{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4RU6PFKPAEGXIRLZUA7AGX5VF6","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":"b2af55d76d6fcbb178a23636d4ca2b8faddcfc3b24ddeacd142e964a8f711c97","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-20T14:01:58Z","title_canon_sha256":"f3776c40ef0916e2eba4f4c0b3cfd5f81c564d6ff54189ac8faab61862b471c3"},"schema_version":"1.0","source":{"id":"2605.21202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21202","created_at":"2026-05-21T01:05:43Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21202v1","created_at":"2026-05-21T01:05:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21202","created_at":"2026-05-21T01:05:43Z"},{"alias_kind":"pith_short_12","alias_value":"4RU6PFKPAEGX","created_at":"2026-05-21T01:05:43Z"},{"alias_kind":"pith_short_16","alias_value":"4RU6PFKPAEGXIRLZ","created_at":"2026-05-21T01:05:43Z"},{"alias_kind":"pith_short_8","alias_value":"4RU6PFKP","created_at":"2026-05-21T01:05:43Z"}],"graph_snapshots":[{"event_id":"sha256:1daeab3df32cabe28d859fc4ddd376a3757a53c23a61bf8ba18ab7420c345dfc","target":"graph","created_at":"2026-05-21T01:05:43Z","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/2605.21202/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the blow-up analysis and quantitative behavior for a sequence of maps $\\{u_n\\}_{n=1}^\\infty$ from degenerating tori $(T^2,g_n)$ or from degenerating cylinders $(S^1\\times [0,\\pi],g_n)$ with free boundary conditions $u_n(S^1\\times \\{0,\\pi\\})\\subset K$ to a compact Riemannian manifold $(N,h)$ satisfying $$E(u_n)+\\|\\tau(u_n,g_n)\\|_{L^2}\\leq \\Lambda<\\infty,$$ where $\\tau(u_n,g_n)$ is the tension field of $u_n$, $K\\subset N$ is a smooth submanifold. We establish generalized energy identities and prove that away from bubbles, the asymptotic limit of the necks are either some geodesics","authors_text":"Jiayu Li, Lei Liu, Miaomiao Zhu","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-20T14:01:58Z","title":"Asymptotic analysis for approximate harmonic maps from degenerating cylinders and applications to minimal surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21202","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":"sha256:72f6cf0c58adf0468debca2bac8f28dfa284988766038df21849a6bfa74d6ce0","target":"record","created_at":"2026-05-21T01:05:43Z","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":"b2af55d76d6fcbb178a23636d4ca2b8faddcfc3b24ddeacd142e964a8f711c97","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-20T14:01:58Z","title_canon_sha256":"f3776c40ef0916e2eba4f4c0b3cfd5f81c564d6ff54189ac8faab61862b471c3"},"schema_version":"1.0","source":{"id":"2605.21202","kind":"arxiv","version":1}},"canonical_sha256":"e469e7954f010d744579a03e035fb52f90218456cc66b17639cda64a5fe89008","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e469e7954f010d744579a03e035fb52f90218456cc66b17639cda64a5fe89008","first_computed_at":"2026-05-21T01:05:43.199689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:43.199689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ehrEEZZ/0NQCShUib6XY9voO5Z8Lgr8LYKfy2VMGz7u/bNqGqewtI/Dc1356V4e8HQavGaSwgQbUZ6ULy/kcDA==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:43.200749Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.21202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72f6cf0c58adf0468debca2bac8f28dfa284988766038df21849a6bfa74d6ce0","sha256:1daeab3df32cabe28d859fc4ddd376a3757a53c23a61bf8ba18ab7420c345dfc"],"state_sha256":"37d8b684cdbab3c4fda236b1c0cd36f2af024a1664d5cff711ef788f9a62cd73"}