{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:4YPMNO4EXW6X4AI33YJRDMRLQJ","short_pith_number":"pith:4YPMNO4E","canonical_record":{"source":{"id":"2605.25462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T06:14:19Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"8fb1cb3b55ec8e29292eb8c3f225a24f7ba4dc9a046a407097732fe69bdb203c","abstract_canon_sha256":"02b2004787d9dbc952c936ae44fde0092cdddcb462be3e73e79b68ddb59a75fa"},"schema_version":"1.0"},"canonical_sha256":"e61ec6bb84bdbd7e011bde1311b22b824636040fc1cf461d22ca1930e3d86961","source":{"kind":"arxiv","id":"2605.25462","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:4YPMNO4EXW6X4AI33YJRDMRLQJ","target":"record","payload":{"canonical_record":{"source":{"id":"2605.25462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T06:14:19Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"8fb1cb3b55ec8e29292eb8c3f225a24f7ba4dc9a046a407097732fe69bdb203c","abstract_canon_sha256":"02b2004787d9dbc952c936ae44fde0092cdddcb462be3e73e79b68ddb59a75fa"},"schema_version":"1.0"},"canonical_sha256":"e61ec6bb84bdbd7e011bde1311b22b824636040fc1cf461d22ca1930e3d86961","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:37.124216Z","signature_b64":"0HK/k5978t53UH313XhMK3+uVPGfkwLMx7+t7vKG2t3vg0FBuqyE6rupGX5Tl32Zp1fMiB6SuHEwLzBRkTFaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e61ec6bb84bdbd7e011bde1311b22b824636040fc1cf461d22ca1930e3d86961","last_reissued_at":"2026-05-26T02:04:37.123345Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:37.123345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.25462","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-26T02:04:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FSy7pt7LW3lYdWwqvl3/EVTCd82yQVfuCU7cUDjjz9vr1C/R1rWySfdPpAD7iQEWbt7YttksifD6+9mjdHyjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T11:55:50.358931Z"},"content_sha256":"a040b48333a368ba7838218e410686417714af8d23157b2a45d3068c8f1a0907","schema_version":"1.0","event_id":"sha256:a040b48333a368ba7838218e410686417714af8d23157b2a45d3068c8f1a0907"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:4YPMNO4EXW6X4AI33YJRDMRLQJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poincar\\'e-Einstein 4-manifolds with cusps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.DG","authors_text":"Hongyi Liu, Mingyang Li","submitted_at":"2026-05-25T06:14:19Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25462","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.25462/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-26T02:04:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ka149e/VWbtas/67p8A8uaEoZUeidK+TlUmcESzzhSXED0DUv1jX73xpzmwnQS5X/NnR8LiZwk9TdoezASIhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T11:55:50.359330Z"},"content_sha256":"f7a057a376ffc938c497430d025028abb91a1c00a6fe0597a20375edab0517ab","schema_version":"1.0","event_id":"sha256:f7a057a376ffc938c497430d025028abb91a1c00a6fe0597a20375edab0517ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4YPMNO4EXW6X4AI33YJRDMRLQJ/bundle.json","state_url":"https://pith.science/pith/4YPMNO4EXW6X4AI33YJRDMRLQJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4YPMNO4EXW6X4AI33YJRDMRLQJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T11:55:50Z","links":{"resolver":"https://pith.science/pith/4YPMNO4EXW6X4AI33YJRDMRLQJ","bundle":"https://pith.science/pith/4YPMNO4EXW6X4AI33YJRDMRLQJ/bundle.json","state":"https://pith.science/pith/4YPMNO4EXW6X4AI33YJRDMRLQJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4YPMNO4EXW6X4AI33YJRDMRLQJ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HKTR2wPiXwMKpe68dsiwuYmajpoYpMuBC1+jucz9PzmilwLbSdY2sU7sWK/EtJZWsUm2dyB0wYTg/vyUg+sSCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T11:55:50.361542Z","bundle_sha256":"8b3a1dafc14dffd5e8c633820de0136be2540700469b20b5553af436559ec78e"}}