{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SNGQCBNNFI76MDZMQGAI7JYYGF","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":"a6d2d4da7aa026547ab263c236eef91e35f67fe50a13b5ad353d1752bb9defa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-04-16T03:06:58Z","title_canon_sha256":"13a8727a5bb34103a35423ea03ca44e1bc5d84a59b3eb84c5b33e95a391c234b"},"schema_version":"1.0","source":{"id":"1004.2750","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2750","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2750v2","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2750","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"SNGQCBNNFI76","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SNGQCBNNFI76MDZM","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SNGQCBNN","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:21dcc1a6e2152b5645286a6e4a85f95fe421a9286d506588a499c385c0939b94","target":"graph","created_at":"2026-05-18T02:33:34Z","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":"The rod-structure formalism has played an important role in the study of black holes in D=4 and 5 dimensions with RxU(1)^{D-3} isometry. In this paper, we apply this formalism to the study of four-dimensional gravitational instantons with U(1)xU(1) isometry, which could serve as spatial backgrounds for five-dimensional black holes. We first introduce a stronger version of the rod structure with the rod directions appropriately normalised, and show how the regularity conditions can be read off from it. Requiring the absence of conical and orbifold singularities will in general impose periodicit","authors_text":"Edward Teo, Yu Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-04-16T03:06:58Z","title":"Rod-structure classification of gravitational instantons with U(1)xU(1) isometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2750","kind":"arxiv","version":2},"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":"sha256:72a64ce79cd0adf70b7de98ff5e57b258fda733d189ba28ad9a33addb9071b59","target":"record","created_at":"2026-05-18T02:33:34Z","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":"a6d2d4da7aa026547ab263c236eef91e35f67fe50a13b5ad353d1752bb9defa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-04-16T03:06:58Z","title_canon_sha256":"13a8727a5bb34103a35423ea03ca44e1bc5d84a59b3eb84c5b33e95a391c234b"},"schema_version":"1.0","source":{"id":"1004.2750","kind":"arxiv","version":2}},"canonical_sha256":"934d0105ad2a3fe60f2c81808fa718314d031a0cda07ef8f460df940d5597ab0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"934d0105ad2a3fe60f2c81808fa718314d031a0cda07ef8f460df940d5597ab0","first_computed_at":"2026-05-18T02:33:34.110065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:34.110065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DWGSSFuM0zpww+JQQFLUQLFJKbTbMv9fwGgMQcf4PPAFpXPkmmrksF/3d2Qvp/PHZgF/AE1ptMhNWxzwrvimDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:34.110636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.2750","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72a64ce79cd0adf70b7de98ff5e57b258fda733d189ba28ad9a33addb9071b59","sha256:21dcc1a6e2152b5645286a6e4a85f95fe421a9286d506588a499c385c0939b94"],"state_sha256":"20dfb7784c1378dbbbf9398c8801f6535eac375963c43bd52eb5a5bf0922d5e3"}