{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VTHXLDPWM6KAWOWYSCWX4SJWTU","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":"559b6d4dc214dd453d9bc0f7c626006a734733e43a4f613edbb335a34ec1142a","cross_cats_sorted":["math.AP","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-30T15:48:33Z","title_canon_sha256":"e0f222dc6e75442c0e3f3db836b29e852b2f42459b6bfe268fb90b278bf9c898"},"schema_version":"1.0","source":{"id":"1204.6673","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.6673","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"arxiv_version","alias_value":"1204.6673v1","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6673","created_at":"2026-05-18T03:56:44Z"},{"alias_kind":"pith_short_12","alias_value":"VTHXLDPWM6KA","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VTHXLDPWM6KAWOWY","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VTHXLDPW","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:d0a5aa99c426ec259cb6081cd756219e9b335b38e6440054f3848ece7499ffe7","target":"graph","created_at":"2026-05-18T03:56:44Z","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 consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham-Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous results for a single phase (arXiv:1202.1979) and prove existence of a global minimizer.","authors_text":"Marco Morandotti, Marco Veneroni, Rustum Choksi","cross_cats":["math.AP","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-30T15:48:33Z","title":"Global minimizers for axisymmetric multiphase membranes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6673","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":"sha256:33d711835e8e8532dca890e2d69c710c40c2aa1b117c030455b6217ab92efd36","target":"record","created_at":"2026-05-18T03:56:44Z","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":"559b6d4dc214dd453d9bc0f7c626006a734733e43a4f613edbb335a34ec1142a","cross_cats_sorted":["math.AP","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-30T15:48:33Z","title_canon_sha256":"e0f222dc6e75442c0e3f3db836b29e852b2f42459b6bfe268fb90b278bf9c898"},"schema_version":"1.0","source":{"id":"1204.6673","kind":"arxiv","version":1}},"canonical_sha256":"accf758df667940b3ad890ad7e49369d085b632cb66e3da098e8df0599016e86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"accf758df667940b3ad890ad7e49369d085b632cb66e3da098e8df0599016e86","first_computed_at":"2026-05-18T03:56:44.155387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:44.155387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g2blUKhMwm1QDoCzJMGJQu135tFGePI0KGHGBGYoGfE0l3zuBG2GssHEqapWdbbkK5951p8DLwPXddstprI1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:44.155913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.6673","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33d711835e8e8532dca890e2d69c710c40c2aa1b117c030455b6217ab92efd36","sha256:d0a5aa99c426ec259cb6081cd756219e9b335b38e6440054f3848ece7499ffe7"],"state_sha256":"efc2647506f4a17475cc986d0b4e9bab8e8e440a6cba0a9ce46a8d43e22401ac"}