{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4YPMNO4EXW6X4AI33YJRDMRLQJ","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":"02b2004787d9dbc952c936ae44fde0092cdddcb462be3e73e79b68ddb59a75fa","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T06:14:19Z","title_canon_sha256":"8fb1cb3b55ec8e29292eb8c3f225a24f7ba4dc9a046a407097732fe69bdb203c"},"schema_version":"1.0","source":{"id":"2605.25462","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25462","created_at":"2026-05-26T02:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25462v1","created_at":"2026-05-26T02:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25462","created_at":"2026-05-26T02:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"4YPMNO4EXW6X","created_at":"2026-05-26T02:04:37Z"},{"alias_kind":"pith_short_16","alias_value":"4YPMNO4EXW6X4AI3","created_at":"2026-05-26T02:04:37Z"},{"alias_kind":"pith_short_8","alias_value":"4YPMNO4E","created_at":"2026-05-26T02:04:37Z"}],"graph_snapshots":[{"event_id":"sha256:f7a057a376ffc938c497430d025028abb91a1c00a6fe0597a20375edab0517ab","target":"graph","created_at":"2026-05-26T02:04:37Z","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/2605.25462/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we construct Poincar\\'e-Einstein 4-manifolds with various kinds of cusps. In particular, we construct:\n  (1) Infinite families of Einstein metrics on $(0,\\infty)\\times \\mathscr{N}$, where $\\mathscr{N}\\to T^2$ is a principal $\\mathbb{S}^1$-bundle over $T^2$, with one Poincar\\'e-Einstein end and one end asymptotic to a real or complex hyperbolic cusp.\n  (2) Infinite families of Einstein metrics on $(0,\\infty)\\times P$, where $P\\to \\Sigma_{\\mathtt{g}}$ is a principal $\\mathbb{S}^1$-bundle over a closed Riemann surface $\\Sigma_{\\mathtt{g}}$ of genus $\\mathtt{g}\\geq 2$, with one Poin","authors_text":"Hongyi Liu, Mingyang Li","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T06:14:19Z","title":"Poincar\\'e-Einstein 4-manifolds with cusps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25462","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:a040b48333a368ba7838218e410686417714af8d23157b2a45d3068c8f1a0907","target":"record","created_at":"2026-05-26T02:04:37Z","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":"02b2004787d9dbc952c936ae44fde0092cdddcb462be3e73e79b68ddb59a75fa","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T06:14:19Z","title_canon_sha256":"8fb1cb3b55ec8e29292eb8c3f225a24f7ba4dc9a046a407097732fe69bdb203c"},"schema_version":"1.0","source":{"id":"2605.25462","kind":"arxiv","version":1}},"canonical_sha256":"e61ec6bb84bdbd7e011bde1311b22b824636040fc1cf461d22ca1930e3d86961","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e61ec6bb84bdbd7e011bde1311b22b824636040fc1cf461d22ca1930e3d86961","first_computed_at":"2026-05-26T02:04:37.123345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:37.123345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0HK/k5978t53UH313XhMK3+uVPGfkwLMx7+t7vKG2t3vg0FBuqyE6rupGX5Tl32Zp1fMiB6SuHEwLzBRkTFaBw==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:37.124216Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25462","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a040b48333a368ba7838218e410686417714af8d23157b2a45d3068c8f1a0907","sha256:f7a057a376ffc938c497430d025028abb91a1c00a6fe0597a20375edab0517ab"],"state_sha256":"23efbaead6a5cc31c0a79664a3a45e15156d8e81b35d70b16ab3ee80a1320a07"}