{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6T7L6HUHCKX2G36POBYVKQ4CH5","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":"8997e9cb7f0cf2d571236829f7fadc9eb9f381cadcc58ef018480bd8c202c05a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-10T18:05:42Z","title_canon_sha256":"ad232163bba35a57b8415b7c7d3e96f1d706125bb0fe9cab5718305b2f990671"},"schema_version":"1.0","source":{"id":"1408.2259","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2259","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2259v2","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2259","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"pith_short_12","alias_value":"6T7L6HUHCKX2","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6T7L6HUHCKX2G36P","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6T7L6HUH","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:f39a0e94a015cafc1b6dbe438805d95d1aa113c4227292e4f7ea042ad13be4a2","target":"graph","created_at":"2026-05-17T23:45:53Z","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":"For an evolution of metrics $(M,g_{t})$ there is a t-smooth family of embeddings $e_{t}:M\\to\\mathbb{R}^{N}$ inducing $g_{t}$, but in general there is no family of embeddings extending a given initial embedding $e_{0}$. We give an example of this phenomenon when $g_{t}$ is the evolution of $g_{0}$ under the Ricci flow. We show that there are embeddings $e_{0}$ inducing $g_{0}$ which do not admit of t-smooth extensions to $e_{t}$ inducing $g_{t}$ for any t>0. We also find hypersurfaces of dim>2 that will not remain a hypersurface under Ricci flow for any positive time.","authors_text":"Mohammad Safdari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-10T18:05:42Z","title":"An example of non-embeddability of the Ricci flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2259","kind":"arxiv","version":2},"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":"sha256:9632c7c7b3ce2869ff6a625bf0073ba3d863fbe11b5abf1783a6b557e56d91e3","target":"record","created_at":"2026-05-17T23:45:53Z","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":"8997e9cb7f0cf2d571236829f7fadc9eb9f381cadcc58ef018480bd8c202c05a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-10T18:05:42Z","title_canon_sha256":"ad232163bba35a57b8415b7c7d3e96f1d706125bb0fe9cab5718305b2f990671"},"schema_version":"1.0","source":{"id":"1408.2259","kind":"arxiv","version":2}},"canonical_sha256":"f4febf1e8712afa36fcf70715543823f4166ce6ac00a7de0f0fd76ad22d52424","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4febf1e8712afa36fcf70715543823f4166ce6ac00a7de0f0fd76ad22d52424","first_computed_at":"2026-05-17T23:45:53.838715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:53.838715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XmMTjdPd3X7ZtZouoc9e+/rZf70iwkivLicDWaNilLIOfCGV950RiUXkc3i/OlpIcdYdO6HU4DtYSvjER/9oAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:53.839133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2259","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9632c7c7b3ce2869ff6a625bf0073ba3d863fbe11b5abf1783a6b557e56d91e3","sha256:f39a0e94a015cafc1b6dbe438805d95d1aa113c4227292e4f7ea042ad13be4a2"],"state_sha256":"a3ff9549e628abf2d15d75d2385ea25232c321e0e98fd77248a4449180e30f66"}