}],"graph_snapshots":[{"event_id":"sha256:e68c171b1e1479f8f196662517011fc7f08a8382ebf1851c0c631418b560c98e","target":"graph","created_at":"2026-07-05T10:12:52Z","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/2502.07697/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study minimizing singular cones with free boundary associated with the capillarity problem. Precisely, we provide a stability criterion $\\`a$ la Jerison-Savin for capillary hypersurfaces and show that, in dimensions up to $4$, minimizing cones with non-sign-changing mean curvature are flat. We apply this criterion to minimizing capillary drops and, additionally, establish the instability of non-trivial axially symmetric cones in dimensions up to $6$.\n  The main results are based on a Simons-type inequality for a class of convex, homogeneous, symmetric functions of the principal curvatures, ","authors_text":"Alberto Pacati, Bozhidar Velichkov, Giorgio Tortone","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-02-11T16:50:40Z","title":"Some remarks on singular capillary cones with free boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07697","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":"sha256:871a2d64e130af6b1d92e519d1e54df3937741695a0bae14b91be3c1bfc43584","target":"record","created_at":"2026-07-05T10:12:52Z","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":"9b796226a41b0ab2a7d903674cf041b197a848bcc51f213f7a2179076fd798a1","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-02-11T16:50:40Z","title_canon_sha256":"46e7b7ea037425449ace46441b1a635515d3184104e16f2683e9b4d67c2d6d1c"},"schema_version":"1.0","source":{"id":"2502.07697","kind":"arxiv","version":1}},"canonical_sha256":"d22e03fe2e90b788c7faff995561e110a99a375bb5a7ce5a1442eedf89331416","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d22e03fe2e90b788c7faff995561e110a99a375bb5a7ce5a1442eedf89331416","first_computed_at":"2026-07-05T10:12:52.732994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:12:52.732994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HLITIbpgTnYKqAurDO0byhBxmBYS0HEvbibHliRvl89GgvmX7htByYjuj/ILUHVTpJZl9dXqz5HV/GaEm49sDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:12:52.733555Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.07697","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:871a2d64e130af6b1d92e519d1e54df3937741695a0bae14b91be3c1bfc43584","sha256:e68c171b1e1479f8f196662517011fc7f08a8382ebf1851c0c631418b560c98e"],"state_sha256":"c166fdc3fec71f3475f3b190cdac0aa0294b3695fe7981d9fa3d67f89f4f484b"}