{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:45UTJXKU2X65PQZP6OEEBNMK7Y","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":"2e79743b8cab62f6bdb82c41f7d8beb2df584005b508553b59e09cbe794b1ac5","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2005-06-14T13:50:15Z","title_canon_sha256":"5c49928c423d891153d8257d848b9d52a498c9277b2d724e28b8cebd0612d914"},"schema_version":"1.0","source":{"id":"math/0506273","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506273","created_at":"2026-05-17T23:45:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506273v6","created_at":"2026-05-17T23:45:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506273","created_at":"2026-05-17T23:45:47Z"},{"alias_kind":"pith_short_12","alias_value":"45UTJXKU2X65","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"45UTJXKU2X65PQZP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"45UTJXKU","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:bd25018a2918110d8919191630312c06ecd668e39e5b481b73f538323848cbf7","target":"graph","created_at":"2026-05-17T23:45:47Z","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 show that almost nonnegatively curved m-dimensional manifolds are, up to finite cover, nilpotent spaces in the sense of homotopy theory and have C(m)-nilpotent fundamental groups. We also show that up to a finite cover almost nonnegatively curved manifolds are fiber bundles with simply connected fibers over nilmanifolds.","authors_text":"Anton Petrunin, Vitali Kapovitch, Wilderich Tuschmann","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2005-06-14T13:50:15Z","title":"Nilpotency, almost nonnegative curvature and the gradient flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506273","kind":"arxiv","version":6},"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":"sha256:148bbf68a23371b958150c8f2f22fb0bc6f11cf24477bdd686014ab76d2093d3","target":"record","created_at":"2026-05-17T23:45:47Z","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":"2e79743b8cab62f6bdb82c41f7d8beb2df584005b508553b59e09cbe794b1ac5","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2005-06-14T13:50:15Z","title_canon_sha256":"5c49928c423d891153d8257d848b9d52a498c9277b2d724e28b8cebd0612d914"},"schema_version":"1.0","source":{"id":"math/0506273","kind":"arxiv","version":6}},"canonical_sha256":"e76934dd54d5fdd7c32ff38840b58afe2d7900d57539179227a8f3b3d67bf863","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e76934dd54d5fdd7c32ff38840b58afe2d7900d57539179227a8f3b3d67bf863","first_computed_at":"2026-05-17T23:45:47.206648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:47.206648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YCNgmZQFMuVZJjv3IGUnyKb+xv8TIDltZtnDPYgEirIUu7R8QVmwbBwi66/2JSS7Aof918Enndn0IR2mdi7aAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:47.207121Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0506273","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:148bbf68a23371b958150c8f2f22fb0bc6f11cf24477bdd686014ab76d2093d3","sha256:bd25018a2918110d8919191630312c06ecd668e39e5b481b73f538323848cbf7"],"state_sha256":"f6c7afed8d694a4766f907651cfc605ba0299a33b515a4e298d6a42285a5c02c"}