{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4FI6THSF5QRNTICDZR2O6QSW6M","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":"77df06dd184f085c9e00938acfb20ab10119f31e8737c34850a1d1b7a11e280e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-17T23:57:36Z","title_canon_sha256":"d7b37eed87041fd841888e1624b4a73cdf6d78baa53925acf8fe5bd07fa6586a"},"schema_version":"1.0","source":{"id":"1606.05709","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05709","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05709v1","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05709","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"pith_short_12","alias_value":"4FI6THSF5QRN","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4FI6THSF5QRNTICD","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4FI6THSF","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:844038822eb6768420675479359cddeb4dbcdc98900af7e05438192abecd411d","target":"graph","created_at":"2026-05-18T01:12:16Z","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":"This is the second paper of two in a series under the same title ([CRX]); both study the quantitative volume space form rigidity conjecture: a closed $n$-manifold of Ricci curvature at least $(n-1)H$, $H=\\pm 1$ or $0$ is diffeomorphic to a $H$-space form if for every ball of definite size on $M$, the lifting ball on the Riemannian universal covering space of the ball achieves an almost maximal volume, provided the diameter of $M$ is bounded for $H\\ne 1$.\n  In [CRX], we verified the conjecture for the case that $M$ or its Riemannian universal covering space $\\tilde M$ is not collapsed for $H=1$","authors_text":"Lina Chen, Shicheng Xu, Xiaochun Rong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-17T23:57:36Z","title":"Quantitative Volume Space From Rigidity with lower Ricci curvature bound II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05709","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:b4acdde04b94aac5e6cce4d24cf09b6053c9ae721afec16c75cbe0052099d89a","target":"record","created_at":"2026-05-18T01:12:16Z","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":"77df06dd184f085c9e00938acfb20ab10119f31e8737c34850a1d1b7a11e280e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-17T23:57:36Z","title_canon_sha256":"d7b37eed87041fd841888e1624b4a73cdf6d78baa53925acf8fe5bd07fa6586a"},"schema_version":"1.0","source":{"id":"1606.05709","kind":"arxiv","version":1}},"canonical_sha256":"e151e99e45ec22d9a043cc74ef4256f31cb40200ca199cdb4aacdb53ec2bc729","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e151e99e45ec22d9a043cc74ef4256f31cb40200ca199cdb4aacdb53ec2bc729","first_computed_at":"2026-05-18T01:12:16.205522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:16.205522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"97frFV2U6TZz4IQd0VMVzYiBgTQtMtpf9E933XMM+Obfh/VQ/ohkDMRyu+7qrRb5JN0C0gd8jQhy+RLZIgeHCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:16.206044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05709","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4acdde04b94aac5e6cce4d24cf09b6053c9ae721afec16c75cbe0052099d89a","sha256:844038822eb6768420675479359cddeb4dbcdc98900af7e05438192abecd411d"],"state_sha256":"2aa3623e1ead3f457ebaff0a5ff3465f35e33efac5d29112fa28049cb0e436f6"}