{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:45HTPVNYX5U6QVZECPDEZUKB7L","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":"00bc155461e337effcc47e136bf27f84c2218615d1c4fd45a0349e9451ab01c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-03T11:17:42Z","title_canon_sha256":"174e7153be479a5857c8d5b914aaaf284141c4fdb31b16a30501d32a9da37cae"},"schema_version":"1.0","source":{"id":"1608.01150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01150","created_at":"2026-05-18T01:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01150v1","created_at":"2026-05-18T01:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01150","created_at":"2026-05-18T01:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"45HTPVNYX5U6","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"45HTPVNYX5U6QVZE","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"45HTPVNY","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:ee4638e2e4ec36e97847b2f454b7f6e77ee32b6c2ac81ade0020d4543e1fad7c","target":"graph","created_at":"2026-05-18T01:09:56Z","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":"Capillarity functionals are parameter invariant functionals defined on classes of two-dimensional parametric surfaces in R3 as the sum of the area integral and a non homogeneous term of suitable form. Here we consider the case of a class of non homogenous terms vanishing at infinity for which the corresponding capillarity functional has no volume-constrained S2-type minimal surface. Using variational techniques, we prove existence of extremals characterized as saddle-type critical points.","authors_text":"Alessandro Iacopetti, Paolo Caldiroli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-03T11:17:42Z","title":"Existence of isovolumetric extremals for capillarity functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01150","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:a4428ab24dc3365600f52970d192065ce6b111fb6f8c6d9333cfd1e768360c73","target":"record","created_at":"2026-05-18T01:09:56Z","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":"00bc155461e337effcc47e136bf27f84c2218615d1c4fd45a0349e9451ab01c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-03T11:17:42Z","title_canon_sha256":"174e7153be479a5857c8d5b914aaaf284141c4fdb31b16a30501d32a9da37cae"},"schema_version":"1.0","source":{"id":"1608.01150","kind":"arxiv","version":1}},"canonical_sha256":"e74f37d5b8bf69e8572413c64cd141fad85288b386d54acb5f939dbcfc9bd064","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e74f37d5b8bf69e8572413c64cd141fad85288b386d54acb5f939dbcfc9bd064","first_computed_at":"2026-05-18T01:09:56.412079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:56.412079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A1R4ZNJQovfKjNCmqUnu5bTv+fRkMikEo+241Yd/Efaef0hMY38Wv0HDOETV+VcYPonMB34tTsSWzh4Go90MBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:56.412869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4428ab24dc3365600f52970d192065ce6b111fb6f8c6d9333cfd1e768360c73","sha256:ee4638e2e4ec36e97847b2f454b7f6e77ee32b6c2ac81ade0020d4543e1fad7c"],"state_sha256":"c4df025f7992b8d976aacd82a999dd7f8b8ccd2e1e18d2832c09291702b21abf"}