{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XYCDOGQS6XAWB6CIO6MUTOUGY3","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":"fa270d9bc75dab82eb7e375ea89f0b58c0a9c7925b56b80426c47d390c81653f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-24T15:39:14Z","title_canon_sha256":"b840069313f33b336d11db1437fb0cf03384d3fa963d6f0740dcd18be2e86f74"},"schema_version":"1.0","source":{"id":"1010.4973","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4973","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4973v1","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4973","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"pith_short_12","alias_value":"XYCDOGQS6XAW","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XYCDOGQS6XAWB6CI","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XYCDOGQS","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:d5dc106c1365a45d3f9eed170c6d7087364241e8bda2dddb41f83c26cf540a87","target":"graph","created_at":"2026-05-18T04:38:49Z","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":"The aim of this paper is to complete the local classification of minimal hypersurfaces with vanishing Gauss-Kronecker curvature in a 4-dimensional space form. Moreover, we give a classification of complete minimal hypersurfaces with vanishing Gauss-Kronecker curvature and scalar curvature bounded from below.","authors_text":"Andreas Savas-Halilaj","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-24T15:39:14Z","title":"On Deformable Minimal Hypersurfaces in Space Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4973","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":"sha256:9085382af18102225845019786ee3642b894dab45ae20ac7c0363635175888c2","target":"record","created_at":"2026-05-18T04:38:49Z","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":"fa270d9bc75dab82eb7e375ea89f0b58c0a9c7925b56b80426c47d390c81653f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-10-24T15:39:14Z","title_canon_sha256":"b840069313f33b336d11db1437fb0cf03384d3fa963d6f0740dcd18be2e86f74"},"schema_version":"1.0","source":{"id":"1010.4973","kind":"arxiv","version":1}},"canonical_sha256":"be04371a12f5c160f848779949ba86c6eed59f92896d737f33e351c6ff8621ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be04371a12f5c160f848779949ba86c6eed59f92896d737f33e351c6ff8621ce","first_computed_at":"2026-05-18T04:38:49.685216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:49.685216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lI9D0N4KuAdRIlKnwCTwVG2bM6AGWov005Za+6PHht2kDBDKvJkfZGH6wlHdlX3LXaiITSMe3IR1l56oc5B3Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:49.685775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4973","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9085382af18102225845019786ee3642b894dab45ae20ac7c0363635175888c2","sha256:d5dc106c1365a45d3f9eed170c6d7087364241e8bda2dddb41f83c26cf540a87"],"state_sha256":"b775874d9d80be9a5fa97a2d14c75c1fe1d1fe3c572ea2ccffac53d1002a2691"}