{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6VRBUKKL5PNBHQ6ZXWGSB4EXNR","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":"561bc96cf1373067542f9b0bd4c29af20bf059539001281c472dfbdfc9bec761","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-28T20:01:23Z","title_canon_sha256":"bc218bddc92b6a89da2f5c1e6dad977128aed20bcba38357edf4d49dc5a7654b"},"schema_version":"1.0","source":{"id":"1203.6361","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6361","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6361v3","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6361","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"6VRBUKKL5PNB","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6VRBUKKL5PNBHQ6Z","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6VRBUKKL","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:4e1c85d1bac39e9a28d69e1e8b5ccd846727fef4255bf4516e7b0e13466af3ab","target":"graph","created_at":"2026-05-18T03:44:47Z","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 apply conformal flows of metrics restricted to the orthogonal distribution $D$ of a foliation to study the question: Which foliations admit a metric such that the leaves are totally geodesic and the mixed scalar curvature is positive? Our evolution operator includes the integrability tensor of $D$, and for the case of integrable orthogonal distribution the flow velocity is proportional to the mixed scalar curvature. We observe that the mean curvature vector $H$ of $D$ satisfies along the leaves the forced Burgers equation, this reduces to the linear Schr\\\"{o}dinger equation, whose potential","authors_text":"Leonid Zelenko, Vladimir Rovenski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-28T20:01:23Z","title":"The mixed scalar curvature flow on a fiber bundle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6361","kind":"arxiv","version":3},"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":"sha256:7588e0dce8565ff45b8e6fdb3381e970a79485966a278f9d3928ce075e775241","target":"record","created_at":"2026-05-18T03:44:47Z","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":"561bc96cf1373067542f9b0bd4c29af20bf059539001281c472dfbdfc9bec761","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-03-28T20:01:23Z","title_canon_sha256":"bc218bddc92b6a89da2f5c1e6dad977128aed20bcba38357edf4d49dc5a7654b"},"schema_version":"1.0","source":{"id":"1203.6361","kind":"arxiv","version":3}},"canonical_sha256":"f5621a294bebda13c3d9bd8d20f0976c706e1f0cffb79b2231a80d7d5b9cc74e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5621a294bebda13c3d9bd8d20f0976c706e1f0cffb79b2231a80d7d5b9cc74e","first_computed_at":"2026-05-18T03:44:47.186203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:47.186203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+sF69ToGsyMRfBWZlxdC+Qi7JYS+aDYqtfr3NhSisBw3RAQLuKz3rkb+ymYHlrepmw6Rhf9RoVE+R/z9HF8FAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:47.186995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6361","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7588e0dce8565ff45b8e6fdb3381e970a79485966a278f9d3928ce075e775241","sha256:4e1c85d1bac39e9a28d69e1e8b5ccd846727fef4255bf4516e7b0e13466af3ab"],"state_sha256":"104022e53a3663458ff800bf6151f4fe842e5f2be92373752c7d5d0236492c81"}