{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BYQBWOYTJUQG6LH3RSVTVYMGI2","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":"98dd7acb2b02ff7f13e0fe613647e06f77d13c0888ef2d99d0c37b98075216a9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-20T19:12:38Z","title_canon_sha256":"ff9578581ae03381690756cc59c617c004f2ae58276c4a048c5b9d48141ef982"},"schema_version":"1.0","source":{"id":"1611.06572","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06572","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06572v5","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06572","created_at":"2026-05-18T00:36:03Z"},{"alias_kind":"pith_short_12","alias_value":"BYQBWOYTJUQG","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BYQBWOYTJUQG6LH3","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BYQBWOYT","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:417440c2060a46d40d4c0f2b45311e9c17ac9c62e21b4836fa883d0a0b374bde","target":"graph","created_at":"2026-05-18T00:36:03Z","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 find necessary and sufficient conditions for a complete $n$-dimensional Riemannian manifold of finite volume, whose curvature tensor has nullity at least $n-2$, to be a geometric graph manifold. In the process, we show that Nomizu's conjecture, well known to be false in general, is true for manifolds with finite volume.","authors_text":"Luis A. Florit, Wolfgang Ziller","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-20T19:12:38Z","title":"Manifolds with conullity at most two as graph manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06572","kind":"arxiv","version":5},"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":"sha256:1c1aa610f5f16b6831b6b43ac37624c6f798ea2791b39f8e0154179abe89cc7b","target":"record","created_at":"2026-05-18T00:36:03Z","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":"98dd7acb2b02ff7f13e0fe613647e06f77d13c0888ef2d99d0c37b98075216a9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-20T19:12:38Z","title_canon_sha256":"ff9578581ae03381690756cc59c617c004f2ae58276c4a048c5b9d48141ef982"},"schema_version":"1.0","source":{"id":"1611.06572","kind":"arxiv","version":5}},"canonical_sha256":"0e201b3b134d206f2cfb8cab3ae18646bbab03b72d8f46ea891840935f23bf5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e201b3b134d206f2cfb8cab3ae18646bbab03b72d8f46ea891840935f23bf5d","first_computed_at":"2026-05-18T00:36:03.700553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:03.700553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4VZAqgYWm9xS04rP3I/IkO7dFvQSIQL0g2pTARowd5JyhE+hYzRmd1OEtktT6F+tmOYQSv7YHZeoJH9E1jlvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:03.701162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06572","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c1aa610f5f16b6831b6b43ac37624c6f798ea2791b39f8e0154179abe89cc7b","sha256:417440c2060a46d40d4c0f2b45311e9c17ac9c62e21b4836fa883d0a0b374bde"],"state_sha256":"931a34236e7a84bfeafe82826cc7f5e884ca415fdcd18d6f5dd6d62acf2276b4"}