{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:LPFSIIVHGTA5IOIQKGTJTUTXVS","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":"58f567400a4e753b02ab46d7e8741c29090ee53cd257926ffd1f46f069e3d367","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2006-12-12T17:08:10Z","title_canon_sha256":"ae95d21b1b495bed82751846cb84332d21180964a9fd7391f9cd455df66c47da"},"schema_version":"1.0","source":{"id":"math/0612314","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612314","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612314v1","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612314","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"LPFSIIVHGTA5","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"LPFSIIVHGTA5IOIQ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"LPFSIIVH","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:00395113a7baeeba5dfabb12571e8ff434c596107a7d290d36bc17385a6a4110","target":"graph","created_at":"2026-05-18T04:22:09Z","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 classify all simply connected Riemannian manifolds whose isotropy groups act with cohomogeneity less than or equal to two.","authors_text":"Andreas Kollross, Evangelia Samiou","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2006-12-12T17:08:10Z","title":"Manifolds with large isotropy groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612314","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":"sha256:26e8ae5ff7c209283aa3f6340cd2e02dc58ebee49c388ff91bc12f097691a7d1","target":"record","created_at":"2026-05-18T04:22:09Z","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":"58f567400a4e753b02ab46d7e8741c29090ee53cd257926ffd1f46f069e3d367","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2006-12-12T17:08:10Z","title_canon_sha256":"ae95d21b1b495bed82751846cb84332d21180964a9fd7391f9cd455df66c47da"},"schema_version":"1.0","source":{"id":"math/0612314","kind":"arxiv","version":1}},"canonical_sha256":"5bcb2422a734c1d4391051a699d277aca1aa7ffd54e65bf856f86c8cbe95f892","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bcb2422a734c1d4391051a699d277aca1aa7ffd54e65bf856f86c8cbe95f892","first_computed_at":"2026-05-18T04:22:09.509813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:09.509813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k/iDXVj6SO/bqPh/EGFGwOZ95euXFqu58/Uw7ph6VpBVFhFlftvw1HTBpecB8qsXJV1Btkx2UlXf+4Zuxp9dDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:09.510517Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612314","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26e8ae5ff7c209283aa3f6340cd2e02dc58ebee49c388ff91bc12f097691a7d1","sha256:00395113a7baeeba5dfabb12571e8ff434c596107a7d290d36bc17385a6a4110"],"state_sha256":"63095cc4cba2d9d0a29676000043f3bbb574e0a1a898026859e2175aad9417a3"}