{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:T36375YCQDOHIXMTQFRKRD3JDB","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":"c0ca182a4b96f6f8a975a6066335ccc57e75df74c7dd5da9b6d818a249e5bc19","cross_cats_sorted":["cs.NA","math.AP","math.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-27T14:43:14Z","title_canon_sha256":"c12dde81e51234e2fd3b4078abc1cbe389ab231991483106b5c54ea37b2f13cd"},"schema_version":"1.0","source":{"id":"2506.22273","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.22273","created_at":"2026-07-05T11:28:24Z"},{"alias_kind":"arxiv_version","alias_value":"2506.22273v1","created_at":"2026-07-05T11:28:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.22273","created_at":"2026-07-05T11:28:24Z"},{"alias_kind":"pith_short_12","alias_value":"T36375YCQDOH","created_at":"2026-07-05T11:28:24Z"},{"alias_kind":"pith_short_16","alias_value":"T36375YCQDOHIXMT","created_at":"2026-07-05T11:28:24Z"},{"alias_kind":"pith_short_8","alias_value":"T36375YC","created_at":"2026-07-05T11:28:24Z"}],"graph_snapshots":[{"event_id":"sha256:79fde0da0d143a58af74c00bbdc8eb2a36354f8b25a9ef912cb7276d051a18ad","target":"graph","created_at":"2026-07-05T11:28:24Z","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/2506.22273/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work focuses on a phase field approximation of Plateau's problem. Inspired by Reifenberg's point of view, we introduce a model that combines the Ambrosio-Torterelli energy with a geodesic distance term, which can be considered as a generalization of the approach developed by Bonnivard, Lemenant and Santambrogio to approximate solutions to Steiner's problem. First, we present a Gamma-convergence analysis of this model in the simple case of a single curve located on the edge of a cylinder. In a numerical section, we detail the numerical optimisation schemes used to minimize this energy for ","authors_text":"Antoine Lemenant, Elie Bretin, Eve Machefert, Matthieu Bonnivard","cross_cats":["cs.NA","math.AP","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-27T14:43:14Z","title":"Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.22273","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:b1a2e0e58c9bd0f992ca8ab85ad50c8796dee61e34e5a50289bbfb1283296b10","target":"record","created_at":"2026-07-05T11:28:24Z","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":"c0ca182a4b96f6f8a975a6066335ccc57e75df74c7dd5da9b6d818a249e5bc19","cross_cats_sorted":["cs.NA","math.AP","math.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-06-27T14:43:14Z","title_canon_sha256":"c12dde81e51234e2fd3b4078abc1cbe389ab231991483106b5c54ea37b2f13cd"},"schema_version":"1.0","source":{"id":"2506.22273","kind":"arxiv","version":1}},"canonical_sha256":"9efdbff70280dc745d938162a88f69186e6493c0e565a09103fddbab9320bb28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9efdbff70280dc745d938162a88f69186e6493c0e565a09103fddbab9320bb28","first_computed_at":"2026-07-05T11:28:24.470496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:28:24.470496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0NPX3DsCr91aAVJMyOMywbAHfr6y+uF2CB4X4BiAWiuI4N5R0eu20SUGBylEWropyTewOO5bcPfkNGqgKl3UCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:28:24.470954Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.22273","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1a2e0e58c9bd0f992ca8ab85ad50c8796dee61e34e5a50289bbfb1283296b10","sha256:79fde0da0d143a58af74c00bbdc8eb2a36354f8b25a9ef912cb7276d051a18ad"],"state_sha256":"bb58d60530121bcae8810a9e7d7417ca43aeb7aa8bf1476ee0b8c55335d324f4"}