{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BEMVPV63EXI7IQG5ZVDOS533GW","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":"d318c6cfb34ae8dd5e1102b01c6456359698708b137960a5e5554f38ea7a9fee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-29T10:57:26Z","title_canon_sha256":"d0bea060cd7f699ba32aced1f72318e41745479cd589b90ef1dc524d8f903e25"},"schema_version":"1.0","source":{"id":"1606.09041","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.09041","created_at":"2026-05-18T00:32:55Z"},{"alias_kind":"arxiv_version","alias_value":"1606.09041v3","created_at":"2026-05-18T00:32:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.09041","created_at":"2026-05-18T00:32:55Z"},{"alias_kind":"pith_short_12","alias_value":"BEMVPV63EXI7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BEMVPV63EXI7IQG5","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BEMVPV63","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:416dd948cfbc0a76266022382bc7f5a950d71e6f6efca93badf2774143e8f27d","target":"graph","created_at":"2026-05-18T00:32:55Z","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":"We give topological conditions to ensure that a noncollapsed almost Ricci-flat 4-manifold admits a Ricci-flat metric. One sufficient condition is that the manifold is spin and has a nonzero A-hat genus. Another condition is that the fundamental group is infinite or, more generally, of sufficiently large cardinality.","authors_text":"John Lott, Vitali Kapovitch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-29T10:57:26Z","title":"On noncollapsed almost Ricci-flat 4-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09041","kind":"arxiv","version":3},"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":"sha256:868ee0b4f0fa8f88ac200b960bccd0b8875fee4700c5ccad360f1b090ac35682","target":"record","created_at":"2026-05-18T00:32:55Z","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":"d318c6cfb34ae8dd5e1102b01c6456359698708b137960a5e5554f38ea7a9fee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-29T10:57:26Z","title_canon_sha256":"d0bea060cd7f699ba32aced1f72318e41745479cd589b90ef1dc524d8f903e25"},"schema_version":"1.0","source":{"id":"1606.09041","kind":"arxiv","version":3}},"canonical_sha256":"091957d7db25d1f440ddcd46e9777b359f48f07ee3e6d6a7c0e9eea2adfc6aee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"091957d7db25d1f440ddcd46e9777b359f48f07ee3e6d6a7c0e9eea2adfc6aee","first_computed_at":"2026-05-18T00:32:55.610850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:55.610850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DlAC0T/oV6Mioh1acGr8G4LDzuB11QYsCEAfn/peowxQbBFMLL2JPK8JeLuRDuif3gcJkCMlaeIFWPF7kW9mCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:55.611437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.09041","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:868ee0b4f0fa8f88ac200b960bccd0b8875fee4700c5ccad360f1b090ac35682","sha256:416dd948cfbc0a76266022382bc7f5a950d71e6f6efca93badf2774143e8f27d"],"state_sha256":"98d0035cb55b32772466acd27fca5d3f69d99ac973b37ce3ef0b2c335d40a533"}