{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FMOZJQORW7ZEPHEQKAZWNIMBHK","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":"dcbc19ac23e666baba53d3ab5e7cc8d4f7fee14d1bed0df7a30dc9abd33c6524","cross_cats_sorted":["math.AT","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-29T18:10:20Z","title_canon_sha256":"156182f94c07c9b1c7425db50fccf0aeba3cbf38dac866383db4c8eb3d3561c1"},"schema_version":"1.0","source":{"id":"1404.7446","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7446","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7446v4","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7446","created_at":"2026-05-18T02:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"FMOZJQORW7ZE","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FMOZJQORW7ZEPHEQ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FMOZJQOR","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:856d465aa60a0dc1a2d50ab47bb7868931269e14346f4cbb864b41b9285b6f3c","target":"graph","created_at":"2026-05-18T02:27:29Z","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":"For $k \\ge 2,$ let $M^{4k-1}$ be a $(2k{-}2)$-connected closed manifold. If $k \\equiv 1$ mod $4$ assume further that $M$ is $(2k{-}1)$-parallelisable. Then there is a homotopy sphere $\\Sigma^{4k-1}$ such that $M \\sharp \\Sigma$ admits a Ricci positive metric. This follows from a new description of these manifolds as the boundaries of explicit plumbings.","authors_text":"David J. Wraith, Diarmuid Crowley","cross_cats":["math.AT","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-29T18:10:20Z","title":"Positive Ricci curvature on highly connected manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7446","kind":"arxiv","version":4},"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:d6c11fb4a0e50c2530a944ba301cb3ca7e71187df8b16b0548b3d07a09cf2730","target":"record","created_at":"2026-05-18T02:27:29Z","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":"dcbc19ac23e666baba53d3ab5e7cc8d4f7fee14d1bed0df7a30dc9abd33c6524","cross_cats_sorted":["math.AT","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-04-29T18:10:20Z","title_canon_sha256":"156182f94c07c9b1c7425db50fccf0aeba3cbf38dac866383db4c8eb3d3561c1"},"schema_version":"1.0","source":{"id":"1404.7446","kind":"arxiv","version":4}},"canonical_sha256":"2b1d94c1d1b7f2479c90503366a1813a9d9b0e3a8afaebe80344d9560924cf49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b1d94c1d1b7f2479c90503366a1813a9d9b0e3a8afaebe80344d9560924cf49","first_computed_at":"2026-05-18T02:27:29.300606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:29.300606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WQRAofllRGJ8qZcYd2gghL+MbNlAgunZAgnumkw1L40L72aB8QbIn17O9+Xz4L5LHjPwh1L5oF9URMRsB96/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:29.301232Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7446","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6c11fb4a0e50c2530a944ba301cb3ca7e71187df8b16b0548b3d07a09cf2730","sha256:856d465aa60a0dc1a2d50ab47bb7868931269e14346f4cbb864b41b9285b6f3c"],"state_sha256":"7c26d228c3c2bd60fc3fd87a5a7fc649c4847cb2bc54a6915138c16c930adc09"}