{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TJSFWPDZU7YEAMROERNPR3RGVR","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":"8d510fbaf958a566742530eabf94a44253fa79de5a5e19da7f9a6838a00db692","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-19T12:21:38Z","title_canon_sha256":"a6beaaf853171cf598278a3736066040fa4a4d86f5eb05a0a066fd52d1671456"},"schema_version":"1.0","source":{"id":"1110.4258","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4258","created_at":"2026-05-18T02:00:08Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4258v1","created_at":"2026-05-18T02:00:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4258","created_at":"2026-05-18T02:00:08Z"},{"alias_kind":"pith_short_12","alias_value":"TJSFWPDZU7YE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TJSFWPDZU7YEAMRO","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TJSFWPDZ","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:610e0a53b2db300a402de38a3510bb44f694b6d613b550286d93197797174170","target":"graph","created_at":"2026-05-18T02:00:08Z","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 obtain several rigidity results for biharmonic submanifolds in $\\mathbb{S}^{n}$ with parallel normalized mean curvature vector field. We classify biharmonic submanifolds in $\\mathbb{S}^{n}$ with parallel normalized mean curvature vector field and with at most two distinct principal curvatures. In particular, we determine all biharmonic surfaces with parallel normalized mean curvature vector field in $\\mathbb{S}^n$.\n  Then we investigate, for (not necessarily compact) proper biharmonic submanifolds in $\\mathbb{S}^n$, their type in the sense of B-Y. Chen. We prove: (i) a proper biharmonic sub","authors_text":"Adina Balmus, Cezar Oniciuc, Stefano Montaldo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-19T12:21:38Z","title":"Biharmonic PNMC Submanifolds in Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4258","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":"sha256:22e4bf4ceeedc7afe76c5212f8b4dc870953b11a6dce4e604ababf5e3c46143f","target":"record","created_at":"2026-05-18T02:00:08Z","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":"8d510fbaf958a566742530eabf94a44253fa79de5a5e19da7f9a6838a00db692","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-19T12:21:38Z","title_canon_sha256":"a6beaaf853171cf598278a3736066040fa4a4d86f5eb05a0a066fd52d1671456"},"schema_version":"1.0","source":{"id":"1110.4258","kind":"arxiv","version":1}},"canonical_sha256":"9a645b3c79a7f040322e245af8ee26ac773208df67454c7d49e6d8bc0f263b3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a645b3c79a7f040322e245af8ee26ac773208df67454c7d49e6d8bc0f263b3e","first_computed_at":"2026-05-18T02:00:08.659277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:08.659277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tXk9a4lluaegc+q07tKj4ftY9D7uhUH1dMwpOpAvF/KABxyZshtgd4/+x/TqQlagT3/YZCP/294c9u8GSUX1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:08.659954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4258","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22e4bf4ceeedc7afe76c5212f8b4dc870953b11a6dce4e604ababf5e3c46143f","sha256:610e0a53b2db300a402de38a3510bb44f694b6d613b550286d93197797174170"],"state_sha256":"6be7b64104ccae711ee3a1e565696faecf5804483f4fb7c0734ec7eb3332c716"}